There is so much that is peculiar, irregular, silly, or downright twisted in mathematical verbiage that, certainly, we could all benefit from some soul-searching on the language of our culture. Some of mathematics usage is confusing (e. g. overuse of “normal” and “regular”) and some irritating (personal peeve: persistent classroom use of “guy” to refer to mathematical expressions – I know anthropomorphization makes things friendly and all, but I’m not sure that thinking of all mathematical objects as “guys” is good for our ongoing gender problem). And then there are other things that just floored me the first time I heard them (um, “clopen,” anyone?), not to mention our obsession/affliction with eponymy and its discontents. There is a dissertation in linguistic anthropology waiting to be written on mathematical usage, and perhaps several that already have been.

It would be all well and good to litigate the social and political aspects of mathematical speech, but who really has the time?^{ 1 }This is a graduate student blog, and, you know, life is already hard enough, so we must have some recreation. Proposed solution: **the mathematical crossword puzzle**, or more accurately, crossword puzzle with a strong mathematical bias – a venue to examine and lightheartedly ponder our field’s history, culture, language and content without needing to delve into heated public debate. On the other hand, maybe the chance for debate is sort of the point.^{ 2 } Entertainment which is presented as critical thinking and that leads to higher-level critical thinking is a high kind of art.

I suppose, based on my own experience, that many crossword solvers will relate to the experience of hating puzzle-makers for clues that make no sense, are elitist, presume familiarity with arcane or dated bits of culture, etc. To draw a parallel, I submit that this is exactly the sort of experience many students are having in math classes, at any level. That you are the kind of person that is willing to put up with being treated with such pomposity and contempt, until you are suddenly on the other side of this diode-like arrangement, is something one might infer from the fact that you are in mathematics graduate school and reading a math blog to boot, which is to say: I bet the intersection of math-o-philes and cruciverbalists is not so small.

But! We must do better than our teachers by seeking to not alienate, condescend, and exclude, and in order to get there first we must try. As a long-time-solver-first-time-constructor, let me say the following:

- Constructing is hard! Harder that you might think, harder than I thought at least. The junky, off-putting clues you find in crosswords are much more likely due to (i) the jams a maker finds them- self in while constructing and (ii) laziness at dealing with these jams, than they are to any kind of elitism or snootery.
- Regarding the handling of such jams, no matter how hard you try you are still a victim of your own biases. There is perhaps no way around this, at least not on an individual level. A diversity of backgrounds among puzzle-makers and solvers (draw the mathematical analogy) will lead to a richer and less homogenized and consistently frustrating experience. This is the general nature of the criticisms levelled at the New York Times editorialship by Rex Parker et al., and it leads to a big and important conversation on power, privilege, who’s being represented and who’s being excluded. I have made a best effort at inclusiveness in the theme and content of this puzzle, which I’m sure is still abjectly deficient in some respects.
- This puzzle has a few more black squares than is typical/admissible for your average newspaper puzzle. Here’s my accounting for this: many puzzles are built around a “theme,” a collection of clues that are linked by some common feature. Clues in this set are called “themers.” I tried to cram too many themers into this one, and in order to cope with the resulting jams, I had to black some stuff out.
- I couldn’t (and this is maybe a relief for solvers) find a way to reasonably make all of the clues mathematics related. So some are intersectional, and some are out of left-field. I learned a lot of trivia while making this, and my hope is that you might learn some too.

I hope you enjoy! If you are moved to create your own math-puzzles, I am also sharing the kinda janky LaTeX file I used to make this one, in case it helps.

^{ 1 }Maybe the same people that spend time making crosswords, ahem.

^{ 2 }Regular NYT puzzle solvers may know the boisterous commentary of Rex Parker and others in the puzzle blogosphere.

*Disclaimer*: The opinions expressed on this blog are the views of the writer(s) and do not necessarily reflect the views and opinions of the American Mathematical Society.

*Comments Guidelines*: The AMS encourages your comments, and hopes you will join the discussions. We review comments before they are posted, and those that are offensive, abusive, off-topic or promoting a commercial product, person or website will not be posted. Expressing disagreement is fine, but mutual respect is required.

The Society for Advancement of Chicanos/Hispanics and Native Americans in Science (SACNAS) is a society that aims to further the success of Hispanic and Native American students in obtaining advanced degrees, careers, leadership positions, and equality in STEM. SACNAS was founded in 1973 by underrepresented scientists to address the representation of Chicanos/Hispanics and Native Americans in STEM. Diverse voices can expand scientific and mathematical knowledge as well as bring creative solutions to scientific problems. This is one of SACNAS’s motivations for building an inclusive, innovative, and powerful national network of scientists, which now includes over 6,000 society members, over 115 student and professional chapters, and over 20,000 supporters of SACNAS throughout the USA. Contrary to the name, the society is welcoming of people from all backgrounds, identities, fields of study, and professions. SACNAS is the largest multicultural STEM diversity organization in the US.

SACNAS has programs and events that train and support the diverse STEM talent that is found in this country. This is done in partnership with the student and professional chapters, the leadership programs, Native American programs, regional meetings, and policy and advocacy initiatives. SACNAS also hosts THE National Diversity in STEM Conference. This year’s 2019 SACNAS National Conference in Honolulu, Hawai’i brought in over 5,000 participants! Next year the 2020 SACNAS National Conference is in Long Beach, California!

Mathematicians and mathematics have always been a strong part of SACNAS. In fact some of the founders of SACNAS include mathematicians, such as Dr. Richard Tapia (Rice University) and Dr. William Vélez (University of Arizona). I am fortunate to have met these two great mathematicians, who at different times in my academic journey have shared their wisdom and thoughtful advice.

My first SACNAS conference was in 2011 in San José, California. I was a second-year undergraduate student attending his first scientific conference. I was eager to learn and excited for all the opportunities that would be presented at this conference, but I did not know what to expect. Fortunately, I found a community of mathematicians who share similar goals for diversifying mathematics and who genuinely care in supporting the success of students. I trace my interest in combinatorics to the 2011 SACNAS National Conference, where I had the opportunity to attended the NSF Mathematics Institutes’ Modern Math Workshop. That year’s keynote lecture on “Counting Lattice Points in Polytopes” was presented by Dr. Federico Ardila (San Francisco State University). As an example of the power of networking, community, and mathematics at SACNAS, four years later Federico became one of my master’s thesis co-advisors. More than that, I found an unconditional mentor, friend, and research collaborator and I owe part of this to SACNAS for providing a space for a student like me to grow academically and professionally.

The Modern Math Workshop is a two-day workshop that takes place in conjunction with the national meeting of the SACNAS conference and showcases the contemporary research happening at NSF-funded mathematical sciences institutes around the country. It became a collaboration with SACNAS in 2006 and has been jointly organized by the Mathematical Sciences Institutes since 2008. Since 2011 this event has been funded by the NSF through the Mathematical Sciences Institute Diversity Initiative. The workshop is a mix of activities including research expositions aimed at graduate students and researchers, mini-courses aimed at undergraduates, a keynote lecture by a distinguished scientist, and a reception where participants can learn more information about the Mathematical Sciences Institutes.

In addition to the Modern Math Workshop, there are scientific symposia organized by mathematicians, there are oral graduate presentations, and both graduate and undergraduate poster presentations.

I do not know if it was because we were in the beautiful city of Honolulu, that the sky was much bluer and the ocean water much clearer, but there was certainly an extra revitalizing energy present at this year’s SACNAS conference. Below are some of the mathematical events that went on (and that I participated in) at this year’s SACNAS conference. I am sure there were more that I missed out on.

This year’s Modern Math Workshop was organized by the Mathematical Sciences Research Institute (MSRI) There were two mini-courses aimed at undergraduate students. One was lead by Dr. Wilfrid Gangbo (UCLA) and Dr. Anastasia Chavez (UC Davis). The workshop also included research talks aimed at graduate students and faculty and were delivered by representative mathematicians from each of the NSF Math Institutes. Additionally, there was a panel which addressed topics such as: imposter syndrome, how to choose a graduate program, how to stay motivated, how to choose a mathematical field, etc. Below are some of the speakers and panelists.

- Katherine Breen (Institute of Pure and Applied Mathematics (IPAM))
- Xinyi Li (SAMSI – Statistical and Applied Mathematical Sciences Institute)
- Gabriel Martins (California State University, Sacramento)
- Robin Neumayer (Northwestern University)
- Marilyn Vazquez (Mathematical Biosciences Institute (Ohio State University); Institute for Computational and Experimental Research in Mathematics (ICERM))

I was able to sit in Dr. Anastasia Chavez’s mini-courses, which was “An introduction to matroid theory.” My discrete mathematical mind was very happy to hear and learn from my friend on a topic that is incredibly interesting. You can find her slides here.

Apart from the Modern Math Workshop there were three great events/experiences that I would like to share with you all.

- Dr. Rebecca Garcia (Sam Houston State University) and Dr. Kamuela Yong (University of Hawai’i – West O‘ahu) organized the very first “Pacific Islanders in Mathematics” session. This was a historic event (the organizers are writing a more detailed article to be shared with the public) and it featured amazing speakers including:
- Kyle Dahlin (Purdue University): Avian Malaria & Hawaiian Honeycreepers – Modeling of the Effectiveness of Vector Control
- Dr. Marissa Loving (Georgia Tech): Determining Metrics using the Lengths of Curves
- Ashlee Kalauli (UC Santa Barbara): Solving the Word Problem for Artin Groups
- Dr. Efren Ruiz (University of Hawai’i – Hilo): Rings Associated to Directed Graphs

- Dr. Pamela Harris and I co-organized, “Latinxs Count!”, an algebraic and geometric combinatorics research talk session at SACNAS. It featured a talk by me and three amazing speakers :
- Andrés R. Vindas Meléndez (University of Kentucky): An Invitation to Ehrhart Theory
- Laura Escobar (Washington University in St. Louis): Polytopes and Algebraic Geometry
- Ryan Moruzzi, Jr. (Ithaca College): Exploring Bases of Modules using Partition overlaid Patterns
- Rosa Orellana (Dartmouth): The Combinatorics of Multiset Tableaux

- Dr. Pamela Harris was also one of the featured speakers at the SACNAS National Conference. Her featured talk titled, “DREAMing,” shared her story as DREAMer and her mathematical journey into research and mentoring.

I am blessed to have such a supportive mathematics/SACNISTA familia. To end the blog post, I want to share something I mentioned at the conference. I overheard several people say that the math they do is not useful, but I want to challenge each of us to think more about the meaningfulness of our mathematics. Sure, my math may not be applicable (at least right now) to anything “useful”, but it is meaningful to me. It has given me a career path, it has allowed me to make wonderful friends and connections, and I get to share the beauty and meaning of it with people all over the world. But, that’s a whole other topic for a blog post (too deep for this blog post), so I hope that you got a glimpse of the mathematical events that I experienced at this year’s SACNAS National Conference! I look forward to seeing and meeting some of you at the 2020 SACNAS National Conference in Long Beach, CA!

*Disclaimer*: The opinions expressed on this blog are the views of the writer(s) and do not necessarily reflect the views and opinions of the American Mathematical Society.

*Comments Guidelines*: The AMS encourages your comments, and hopes you will join the discussions. We review comments before they are posted, and those that are offensive, abusive, off-topic or promoting a commercial product, person or website will not be posted. Expressing disagreement is fine, but mutual respect is required.

For reasons still partly obscure to me, my department has given me the opportunity to teach an introductory probability and statistics course for a second time. People often speak of impostor syndrome in mathematics, but this is something more like double agency. I feel like an embedded resistance fighter, my mind at intervals crafting subtle acts of sabotage, constantly wary that I might be found out.

I won’t deny the usefulness of adopting a probabilistic perspective, but its utility is also my chief complaint. It is attractive to view the world probabilistically because it allows the simplification of complicated processes into rules whose efficiency outweighs the sacrifice of accuracy. This preference is very human, but it can also lead to convenient fictions which are destructive. In the scariest cases, these hazards become amplified through algorithm and automation, as described in O’Neil‘s *Weapons of Math Destruction*, for instance. We are nobler, and maybe more human, when we take the time to get the whole story right.

So here I am, in front of a fairly large class of largely business majors, charged with teaching them a mathematical framework for the shorthands they will need to operate in an economy that pressures them (us?) to, above all else, *produce,* to our collective peril. How can I convey my concern to the students without giving myself away, without demeaning our purposes? Where can we find space for reflection on the apparatus that brings us together when there are eleven chapters to get through and everyone is like freaking out about how to use Bayes’ theorem before the first exam?

It’s not clear to me that this is possible, or at least that it’s not mutually exclusive to my having reasonable expectation of further opportunities to win my bread teaching mathematics to college students (see: economic pressures). So, one resorts to seeking nourishment from the mathematical substance of the course (it helps that we start with a good dose of combinatorics). So let me turn to the fun which motivates this post, with apologies to probabilists and statisticians everywhere for any misrepresentation of which I may be guilty.

**Discussion Question:*** What’s your favorite infinite discrete probability space?

**Do not attempt use in real classroom situations. The author denies any first-hand experience.*

Here’s, I think, the simplest natural example: toss a coin until a heads appears, and count the number of tosses it takes. The points of the sample space can be identified with the positive integers, and so we have a discrete random variable $X$. Supposing the coin is fair, our probability function says that the chances it takes $n$ tosses to get a heads is $P(X = n) = \frac{1}{2^n}$, just by the multiplication rule for probabilities of independent events.

I shied from going further into this example with my class because it occurred to me that showing that this all makes sense requires one to know a thing or two about convergent series (they don’t, mostly). That is, you should have to prove that the sum of all probabilities in this experiment,

\[ \sum_{n=1}^\infty \frac{1}{2^n} =1. \]

But what if we could flip the script . . . Does the fact that this *is* a sum over the values of a valid probability function for an actual experiment *mean* that the sum *does* converge to 1? More broadly, can we prove things in mathematics by reference to real-world (albeit, probabailistic) phenomena?

This all reminded me of a bit of combinatorics folklore:

**Theorem.** If $k$ and $n$ are natural numbers with $k\leq n$, then $\frac{n!}{k! (n-k)!}$ is a natural number.

*Proof.* This is $\binom{n}{k}$, which counts something. $\square$

This is actually a common technique in combinatorics: one proves the integrality of some rational expression by giving it a combinatorial interpretation, which is to say that it counts something. In the case of the binomial coefficients, this thing is size $k$ subsets of an $n$ element set, but one might also consider rational expressions that count set partitions, lattice paths, or domino tilings, to name a few. The fact that all of these examples can be rendered mundanely (“How many ice cream combinations can you make choosing $k$ flavors from a menu of $n$?”, etc.) and are thus *finite* makes this sort of proof-by-reference-to-phenomenon untroubling. But something spooky must happen when we consider the infinite.

The philosophical problems known as Zeno’s paradoxes were contrived to support an argument that motion is an illusion, and they rely on the unwieldiness of the infinite. In the “dichotomy paradox,” Zeno says (through Hofstadter):

‘. . . in getting from A to B, one has to go halfway first — and of that stretch one also has to go halfway, and so on and so forth.’

It’s ordinary that each number has a successor and that one can always split an interval in two, but, in extrapolation, we find ourselves with the tricky business of completing an infinite number of tasks in order to get from A to B. How can we possibly arrive?

It is said that, upon hearing Zeno’s paradoxes, Diogenes the Cynic^{2} said nothing, stood up, and simply walked (presumably away from whomever was explaining) to demonstrate the absurdity of the argument. At some point in the last few millennia, this incident became entwined with the phrase *solvitur ambulando*, “it is solved by walking,” now a motto for peripatetics everywhere. But this phrase also captures the spirit of the kind of proof-by-(probabilistic)-phenomenon wished for above. Diogenes’ demonstration is more compelling if we regard it as alternative proof-by-phenomenon of the convergence of the sum $\sum_{n=1}^\infty \frac{1}{2^n}$, which fact actually resolves Zeno’s paradox. For the walker, the time it takes to complete each task necessary to get from A to B diminishes by a constant proportion at each stage, just as the distance does. This is obvious if one already knows from experience that it only takes a finite amount of time to get from A to B, which is I guess what the Cynic was getting at.

In any case, because we *can* get from A to B, and because the fair coin tossing *is* an honest experiment, we have $\sum_{n=1}^\infty \frac{1}{2^n} =1$. But there’s more! We can soup up either of these proofs-by-phenomenon to get ourselves convergence any positive geometric series^{2}, without the advanced technology of limits. Let’s just do the probability phenomenon proof, leaving the walking proof as an exercise. : )

**Theorem.** For any $0<r<1$,

\[\sum_{n=0}^\infty r^n = \frac{1}{1-r}.\]

*Proof.* Think of a coin which is biased to give heads with probability $1-r$ and tails with probability $r$ when tossed. We toss until we get a heads and count how many tries it takes. Then the probabilities associated with each outcome are given in the table below.

$n$ | 1 | 2 | 3 | 4 | … | |
---|---|---|---|---|---|---|

$P(X=n)$ | $(1-r)$ | $r(1-r)$ | $r^2(1-r)$ | $r^3(1-r)$ | … |

Summing over all outcomes, we obtain

\[ (1-r) \sum_{n=0}^\infty r^n =1. \]

Divide by $(1-r)$. $\square$

And it could go further: If you have a convergent series of positive terms, you could always view (normalized) partial sums as giving the cumulative distribution function for an infinite discrete probability space. I wonder which series among these have “easy” interpretations as real experiments.

In algebraic combinatorics, there are famous collections of numbers (e. g. Kronecker coefficients, Somos sequences) that are known to be integral but lack a combinatorial interpretation. Other collections which do admit combinatorial interpretation, like the binomial coefficients, can be used used to give the information of a (finite) probability space. It seems there should be a brand of “phenomenal calculus” to bridge the gap to the countably infinite. Say, has any one cooked up probability experiments that can be interpreted to compute values of the Riemann zeta function?^{3}

And now I’ve wandered far enough with this that my original dilemma is no longer pressing, *solvitur ambulando*. The probabilistic perspective has proved itself more than just useful. On a good day, it might even be interesting.

^{1} Winner: Best Epithet Category, Panhellenic Philosphers’ Games, 383 BCE.

^{2 }Indeed, the probability distribution involved is called a “geometric distribution.”

^{3 }Apparently $\frac{1}{\zeta(2)}=\frac{6}{\pi^2}= 0.6079\dots$ can be interpreted as the probability that two randomly chosen integers are relatively prime. You could “phenomenally” deduce the convergence of $\sum_{n=1}^\infty \frac{1}{n^2}$ from the fact that any two integers must have a GCD, but as far as I can tell you can’t really get at the actual value through this game. See Section 3.5 of Kalman’s recently discussed article and references for more.

*Disclaimer*: The opinions expressed on this blog are the views of the writer(s) and do not necessarily reflect the views and opinions of the American Mathematical Society.

*Comments Guidelines*: The AMS encourages your comments, and hopes you will join the discussions. We review comments before they are posted, and those that are offensive, abusive, off-topic or promoting a commercial product, person or website will not be posted. Expressing disagreement is fine, but mutual respect is required.

En route to my first year of graduate school, I packed up the three good pillows I have, moved a couple hundred miles, and planted myself in an apartment I had only seen in a grainy Face Time video. Hopefully in five or six years, I thought, someone will begrudgingly call me Dr. Zell.

Then, the start of graduate school felt something like:

Welcome! Everyone here is looking forward to seeing you succeed. Now, let’s not waste time. It is graduate school after all. Undergraduates waste time, but not *us* thrifty graduates! Are you ready to teach? Not quite? Well, up and at ’em anyway! Oh, and expect to be challenged in all your classes. Bon voyage!

Even though the transition from Virginia to Michigan felt gigantic to me, I quickly realized my immense privilege as I befriended peers who only recently arrived in America. It’s hard to compare the international students at Michigan, because they are so obviously different. At the same time, they do agree on a handful of things: it’s confusing (and sometimes intimidating) applying to graduate school in America. Getting a visa is annoying. Family should be closer than they are. And of course, American food is way too sweet.

While the transition to graduate school may be confusing, and at times stressful, the international students at Michigan prove that graduate school is ultimately worthwhile. In order to share a little bit of the international student experience, I found some interview victims.

Anyway! Here’s what they had to say (split into two parts):

]]>*We like to think that our life stories have happy endings, perhaps that we can carefully partition our lives into fourths of each year, and successfully say, “Well, after I learned this, my life was great!” But anyone who has lived life — so, I suppose, anyone reading this — knows that that is not what life is like. Life is a continuous (not discrete!) story with continually changing hurdles. The gist of this series called “Dear first year, this isn’t something you can plan for,” is that if anything has, grad school has shown me how much truth the quote “the best-laid plans of mice and men often go awry” holds. Every quarter of my first year had some unexpected obstacle or victory and sometimes both, and sometimes the victory turned into an obstacle. The following is the story of my second quarter as a math Ph.D. student at Oregon State University, along with some thoughts that stay with me from that time.*

The day I turned in my Partial Differential Equations final, I left my first term of grad school to visit my analysis mentor at my alma mater, Central Washington University. I returned to Corvallis in mid-December. Naively, I hoped that I’d come back and feel “normal.”

It has been nearly fourteen months since I started graduate school, and I am still learning that normalcy doesn’t exist.

I thought “back to normal” meant returning to my thinking processes and mathematical maturity level of my undergraduate days. I thought it meant returning to the childlike joy I found in the concepts of analysis. Instead, I came back to Corvallis to find the bitterness of the last three months still chipping away at my heart. I still felt only frustration and oppression when I tried to study analysis. I was disgusted with myself and my inability to focus and work long hours.

I was meant to take my first crack at qualifying exams in April. I had started studying in September, before I was overcome with depression and barely had the energy or time to complete my homework assignments, let alone anything extra. Because qualifying exams were coming up all too soon, I should have spent December deep in the grip of linear algebra and real analysis — but I was angry with mathematics and the hand life had dealt me, and I threw in the towel on studying, telling myself I needed to recuperate from fall quarter.

Classes started again in January. The early days of winter quarter were highly reminiscent of some of my better days in November — going to bed pretty sure I was going to tell the graduate chair I was dropping out in the morning, knowing I wasn’t good enough for grad school, and wondering why the hell I was here in the first place.

In December, I spent a week strictly Paleo. I’ve done bouts of the Paleo/Whole30 diet before, and found it to be tremendously helpful in controlling my anxiety and depression. The problem is that Paleo can be really difficult to maintain long-term and take a lot of prep time — and time isn’t something one has much of in grad school. I wanted to go Paleo completely, but it didn’t seem feasible, especially when one of the major stressors in my life was a shallow, manipulative roommate who I avoided as much as possible. I spent about fifteen hours on campus daily to prevent myself from crossing paths with her. (It can be surprising how much those little irritations and anxiety-inducing moments wreak havoc on your well-being.) So instead I took a step I didn’t think I’d ever be willing to take: I went to the student health clinic and was prescribed anti-depressants in February.

The effect was almost immediate. The change wasn’t enormous, but I slowly started to find more joy in my work again — until the week I found out I failed my PDE II midterm (which is still my favorite of all the classes I’ve had at Oregon State — any other distribution and Sobolev space fans out there?) . . . *and* my real analysis midterm.

Yet more crushing than the fact that I failed my PDE II midterm was the fact that my PDE professor was the woman I wanted to be my Ph.D. advisor. In late November, I had walked into her office and asked her a question on my PDE homework. I walked out of her office with a sense that I understood her — and that I would do anything to be her student. In January, I asked her only other Ph.D. student about working with her, and subsequently set up a meeting with her to chat about her work and let her know about my interest in being her student. Barely a week later, I found out that I failed my PDE midterm.

I tried to talk with my professors about my exams and figure out how to put in more hours of work. I started forcing myself to be more disciplined (getting up at 7 a.m. and basically working all the way till 11 p.m. if I could muster it), but couldn’t keep up sixteen-hour days for very long; I was too mentally and physically exhausted, and having chronic insomnia didn’t help matters any. Like many have, I found that the more I forced myself to try to be perfect, the more poorly I managed to do a lot of things, but my inability to do everything well only discouraged me more. Some days I couldn’t get out of bed. I started skipping a lot of classes, especially real analysis. I had very little hope that I could understand enough to do well on finals.

But if nothing else, I had to really try in PDE, because I knew I ultimately wanted to work in analysis, and I knew I wanted to work with my PDE professor. So on Friday, March 1, after my PDE class ended at 1:50, I asked her a question about the proof of the Mean-Value Property, and then blurted out, “I really want to work with you but I was afraid my exam score would affect your decision.” She looked at me and said, “No, it was one exam score.”

I reread the above couple of paragraphs, and think that subconsciously, I must have been astonished that anything good would happen after I had decided I was a failure. But yes, it is true that even if you are not perfect, people will still accept you. I have heard all too many horror stories of advisors who lack patience, empathy, and tact, and mine has exhibited only kindness and understanding. “She has to be the calmest person in the department,” said my graduate chair at one point to me — me, probably the most consistently high-stress person in the department.

You might call that irony, or coincidence, or a miracle — and no, I didn’t end that quarter with the best grades in my life, and no, life still was not perfect after that. I don’t think I did very well on my PDE final either. But I did find an exceptional advisor, successfully start medication, and make some amazing new friendships — and I did start walking out of the intensity of the flames of mental anguish into a valley where the smoke had begun to clear. It won’t ever clear completely, I’m afraid, and such is life — but I wouldn’t trade the refinement of this fire for a valley with less putrid air.

*I said in the first part of this series that I served on a panel for incoming first-year grad students and that I shared with them that I was so happy I would never have to survive parts of my first year again. I also told them that I am living proof that one can make it through. You might have failed an exam or two (or many). You might feel you have disappointed people you respect. You might be overwhelmed by how much life has thrown at you. You might be exhausted and trying to be brave. But just because you don’t meet a numerical requirement on an exam doesn’t make you a failure — and I know that sounds trite, but it really is true. I have failed more exams than I can remember in grad school, and guess what? I passed my real analysis qual in September — and that’s the exam that actually matters! You are probably harder on yourself than anyone around you is. If you are overwhelmed with how hard life is, know that there are others out there who know what that feels like — and I’m one of them. It might not help you feel better in the moment, but it does mean you’re not alone. And I don’t know what you think, but living as a grad student is the most courageous thing I’ve ever done. Get some sleep and if no one else tells you this today, you’re one of the bravest people around. Oh: and when you’re struggling, don’t force yourself to be better. As my dear friend and office-mate said to me once as I agonized over my impending thesis/reading meeting, “You are enough as yourself.”*

*Disclaimer*: The opinions expressed on this blog are the views of the writer(s) and do not necessarily reflect the views and opinions of the American Mathematical Society.

*Comments Guidelines*: The AMS encourages your comments, and hopes you will join the discussions. We review comments before they are posted, and those that are offensive, abusive, off-topic or promoting a commercial product, person or website will not be posted. Expressing disagreement is fine, but mutual respect is required.

This week I’m here to tell you about an unlikely mathematical community that you might be interested in, particularly if you’re interested in applying to grad school, or if you’re a grad student wondering about life after grad school.

Perhaps surprisingly, the community that I’m talking about is /r/math, a subreddit on reddit.com. And the reason that you might be interested is because /r/math will be holding a **Graduate School Panel** starting from **October 21st, 12pm Eastern**.

At this panel, graduate student volunteers will be answering your questions and sharing their perspectives and opinions about graduate school, the application process, and beyond. There will also be a handful of panelists that can speak to the graduate school process outside of the US. In addition, there will also be postdocs, professors, and graduates in industry that can speak to what happens after you earn your degree. Furthermore, there are also panelists that have taken non-standard paths to math grad school, that are in grad school in related fields (such as computer science), or have taken unique opportunities in grad school!

Of course, this is a panel comprised mostly of graduate student volunteers, and don’t have much insight into the admissions process. However, this is a valuable resource to ask questions and chat with current grad students in a variety of schools and subject areas.

So again, the panel will run for about two weeks starting from **October 21st, 12pm Eastern**. It’s also bi-annual, so keep an eye out for the panel again in March, when US grad schools have begun to send out admissions decisions.

Disclosure: I’m a moderator of /r/math (which is even less interesting than it sounds), and I am running the panel.

—

For those of you not familiar with reddit, it is a link aggregator website perhaps best known for posting memes and gifs. Notably, once you’ve created an account, you can also discuss and comment on specific posts.One main feature is that instead of looking at all of reddit at once, you can join smaller communities (known as subreddits), and look at and discuss content related to that community (such as /r/math).

In particular, on /r/math there will often be links and discussions about math news articles, educational videos, recent papers, etc. Some of the other content on /r/math include weekly discussions such as the *Simple Questions* discussion thread, a *Career and Education Q&A* thread, and a *What Are You Working On?* thread for discussing the mathematics that you have been thinking about.

Another thread to watch out for is an upcoming **AMA thread with Brendan Fong and David Spivak** on **October 24th, 2PM EST**, where you can ask questions to these two mathematicians.

So if you feel like having an excuse to perform some mathematical procrastination, join in the discussion over on /r/math!

*Disclaimer*: The opinions expressed on this blog are the views of the writer(s) and do not necessarily reflect the views and opinions of the American Mathematical Society.

*Comments Guidelines*: The AMS encourages your comments, and hopes you will join the discussions. We review comments before they are posted, and those that are offensive, abusive, off-topic or promoting a commercial product, person or website will not be posted. Expressing disagreement is fine, but mutual respect is required.

I had, as my friend and fellow grad student Sarah Hagen says, “been burdened with the love of analysis” quite early. I found calculus utterly beautiful when I took the first three courses in the sequence. When I transferred from Columbia Gorge Community College to Central Washington University in fall 2016, I stumbled upon some seniors in the math major and asked what they were working on. “Analysis,” they said. “It’s basically like proving everything you learn in calculus.” I knew instantly that analysis and I would share a special connection. When I finished all the analysis Central offered, I spent a term independently studying Walter Rudin’s *Principles of Mathematical Analysis.* Baby Rudin became my all-time favorite mathematics textbook, and I cherish the memories I have of learning out of that text.

When I came to Oregon State, my identity was quite wrapped up in my adoration of analysis. Usually an introduction of myself, especially to others in the department, was quickly followed by how excited I was about learning more analysis, measure theory, and probability. I came to Oregon State expecting to work under one of the professors studying PDE theory.

So, yes, I was excited about embarking on the next step in my mathematical journey (with analysis in tow — for some reason I have always given the subject of analysis an almost human personality). I should also say that I was warned, repeatedly, about how soul-crushing graduate school can be. I was told that graduate school offered one of the highest rates of depression and suicide of any job. I had already deeply struggled to get through my undergraduate career and manage my stress while taking 17-18 credits of upper-division math every quarter. Certainly, I thought, graduate school can’t be as bad as my last year of undergrad was, when my grandmother passed away in the middle of the school year and grief hit me full force as I attempted to learn abstract algebra, analysis, topology, and numerical analysis at the same time? After all, I had my own office, I was surrounded by other people excited to study math, I was teaching, I was solving problems — grad school sounded like heaven!

But somewhat unexpectedly, I found that I missed the community so carefully created by my wonderful professors, mentors, and friends. Many of my good friends were still students at Central, so I still got firsthand information from them about how things were going — and while this seemed a blessing, it was a curse in disguise. My heart started to feel weighed down, and I remember thinking that I felt like I was grieving all over again. One Sunday in early October, I left my apartment in Southtown Corvallis and started crying uncontrollably — and I couldn’t stop.

It wasn’t just for a few hours, either. I couldn’t stop crying for two weeks. And I don’t mean sniffling crying — I mean tears streaming down my face, wads of tissues in the garbage every day. My eyes were always red and burning from the constant tears. I had no idea the human body could produce that many tears. The weight of my unhappiness made it almost impossible to get work done, no matter how long I stayed at my office every day, how early I got up to start working, and how much I tried to stay on top of deadlines. For someone who had been used to being at the top of every class, acing all my homework, and being praised for my careful mathematical mind, the change was simultaneously shocking and frustrating.

As the term progressed, my frustration mounted. The mathematical maturity I felt that I had developed my last year of working on my bachelor’s degree seemed to have evaporated. I was struggling to build friendships and relationships with my cohort of grad students. In undergrad, my professors had been welcoming of me coming into their office at any time during the work day to ask questions. Now, I found it monstrously intimidating to go to a professor’s office for office hours. I was convinced I needed to know everything, and yet I simultaneously felt that I knew absolutely nothing. In a matter of weeks, I went from being the most highly-recruited member of the cohort to being certain I was stupid and incapable — and I convinced myself that my professors thought the same thing. (For the record, I have only known every single professor in OSU math to be caring and generous. Still, facts of life were passed over by my fear of not being good enough.) I thought I had suffered from impostor syndrome in undergrad, I thought that I had experience dealing with my (sometimes poor) mental health, I thought I knew how to study math. Now I felt like someone had ripped a rug out from under me and catapulted me onto a concrete floor.

My mental health eventually became so poor that my mom told me that I had to contact a local counselor. I was informally diagnosed with clinical depression in November. By this point, I had already seriously considered dropping out of the graduate program multiple times. For someone who expected to come into grad school and at least have a chance at acing everything and still being the best student in the room, my apparent inability to keep up with deadlines and get 100%s on exams crushed me.

No, this was not something I ever saw happening to me. And, dear first year, unfortunately, you can plan all you want and learn all the mathematics you can and strive to do well in all your classes — and you can still not be prepared for the biggest enemies in graduate school: Self-Doubt and Self-Criticism.

A few days ago, I was on a panel for incoming first-years about life as a graduate teaching assistant and graduate student at Oregon State. I reminisced with them that my first three months as a math grad student were the most difficult three months of my life. I told them that I was incredibly grateful that my first quarter of grad school would never ever happen again. But I also told them that I *am *living proof that one can make it through extreme difficulty, and come out triumphant on the other side. (More about that in the next two parts of this series.)

And I want to tell *you* that, too. I share an admittedly vulnerable story because I have been blessed by others’ vulnerability in the past, and I hope that you will be as well. If you are struggling, you *can* make it through. When I think about last year, I’m not quite sure how I lasted in grad school that long, when I woke up in tears and went to bed in tears. I do know that if I didn’t have an incredibly tight-knit support system in my family, mentors from Central, and friends, I may not have had the courage to return to Oregon State in January.

If you are struggling, know that you are not alone. Graduate school is tough. What is that quote from *The Help*? “You are smart, you are kind, you are important.” Regardless of your performance in graduate school, you are still a wonderful person, and you still have immeasurable worth. It may feel like mathematics and your accomplishments define you. They do not. You *are* smart. You *are* strong. You *are* important — and grad school does not have the power over you to change that!

I will end by sharing a meme I found from the Facebook page “grad school memes with relatable themes” (check it out if you’re on Facebook; I always get a good laugh about their posts, and I emotionally relate to nearly all of them):

*Disclaimer*: The opinions expressed on this blog are the views of the writer(s) and do not necessarily reflect the views and opinions of the American Mathematical Society.

*Comments Guidelines*: The AMS encourages your comments, and hopes you will join the discussions. We review comments before they are posted, and those that are offensive, abusive, off-topic or promoting a commercial product, person or website will not be posted. Expressing disagreement is fine, but mutual respect is required.

I’m Richard Wong – a fifth year grad student working in homotopy theory at UT Austin, and I’m a new blog writer this year. I’m excited to contribute to the grad blog, and share some of the tips and knowledge from my graduate career experience – hopefully they’ll be of use to new or prospective graduate students. One of the themes that I’d like to focus on in my series of blog posts is ways to communicate and engage with the mathematical community (and beyond!).

To that end, what I’d like to share today is one quick tip to keep up to date with the endless tide of current mathematical research:

**Subscribe to the arXiv!**

Setting up your subscription, once you decide what subject areas you’re interested in, is quick and easy! It takes maybe 30 seconds to set up, and then a minute or two a day for the rest of your life (but you can do it while eating breakfast!). If you want the TL;DR summary, skip ahead to the end of the post!

If you don’t know what the arXiv is, it’s an online and open access repository of papers in mathematics (and other sciences). What this means is that mathematicians upload preprints of their papers to the arXiv for others to freely view and access. However, though there is a moderating and endorsement system on the arXiv, the nature of such a repository is that there is no intrinsic peer review system (though most papers have been submitted to peer review journals and are awaiting publication).

Sounds neat, right? The thing is, it turns out that there is a lot of mathematics being done, and a lot of papers being published. In the 2018 calendar year, there were over 32,000 new submissions to the math section of the arXiv alone (arXiv stats).

That’s a lot of papers to subscribe to! Luckily, you don’t have to subscribe to them all, and you can subscribe to specific areas in math, instead. The math section is sorted into 32 subject classes including algebraic geometry, analysis of PDEs, history of mathematics, mathematical physics, etc.

This means that you can pick and choose the categories you restrict your attention to, which drastically reduces the number of papers that you might want to read. For example, I am currently subscribed to math.AT (algebraic topology) and math.CT (category theory). On a typical day, there are maybe about 3-10 new submissions in these two categories combined.

Once you’ve chosen the categories you might be interested in, you can now subscribe to them! Subscription means that you will receive a daily email of a list of titles, authors, and abstracts of the papers that were submitted (or updated) in the past 24 hours with the subject tags that you selected. Also, it is extremely easy to subscribe to additional categories, as well as cancel your subscription, so don’t feel the need to agonize over your initial selections.

To subscribe to the arXiv, you simply need to send an email to math@arxiv.org, with the subject “subscribe”, and in the message body, add the subject tags that you’d like to subscribe to. (You can also subscribe to other fields by separately emailing the appropriate email address)

Here’s an example of the email I would send if I wanted to subscribe to math.AG (algebraic geometry):

To: math@arxiv.org

Subject: subscribe Richard Wong

add AG

If, after a week or two, I decide that I’m not interested in being subscribed to algebraic geometry after all, I can also cancel my subscription as follows:

To: math@arxiv.org

Subject: subscribe Richard Wong

del AG

It’s that easy! So now, as part of my daily routine, I take (literally) a minute or two to look at the new arXiv postings, and read the titles. If the title sounds interesting, I’ll skim the abstract. And if the abstract sounds interesting, I’ll do two things – first, I’ll pin the email to make sure I don’t forget to look at the paper. Secondly, when I have time, I’ll take a look at the paper.

If you’re a new grad student, I would actually recommend reading both the titles and the abstracts of new submissions to get a feel for the keywords and ideas that seem to pop up a lot – this is a sign that these ideas are useful and/or interesting! But as you get a handle on what’s going on in the subject, feel free to scale back and be more discerning with the abstracts and papers that you read. Now go ahead and subscribe!

TL;DR:

Step 1. Pick your subject classifications.

Step 2. Subscribe to them by sending an email.

Step 3. Keep up to date by reading the titles (and maybe abstracts) every day!

*Disclaimer*: The opinions expressed on this blog are the views of the writer(s) and do not necessarily reflect the views and opinions of the American Mathematical Society.

*Comments Guidelines*: The AMS encourages your comments, and hopes you will join the discussions. We review comments before they are posted, and those that are offensive, abusive, off-topic or promoting a commercial product, person or website will not be posted. Expressing disagreement is fine, but mutual respect is required.

For many people, in particular for students from underrepresented backgrounds and identities in mathematics, it is difficult to express your thoughts and experiences on applications (why this is requires a longer reflection and current research exists… so look into it!). In fact, many people I reached out to were hesitant to contribute to this post because many felt that they were “just lucky to get them.” I believe, THIS IS NOT TRUE. While there are human components to getting chosen to receive any award, we must acknowledge that we have worked hard and deserve every chance to apply and win these prestigious awards.

Dr. Jiuya Wang (Phillip Griffiths Research Assistant Professor and Foerster-Bernstein Postdoctral Fellow at Duke University) who won an Association for Women in Mathematics Dissertation Prize in 2018 for her dissertation in Number theory, wrote to me and mentioned that she let her advisor nominate her for that award. This may seem unusual for some, but sometimes it is in our best interest to self-nominate or ask others to nominate us for the prestigious awards that exists. In winning this award, not only did Dr. Wang get national recognition for her amazing work, she writes that “she [got] the chance to say thank you to the people [she] values in public.” As a recipient of a 2017 NSF Graduate Research Fellowship (NSF GRF), I can also add that we should not be embarrassed, afraid, etc., to ask for nominations or help. When I was applying for the NSF GRF, I recognized that I did not have the strongest writing background, so I sought the help in mathematical writing from my two master’s thesis advisors and my now PhD advisor and for the personal statement I sought the help from the fellowships advisor at my master’s institution (Advice: look to see if your institution has a Fellowships Office or Office of Nationally Competitive Awards, or something similar and seek out support from them).

While I hope that some of the advice shared in this post will help current applicants submitting applications to prestigious awards, I also hope that some of the readers are also people that will consider applying in the future (advice here applies also to finishing undergraduate students). With that said, TIME AND PLANNING ARE IMPORTANT! Dr. Marissa Loving (NSF Postdoctoral Fellow at Georgia Tech) mentioned to me that she began preparing for fellowship applications “(both mentally and by purposefully building [her] broader impacts/research portfolio) years in advance.” For her, the NSF Postdoc application was already on her mind from Day 1 of graduate school. While this may not be the case for some of you, I hope that you do consider applying to the NSF Postdoc and realize that time is essential for planning. One influential piece for her NSF Postdoc timeline was some job advice listed on Dr. Chelsea Walton’s website: https://faculty.math.illinois.edu/~notlaw/JobAdvice.pdf

Below are the experiences and advice of a diverse group of students and professionals who have received prestigious awards during their time as graduate students or shortly before/after. As my friend, Dr. Loving also mentioned to me, it is also helpful to share that she along with some of the other contributors on this blog post are women and people of color who have been very successful in applying for these awards. My hope is that as you read their replies to certain comments, you can get ideas on how to better your applications, manage the application timeline, and realize that there is a support system when applying for these awards. Additionally, I hope that readers recognize that the applicants are more than “just mathematicians”: they are people who come from all backgrounds, perspectives, experiences, and mathematical/personal interests, which you see below.

Thank you to all the contributors, many of whom I consider great friends!

Contributors: Jessica De Silva, Katie Taylor, Amzi Jeffs, Theo McKenzie, Elaina Aceves, Rob Davis, Nohemi Sepulveda, Darleen Perez-Lavin, Chase Ashby, Liam Solus, Anastasia Chavez, Jiuya Wang, Marissa Loving

Awards Represented: National Science Foundation Graduate Research Fellowship, Ford Foundation Predoctoral Fellowship, Fulbright Award, Department of Defense’s SMART Fellowship, NASA Pathways, National Science Foundation Postdoctoral Fellowship

_____________________________________________________________________________________

** Name:** Jessica De Silva

** Current Position/Institution:** Assistant Professor of Mathematics at California State University, Stanislaus

** Award Received and Year:** NSF Graduate Research Fellowship awarded in 2013

__Advice for future applicants:__* *Do your best to give the application reader a good sense of who you are, what you value as a person, and how it leads to you pursuing a graduate degree in Mathematics. I suggest trying to connect the reader to you in this way at the beginning of the personal statement, that way they feel invested in you while reading the rest of your application. For the personal statement, this also allows you to have a less modest (and therefore prouder) tone when discussing your accomplishments and their broader impacts. At the end of the personal statement, be sure to include your plans and goals as a graduate student and in your professional career.

__Application timeline/schedule/goals: __

**First two weeks of September:**

- Identify who will write your letters of recommendation. Meet with them (in person) to ask if they will write one for you. Let them know that this is different from a graduate school recommendation and give them print-out information about the fellowship.
- Write a first draft of the personal statement.
- Determine the premise/title of your research proposal.

**Last two weeks of September:**

- Have at least three different faculty members (letter writers in particular) read your personal statement.
- Write a draft of your research proposal.

**Until the deadline:**

- Have peers read your personal statement to fix any last minute typos.
- Have at least three different faculty members (letter writers) read your research proposal.
- Revise and submit!

__Benefits from receiving this award__*: *The application experience in and of itself was extremely beneficial. Since the due date was early in the Fall of my senior year as an undergraduate, I already had letter writers and a personal statement ready to go for graduate school applications. The research proposal gave me a glimpse of a researcher’s perspective in identifying and motivating the questions they aim to answer. I also made sure to include a sentence in my personal statement stating that I applied for this fellowship. I believe this showed that not only do I set goals for myself, but I am able to commit to executing the appropriate steps to achieve that goal.

** Non-mathematical activities:** Spending time with my hilarious family is my favorite way to spend my non-mathematical time. When I’m not at my parents’ house barbecuing tri-tip and ribs, you will probably find me at the gym lifting weights and putting that protein to use!

__Other accomplishments:__

Co-PI on an NSF grant to hold the 2019 Pacific Math Alliance Conference (Fall 2019)

Women and Mathematics Ambassador for the Institute for Advanced Study (Fall 2017)

PureMath@SACNAS Mini-Collaboration Grant (Fall 2016)

__Additional comments:__* *Although my advice is primarily for the personal statement, don’t forget that the research proposal needs to be equally as strong. In the comments I received from the reviewers, they noted that my research proposal was not as strong as others. I strongly encourage you to seek advice from research advisors and mentors on how to best prepare this portion of the application.

______________________________________________________________________________________

** Name:** Katie Taylor

** Current Position/Institution:** 1st Year PhD Student in Mathematics

** Graduate Institution & Research Area**: The University of Alabama, Undergraduate Research in Mathematics Education

** Award Received and Year:** National Science Foundation Graduate Research Fellowship, 2019; I did my proposal in STEM Education.

__Advice for future applicants: __

- Utilize prior applicant examples to gain ideas of how to format your application (you can find these online or possibly reach out to students who have one at your school).
- Pay attention to the formatting requirements as they are REQUIREMENTS, and there is no need for something like font or text to cause issues in your application.
- Ask your possible recommenders if they would be willing to support you at the start of your application process…mention to them that you will send along a draft of your application/completed application closer to time.
- Having done previous research will be extremely helpful in the application process as this fellowship application asks you to do a research proposal.
- Aim to find someone, even if not in your department, who has experience with the application and would be willing to read over your applications. If you have done research, your PI is also a wonderful person to have look over your application as your application will likely reference that research often.

__Application timeline/schedule/goals: __

I did not find out about the program until mid-September. That was enough time to set up a timeline, receive feedback from mentors, and really create an application that told my story. I wanted to make sure that my passion was clear as well as explain well what activities/past research I had done that confirmed this passion. I had over 5 full drafts where one or two of them were complete redos.

** Benefits from receiving this award (more than financial benefit):** This award allows you to focus on your coursework and research without an additional workload. During the decision process, it can also act as a reason for Universities to want you in their program.

** Non-mathematical activities:** I love to play piano, pet kittens, and spend quality time with my friends (game nights are frequent).

** Additional comments:** Remember you can only apply as a graduate student if you have completed no more than 12 months of graduate study at the time of application (i.e. you are a first or second year student), and you can only apply ONCE as a graduate student. Thus, if you do not feel your application is strong enough in your first year, there is no benefit to sending it in the first year as you will not be able to try again.

______________________________________________________________________________________

** Name:** Amzi Jeffs

** Current Position/Institution:** 4th year graduate student at University of Washington Seattle, working with Isabella Novik as my advisor.

** Research area:** Convex and discrete geometry.

** Advice for future applicants:** I received the NSF GRFP after my second year of grad school. I had also applied unsuccessfully two years earlier, during my senior year of undergrad at Harvey Mudd College. I think there were two main improvements in my second application. First, I had a

Lastly: Take your application to your local campus writing center!!! I did this with mine and ended up with a far more effective and “punchy” structure, as well as improved wording and grammar.

__Application timeline/schedule/goals:__** **It gets said a lot, but you should plan to complete a rough draft (however shoddy) of you *entire *application at least two weeks before the submission deadline. This will give your letter writers something to reference and build from, which is hugely helpful. It will also give you the chance to make lots of edits. An application which has been worked over for style and flow will go a long ways.

__Benefits from receiving this award (more than financial benefit):__** **The most significant benefit of the GRFP—besides being slightly more able to afford rent in Seattle—is that it freed me from teaching duties. This gave me a huge amount of free time, which I’ve used to get involved with all sorts of exciting activities on campus and beyond (see below). With time to pursue my interests further, I was more excited and motivated to return to research, and also had the ability to travel to various conferences/talks when the opportunity arose. Another opportunity I wouldn’t have been able to take if I had teaching duties: I was offered the chance to teach a “math in society” class at Cornish College of the Arts this Fall. It’ll be my first time teaching my own course, and I’m excited to teach in the context of an art school. Class started; wish me luck!

** Non-math activities:** I’m an active organizer with UAW4121, the union of grad students and postdocs at UW. Through the union I’ve had the chance to fight for demands that benefit the whole campus: better mental health care, justice for trans students and workers, robust protections from harassment and discrimination, and better wages to name a few. The union gives us a lot more power than our graduate senate or other forms of activism: our contract is a legally binding document that we can hold the university accountable to, and with 5000 members we have a lot of collective power to enforce it!

I’m also active in the Seattle branch of Socialist Alternative, and have been involved with campaigns for renters’ rights, indigenous struggles, anti-ICE work, and more through them. The synergy between my work with UAW and my work with SA has been a huge benefit to both. vMore recreationally, I enjoy a hell of a lot of cooking, some parkour around town, and rock climbing in the Cascades.

** Other accomplishments:** During the last year I’ve managed to produce a whole lot of papers, including my first published single-author paper, which you can check out here.

______________________________________________________________________________________

__Name:__** **Theo McKenzie

__Current Position/Institution:__** **PhD Student at UC Berkeley

__Graduate Institution & Research Area:__** **Probability theory and combinatorics

** Award Received and Year:** Ford Foundation Fellowship and NSF Graduate Research Fellowship

__Advice for future applicants:__** **Get a large set of people to look at your application. Advisors should look at it as they’re familiar with your research and known what it takes to receive a grant. You can swap fellowship applications with other STEM students to see what ideas they have. Have someone in writing/humanities look at your application to complement on your writing style.

__Application timeline/schedule/goals:__** **Over the summer I talked to my advisor about what would make sense to submit as a research project. I also made sure to have a final draft ready at least a month before the deadline so that you can get feedback. This was crucial for me.

** Benefits from receiving this award (more than financial benefit):** This has given me a lot of flexibility. I’ve had the ability to go to conferences and present my work without worrying about missing teaching duties. Also I’ve built a network of other scholars through meeting people who have also gotten the fellowship.

** Non-mathematical activities:** I’m the lead instructor for a math class at a California State Prison. I also play squash.

** Other accomplishments:** I’m proud to have won a mentorship award last year.

** Additional comments:** I would start on your application as early as you can! Things can always get crazy during the semester. Good luck!

______________________________________________________________________________________

** Name:** Elaina Aceves

** Current Position/Institution:** Math PhD student (fourth year)

** Graduate Institution & Research Area:** University of Iowa, Topology

** Award Received and Year:** Ford Foundation Predoctoral Fellowship received in 2018-2019 academic year

** Advice for future applicants:** The most important advice I can give is to have non-mathematicians read your application and make sure they can understand the research centered essays. I think that as mathematicians we get too comfortable thinking only other people in our research area or other mathematicians will read our work. However, in a fellowship application like this, it is essential that someone from any area of study can read and take something away from your essays about your work.

** Application timeline/schedule/goals:** I began working on my application in September 2018 when I started writing all of the essays needed for the application. My adviser was very supportive and took the time to read through a draft of one of my essays every week so I was continuously improving my essays throughout the semester. Once my essays were all mathematically correct and the prescribed page limit, I took my essays to the Graduate Success Office at the University of Iowa. This office has personnel who are available to read scholarship and fellowship applications, provide feedback, and meet with students to discuss their comments and suggestions. This step was crucial because after the revisions, I was sure that my essays were readable by a general audience and still maintained their mathematically correctness especially in the Previous Research and Proposed Plan of Research essays. In regard to the letters of recommendation, I selected professors who could speak about the various experiences I had described in my essays. One of my letter writers was my adviser who could speak about my research. Another writer was a previous teaching supervisor who could discuss my teaching ability and positive reviews from students. Since I had talked about outreach to the community through Sonia Kovalevsky Day, I had one of my letter writers be the organizer of SK Day who could testify to my participation and leadership in the activities of the event.

** Benefits from receiving this award (more than financial benefit):** I am now a part of a large organization of very supportive and encouraging students and professionals. As a mathematician, I have a great opportunity to talk about mathematics to scholars from other fields of study and represent a field that doesn’t receive enough attention or appreciation.

** Non-mathematical activities:** Binge watching Psych episodes, reading fantasy books, Listening to 80’s music

__Other accomplishments:__

Alfred P. Sloan Foundation’s Minority Ph.D. (MPHD) fellowship recipient

Graduate College Iowa Recruitment fellowship recipient

Graduate Assistance in Areas of National Need (GAANN) fellowship recipient

** Additional comments:** I was the only mathematician to receive the Ford Foundation Predoctoral fellowship during my year of admittance. Please everyone, apply to this fellowship program if you qualify! Mathematics needs more representation in these national programs.

______________________________________________________________________________________

** Name:** Robert Davis

** Current Position/Institution:** Assistant Professor, at Colgate University

** Graduate Institution & Research Area:** University of Kentucky; Combinatorics, discrete geometry, applied algebraic geometry.

** Award Received and Year:** U.S. Student Fulbright Grant. I spent the 2013-2014 working with Alex Engström’s research group at Aalto University in Espoo, Finland.

** Advice for future applicants:** The Fulbright website has statistics on applications and awards funded in recent years. You can use this data to see (very) roughly how “competitive” it is to receive a grant from a particular country. That said, don’t read too much into these statistics, as each application cycle contains a ton of unpredictable elements that are out of your control. Do keep in mind that programs in different countries may have different expectations, even though they are all Fulbright programs, so make sure that your goals mesh well with the particular program to which you apply. Make sure to reach out to your institution’s office for external grants, as they will almost certainly need to submit some information as well. They should also be able to help you out with any statements you write, which you should give yourself a lot of time to do. The people evaluating your application will very likely have little mathematical background, so you have to convey the importance of your project without getting bogged down in technical jargon. I found that very difficult to do, and I had to start my statements from scratch several times until it was in good shape. If you are awarded a grant, make sure you look into the process for obtaining a visa or residence permit promptly, because it can take a while.

** Application timeline/schedule/goals:** I brought the idea of studying abroad to my adviser, Ben Braun, in the early summer of my second year of grad school — around June 2012. I originally just intended it to be for a summer or semester, but the most straightforward way to spend some extended time abroad seemed to be through a Fulbright grant, which was a year long. Since my goal was to finish grad school in five years, I was about to enter my third year, and my last year would be filled up with teaching and a job search, I had to apply the following October, about four months later. That seemed to be an appropriate length of time, since I had to rewrite my statements multiple times. Looking back, I wish I had given myself another month or two, but four months worked.

** Benefits from receiving this award (more than financial benefit): **One of my goals during the grant period, which I was able to do, was to give talks and attend conferences at other universities that I wouldn’t normally have had the chance to visit. They gave me great opportunities to meet lots of people who work in my area and nearby areas. I learned a lot about how academia in Europe works, how to find out about more job opportunities, and a whole lot of new math. Even just the process of applying to the Fulbright was very helpful. I’ve applied for a variety of different awards and grants since then and had a much easier time writing project descriptions and summaries because of it.

** Non-mathematical activities:** The Fulbright group in Finland organized a number of trips during the year, which gave us a chance to see much more of the country than we otherwise might. Also, I lived in a building occupied mostly by students of the University of Helsinki, and I was fortunate to get swept up with a great social group. We were from all over the place: the U.S., Mexico, Ukraine, Italy, France, Spain, Germany, and lots more were in the group. We often took trips together, ate meals together, and generally got to be good friends, which really helped out with being away from home for so long. And of course, I became very familiar with saunas: going to them is practically a required activity in Finland.

** Other accomplishments:** In terms of external math awards: AMS-Simons Travel Award; NSF Collaborative Grant (co-PI with Tianran Chen at Auburn University in Montgomery), under the

** Additional comments:** If you’re reading this and have any questions about applying for a Fulbright grant that I didn’t answer, feel free to send me an email directly! I had such a great time that year and would be happy to help others how I can.

______________________________________________________________________________________

** Name:** Nohemi M. Sepulveda

** Current Position/Institution:** Williams College Alumni

** Graduate Institution & Research Area:** N/A at the moment

** Award Received and year**: Fulbright Teaching Assistantship in Spain, 2018

** Advice for future applicants:** Go for it and apply! Sometimes these prestigious awards can seem a bit intimidating, and perhaps impossible to get, but at the end of the day everyone has something strong to offer the program, and you may be just exactly what they’re looking for. I didn’t learn about this fellowship until late in the summer before I applied, so even if you feel like the deadline might be slowly approaching, still try and get that application in! Don’t let fear keep you from applying. There’s so much potential that each and every single one of us has to offer. Simply taking that first step and deciding to apply is very important and you deserve credit for it!

** Application timeline/schedule/goals**: As I mentioned above, I actually didn’t learn or know about the Fulbright fellowship until late in the summer before applying—sometime in August to be exact. After I finished a teaching internship that I was doing in India that summer, I returned home for about 3 weeks, and this is when I was able to work on the application and on the essays. I returned back to college early September, and the campus application deadline was in mid-September. After submitting my application to my school, I had to do a little mini interview with the fellowship office where I was asked questions like “Why do you want to do this fellowship?” and what qualifications I had. They also ended up reviewing my essays and they gave me feedback on them. This was very useful in that I was then able to make some last-minute changes that later strengthened my application. After this, you’re basically in charge of submitting the application online yourself by the deadline that Fulbright gives you, which is in early October.

** Benefits from receiving this award (more than financial benefit):** The greatest benefit in receiving this award was honestly having the opportunity to live in another country for a year, and also meeting some very wonderful people in the process. I was a teacher in a private catholic school in La Rioja, Spain and I really enjoyed my time there. I taught some really cute 5

** Non-mathematical activities:** Some non-mathematical activites that I included in my application were being a college senior advisor for a program called Matriculate, volunteering at my local immigrant center, interning at the Williamstown Historical Museum, working at the Mexican Red Cross, being a teacher in India as well as in Mexico, and doing human rights research abroad in Nepal, Jordan, and Chile.

** Other accomplishments:** I received some awards from my college such as: The Class of 1951 Scholarship, The International Public Service Fellowship, and The Ware Scholarship.

** Additional comments: **Apply, apply, apply!

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** Name:** Darleen Perez-Lavin

** Current Position/Institution:** Graduate Student at University of Kentucky

** Graduate Institution & Research Area:** University of Kentucky, Number theory

** Award Received and Year:** SMART Fellowship funded by the DoD, awarded 2017

** Advice for future applicants:** Pick your top 3 labs you would like to be placed at. Do some research on each lab and try to understand what they do. Answer questions like: What type of research do they do? Who do they actively service? During these searches, you should be asking yourself: How do I fit in? Are these things something I want to work on? The application has various writing statements. Each statement should encompass your strengths. I would encourage portraying your strengths and how they would benefit the lab in their current research goals. Talk about why you want to be there as well as how you are qualified to be there.

** Application timeline/schedule/goals:** The application is due early – mid January. I highly recommend you start as soon as possible since this application has a lot of parts. To help with length and time, I set weekly goals. Even if it was a section that took 5-10 minutes, it was better than doing everything at once. It felt less taxing this way. I also had various people read over my statement drafts. Pick letter writers that will display your strengths in different areas. For example, have someone outside your department write a letter that will show a strength outside of your academic achievements.

** Benefits from receiving this award (more than financial benefit):** With this fellowship, you get a lab sponsorship. I am required to do internships during the summer while in graduate school and work at the lab for the amount of years funded. I find this extremely beneficial because I have a job when I graduate that will provide me with work experience on research areas outside my thesis work. During each summer, I get a taste of what my life will be like when I graduate. I spent this past summer at the naval lab in Charleston, SC and it was a great experience. I have a better understanding on how the lab functions and what I may be working on when I get there. You also get the benefit of getting a security clearance. This process takes over a year sometimes and heavily delays you being able to be hired at the NSA, for example, or other government agencies. If you decided to leave after your years of service, having clearance will be a bonus if you would like to move to a different government agency.

This fellowship allows you to continue teaching if you would like but does not require you to teach. This allows you to have more time to focus on your research. It helped reduced my stress level since I had less demanded requirements to do each week. I chose not to teach but I have met other fellows that teach one class each semester so they can get an academic job once they finish their time at the lab. The lab does allow you to teach while you work there but you still required to do your 40 hours a week.

** Non-mathematical activities:** (As part of the SMART Fellowship) You are encouraged to do community outreach event and attend workshops / conferences. Since I work for a naval lab, there are different rotations to apply for at the office of naval research.

(Personal) Dancing to salsa, jazz and hip hop. I enjoy yoga, hiking and paddle boarding.

** Other accomplishments:** Awarded the NSF – MSGI internship program with the Department of Energy. To be honest, I’m most proud of getting the SMART Fellowship. With the lack of support from the department since I struggled to get my prelims done, it gave me purpose, hope and sense of belonging to be award a competitive fellowship. It made me feel like I deserved to be here. I just have a different purpose.

Personal accomplishments: Doing yoga on a paddle board! I’m still working on it but it’s a rush to be able to achieve balance on the water.

__Additional comments: __

Since you will be working for the government, they only expect you to work 40 hours a week. If you work over 40, you can save those hours for time off. For example, some people work 4 – 10 hour days to have a long weekend every weekend. There are limitation and rules to follow but you get the make your work week within reason. This forces work – life balance, which I find to be important. This also allows you to do something outside of work, maybe continue your thesis work or collaborations, maybe even learn a new sport or hobby.

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** Name:** Chase Ashby

** Current Position/Institution:** Ph.D. Student at University of Kentucky and Civil Servant working in the Computational Aerosciences Branch of the NASA Advanced Supercomputing Division at NASA Ames Research Center.

** Graduate Institution & Research Area:** I’m currently a Ph.D. student at the University of Kentucky researching in the field Computational Fluid Dynamics with applications in Aerospace Engineering. My research is focused on developing approximation methods for adjoint PDE solutions on structured curvilinear meshes.

__Award Received and Year:__** **Accepted into NASA Pathways Intern Employment Program in 2019.

__Advice for future applicants:__** **Network. Network. Network. NASA employees are a passionate group of individuals who enjoy both sharing their experiences and assisting motivated students. Be willing to explore and put in the hard work. NASA truly seeks people who have a passion for research and community. Email current employees, even if you’ve never met them before. Someone will likely respond, and you may just end up with a spontaneous interview.

Last year I was a struggling graduate student, however, simply being willing to ask for and take opportunities allowed me to find a solid foundation within a year’s time. Thus, my main advice is to be daring even in the presence of overwhelming self-doubt. Knock on those unopen doors and don’t be afraid of the work waiting on the other side.

__Application timeline/schedule/goals:__** **Applications appear on USAJOBS.gov as funding becomes available throughout the year. I first scheduled a phone call with someone to simply discuss what they worked on and my interests (this was obtained from a distant family connection). I simply couldn’t hide my excitement for the work being done at NASA Ames and they decided to forward my resume to their supervisor. Within a few minutes, they emailed me to schedule a phone call, which ended up being a surprise interview for an internship and the only interview throughout the whole process. After the interview, which took place in late December 2018, they decided to offer me an internship position for Summer 2019 in early February. They remained in close contact to ensure I found housing arrangements and eventually suggested that I apply for the NASA Pathways Program. Once the link went live on USAJOBS.gov, I filled out a medium length application that took around an hour to complete, including intermittent coffee breaks. On my way to the internship, I was notified of the offer!

__Benefits from receiving this award (more than financial benefit): __

- Hired on as a Civil Servant (federal employee), which comes with Federal Employee Health Benefits, retirement plan, life insurance.
- Competitive Salary. For my position as a student trainee in engineering: $75,000.
- Most Pathways students transition to fulltime employees after graduating.
- Students can actually be converted to other federal positions after graduating, e.g. FBI, CIA, NSA, DOD, DOE.

__Non-mathematical activities:__** **Acoustic guitar, hiking/camping, reading.

__Other accomplishments:__

- First-generation college student
- Graduate Scholar in Mathematics Fellowship
- Bob Gaines Research Fellowship

__Additional comments:__** **Readers may feel free to connect with me via LinkedIn or my university email. I’m very willing to and happy to discuss my experiences in further detail.

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** Name:** Liam Solus

__Current Position/Institution:__** **Assistant Professor of Mathematics, KTH Royal Institute of Technology, Sweden

** Graduate Institution & Research Area: **University of Kentucky, Combinatorics and Statistics

** Award Received and Year:** 2016 US NSF Postdoctoral Fellowship

__Advice for future applicants:__

0. Ask previous winners of the fellowship you are applying for if you can see their application as an example. While the content of your project is fundamental and novel to you, writing a grant/fellowship application that presents your proposed work in a clear, concise, and well-supported way is formulaic. A well-structured proposal will make it easier for the reviewers to follow your points, and it can even make it easier for them to argue on behalf of your proposal when discussing with the rest of the committee. Successful proposals will often have such a structure, and there is no reason for you to re-invent the wheel. Ask people who you know have been successful if you can see their successful proposal as an example when writing your own. If you don’t know such people, ask your mentors or other mathematicians you know if they know someone who you could ask. Just like in math, grant writing should start with an informative example.

- Get detailed feedback from mentors and get it from more than one of them. Get as much feedback as you can, and if you can get it from people who have written successful grant or fellowship applications then even better! Writing fellowship/grant proposals, like mathematics, is not something are born able to do. Just like mathematics, we need to learn from people who have been doing it longer than ourselves. Using the examples of successful proposals, you have available as guidelines, write the best proposal you can, and then send it off to at least two mentors for feedback. Different readers will see different things, so having more than one take a look at it will be helpful.

- Don’t fear critique. Remember the people who you picked to read your proposal are your mentors. They are people that support you and your ideas, and they want to see you succeed. Any comments they have or changes they suggest, no matter how seemingly drastic, are aimed at helping you present your ideas in the best possible way. More comments are not a sign of your failure, but a sign that your readers really care and want you to succeed!

- Don’t be afraid to start over. Sometimes the feedback you get is going to suggest a lot of changes. So many in fact, that you may realize that you are essentially rewriting the whole proposal. Be willing to do this. Think about it like a math problem: you were trying one approach to the problem, and then your mentors came by and gave you good evidence why that approach may not work. So, try attacking the problem from a new angle based on their expert advice.

- Start early. A well-thought-out proposal takes time, and the time invested in the proposal often shows. Having a first draft months in advance of the deadline gives you ample time to let your mentors read it, and for you to make major changes. Even before that, just musing about the problems you will propose and the general structure of the proposal months before you start writing it can really help you present clear, and well-thought-out ideas.

- Always apply and apply to everything. There is no reason not to apply to a fellowship that you think you might want. In the worst-case scenario, you don’t get the fellowship, but you did learn a ton about writing a proposal. This is still better than if you had not applied at all. The experience of writing a rejected proposal still gives you insight into how to better prepare the next one. Which is why you should apply to anything that seems of interest. Just like with mathematics, the more experiences you have with writing proposals, the more success you will have on future ones.

** Application timeline/schedule/goals:** My personal application timeline starts about 6 months before the due date. At this point I’m thinking about what I want to include in the proposal, and perhaps the general structure of how I will include these things. This is also the time when I’m asking people for examples of the successful applications. During this time, I write a lot of outlines, and small pieces of what I think I’d might include, by hand. Three months before its due I try and have my first draft prepared, and then I send it out to mentors/colleagues/etc. for their opinions.

** Benefits from receiving this award (more than financial benefit):** The NSF postdoctoral fellowship really changed my future. It gave me ample time, time that I would otherwise not have, to really engage with my research. During this time, I believe I produced some of my best work to-date. I was also able to broaden my mathematical interests significantly, investing time in learning things about new and exciting fields related to the problems in my proposal. Beyond this, the NSF postdoctoral fellowship took me to Stockholm, which has since become my home.

** Non-mathematical activities:** Surfing, snowboarding, rock climbing, exercising, skateboarding, and playing violin

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** Name**: Anastasia Chavez

** Current Position/Institution:** NSF Postdoctoral Researcher and Krener Assistant Professor at UC Davis

** Graduate Institution & Research Area:** University of California, Berkeley; Combinatorics

** Award Received and year:** Ph.D. in mathematics in 2017; NSF Postdoctoral Fellowship 2018

__Advice for future applicants: __

Some of the best advice I received was to make the research statement include enough evidence showing you fully grasp the difficulty level of your research goals and the necessary plan to achieve them. Personally, this meant doing a little extra work to gather examples, work out small cases, employ computer algorithms, and do whatever seemed appropriate for the tasks outlined to ensure I could show I knew what these projects really required. Also, it showed I could be realistic about my goals and what was achievable in the time period the award offered. That means, if a problem seems hard, it is ok to acknowledge that then followed by how you will address it. Be clear, concise, and honest.

Another great piece of advice I received was to find and include collaborators who were skilled in the machinery needed for the research program outlined. This, again, shows the feasibility of success for the project and that experts are interested and want to work on your problems. Plus, it means you can begin building a network of collaborators and expand your math community.

If possible, it is great to have a diverse group of folks willing to read and edit your statements. These can be people who are experts in your field and those who are tangential. Not too many of course, but enough to have a diverse opinion if your statements are well written, your research program is outlined clearly, if your program shows agency, and if the purpose of the research program is clear. Moreover, you will generate many iterations of your statements, which is great! Make every word used count!

Ask fellow applicants (perhaps fellow grad students, former grad students, new faculty) if they are willing to share their application packet with you. There is a lot of technical formatting that you need to adhere to, and documents types that are not so common. Getting examples from others, especially successful applicants, will be a great guide to developing your own. Plus, it’s great to have a work buddy to keep you on track. So, finding a comrade during the application season you can share tasks of editing, reading each other’s work, and setting deadlines to complete drafts, will make it a much more enjoyable process.

Last, imposter syndrome is something that can creep up, if it hasn’t prior to the application process. If you find yourself feeling lacking in any way around your abilities, competency, and value during this time, here’s a small exercise I use often (actually, I used it just the other day preparing for a talk!). I first recognize the nervous, anxious energy that wants to eat up my time worrying about my competency and confidence. Then, I ask myself, “Do you want to spend the next chunk of time worrying? Or would you like to take the action that will prevent the outcome you are so worried about?” Often, that builds enough strength and resolve to diminish the worry so I can complete my tasks at hand. The best part is, I have evidence that I am capable, and I can build that confidence back.

I hope this of use to you, and best of luck in your application process and award acceptance!!!

** Application timeline/schedule/goals:** I am currently finishing my 2nd of a 3 year NSF postdoc and plan to be applying for academic and possibly non-academic jobs in Fall 2021. My goals are a little vague, but I believe the next step will include elements of mathematics, education, and technology.

** Benefits from receiving this award (more than financial benefit):** The greatest benefit has been the opportunity to explore new mathematics and branch out of my graduate research while building a great mentorship relationship with my research mentor. It has also allowed me the time to dive deeply into projects on my own schedule, without juggling classes, teaching, etc. so common in graduate school.

** Non-mathematical activities:** I enjoy camping with my family, playing softball, learning the guitar, walking our two dogs Big Boy and Hope, and dancing.

** Other accomplishments:** I have an amazing, supportive partner and together we have been blessed to be parents to two incredibly inspiring and creative children. My daughters are probably my greatest gift and I’m profoundly grateful for all they teach me.

** Additional comments:** I’m a firm believer in the following advice from a mentor on how to find the right work-life balance: “You first have a life, then you find out how to fit your work in, not the other way around.” If that resonates with you, enjoy!

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Now, go and APPLY! You got this!

*Disclaimer*: The opinions expressed on this blog are the views of the writer(s) and do not necessarily reflect the views and opinions of the American Mathematical Society.

*Comments Guidelines*: The AMS encourages your comments, and hopes you will join the discussions. We review comments before they are posted, and those that are offensive, abusive, off-topic or promoting a commercial product, person or website will not be posted. Expressing disagreement is fine, but mutual respect is required.

As Sarah introduced, my name is Caleb McWhorter and I am the new editor-in-chief for the AMS Graduate Student Blog. I am a Ph.D. student at Syracuse University studying Algebraic Number Theory and Arithmetic Geometry. I am excited to be working with the many wonderful writers that have already volunteered their time and energy to bring you new and exciting articles. While we will strive to produce a wide-ranging collection of articles for you over the next year, we will be focusing on a few themes:

- Diversity in Mathematics, Mathematicians, and Mathematical Life: Though our lives tend to shrink as graduate students, we come from a broad variety of genders, ethnicities, ages, orientations, backgrounds, countries, universities, etc. We all also live varied (mathematical) lives. We will work to highlight the diversity of mathematics graduate students, their activities/accomplishments, and the lives they lead.
- Teaching and Graduate Resources: Graduate students have the delicate task of balancing their teaching, coursework, and research. But there are many gems out there to help mathematics graduate students along the way! We will work to highlight the resources out there for teaching, studying graduate Mathematics, preparing for qualifying exams, etc. We will also work to create original content to help graduate students complete their studies and their teaching to the best of their abilities!
- Mathematical Distractions/Tidbits: To say the least, life as a graduate student can be overwhelming. We will try to help with the stress by bringing you fun and interesting short articles, rather than always delivering you ‘heavy reads’. So look out for fun short articles including crosswords, comic strips, and quick math reads that can also be shared with interested undergraduates!

But of course, *the AMS Graduate Blog is for you*! We want to hear your ideas and hear what types of articles you would like to see over the next year. Feel free to contact me, cgmcwhor@syr.edu, or any of the other writers to suggest ideas. However the best way of seeing content that you would like is to write for the Blog yourself, see the recent advertisement calling for writers! If are interested in writing for the AMS Graduate Blog, send in an application! We would love to hear from you!

*Disclaimer*: The opinions expressed on this blog are the views of the writer(s) and do not necessarily reflect the views and opinions of the American Mathematical Society.

*Comments Guidelines*: The AMS encourages your comments, and hopes you will join the discussions. We review comments before they are posted, and those that are offensive, abusive, off-topic or promoting a commercial product, person or website will not be posted. Expressing disagreement is fine, but mutual respect is required.