I didn’t go to the joint meetings (JMM) this year. This is despite the following good reasons I had to go:

- I’m in my fifth year, applying for jobs, and this is the time when you’re supposed to get out there and spread your name.
- I’ve been a few times before and actually kinda enjoy the spectacle of the “world’s largest gathering of mathematicians.”
- Flights to Denver were mega cheap, even as of like two weeks ago.

I even resisted some light pressure from peers and professors by staying put, and given the low airfare and reliable sources of on-campus support for academic travel, the trip would have cost me next-to-nothing. So why not?

A large chunk of the academic apparatus is set up to encourage you to travel. There are many grants available from many organizations to attend conferences, and travel support for attendees is one of the major budget items for many conference organizers. Many jobs include travel allowances, or require travel to present at conferences as part of the job description. Departments like mine seem to have sizable budgets for the express purpose of covering the travel expenses (and honorariums) of invited speakers who seem quite willing to travel many miles to spread their gospel. Travel is part of the job it seems – both a perk and a responsibility for the academic mathematician. Insofar as I can tell, there are a few source causes of the fact of academic travel, which I guess are obvious, but are worth recounting for what I want to say.

The first reason is personal. By disseminating your knowledge through the unique performative medium of a live-action talk, your work penetrates into mathematical culture and you become better-known to the community. You can also build your network by meeting folks with common interests in person, and perhaps sharing a drink or a bite. This can lead to collaboration, the production of new mathematics, and further opportunities to disseminate it, which I’m told also leads to jobs with greater prestige and pay. Briefly, geographic mobility begets social mobility.

The second reason is institutional. Imagine you already have a position of great prestige and pay. What cause do you have to get off your butt and go preach to the unwashed mathematical masses? Well, besides all of the personal incentives, your employer wants you to go out there because your renown is ultimately their renown. An institution accrues and maintains prestige by the the fact that its members are invited to speaking engagements, so they will want to make the mechanics of academic travel as easy as possible for you. The actual (as in non-rhetorical) you may have witnessed this system in action whenever a professor cancels class because they are out of town, or when you have been excused from your duties for same.

The last reason is similar, though more deeply cultural. Academia is replaying a decades-old fantasy which I think is common to many sectors of society: that the upper-classes are the jet-setters. Frequent travel is an emblem of status, and the other modes of academic life, namely those which demand contact with the immediate community, are subordinate to the higher purpose of missionary work. The work that requires travel, by its resource-intensive nature, must be limited to those of rarefied talent and ability. And while scarcity is the origin of this regard, in the present age of commodified luxury and full capitalization of earthly resources, it has become the norm – now you have to travel just to keep up with the Joneses. The gross domestic product thanks you.

A small perversion of this fantasy, it is no wonder that our community so celebrates the myth of Paul Erdös, the mathematician whose life was an amphetamine-fueled itinerant rampage of collaboration. From Erdös’ claim that mathematics was set back commensurately by his one-month abstinence from stimulants, one might also suppose that a refusal to travel could be injurious to mathematical progress. What self-respecting mathematician would abnegate their responsibility to speedily delivery the bounties of their enterprise by such refusal?

So here’s my real question. As highly educated people, we know that air travel is a particularly energy-intensive form of transportation. The emissions-per-passenger produced by a single transatlantic flight yields more CO2 than the average citizen of many countries produces in a year. Can we continue to justify our privilege of air travel for the sacred purpose of scientific progress when scientific progress also tells us that we, as a planet, cannot all afford to travel by air? Can we expect the peoples and nations of the world to take the scientific community seriously on climate change if we are not making strenuous efforts to reshape our own behaviors in accordance?

Don’t get me wrong: I love a good conference as much as the next person. I’ve had the good fortune of visiting places I would never have been able to afford or justify if not for academic travel. I’ve met wonderful people and been blessed to share a room or even a conversation with many mathematicians I greatly admire. I know there are experiences enabled by conference-going which have no substitute, and collaboration over video chat may never quite be the same as working at the same chalkboard. The expense of academic travel does bear value, yet I still don’t know if things have to be exactly the way they are.

It’s true, aviation only accounts for about two percent of all carbon emissions. But this is complicated by the fact that the particular type of high-altitude emissions from airplanes can be more dangerous in the short term. Also, in the US, two-thirds of air travel is accounted for by the twelve percent of the population that takes six or more round-trip flights per year — the “frequent flyers.” I’m certain many academics are among this class. Do we need to stop flying? Probably not entirely, but I feel some hypocrisy knowing that we would be in real trouble if everyone started flying as much as we do. I felt this sort of guilt before I learned the Swedes had a name for it: *flygskam*, or “flight shame.” As soon as I learned this, I felt the rush of relief that comes with learning there are other people out there like you, and that there’s a name for you, probably like how X-Men (I assume the term is gender-inclusive) feel when Dr. X taps them and gives them context and purpose. Needless to say, now I’m devoted to spreading awareness of the term.

In the interest of full disclosure, I should probably confess that I attended an AMS sectional meeting in Hawaii last year, and I have to say it was great. But I feel complicated about this privilege. This meeting was very well attended, and I’m sure organizers bank on the appeal of a meeting in Hawaii, but the decision to hold it there is demonstrably not good for the planet when compared to alternatives. As Denver is relatively centrally located, maybe JMM should be there every year? Or if we really want to go for it, we could campaign for the construction of a carbon-neutral/negative conference center at the geographic/population center of the US (near the Nebraska-Kansas border, or somewhere in central Missouri, or somewhere else depending on how you measure), with connecting high-speed rail, to be used for all national scientific conferences.

There are also advocates of the video-conferencing approach. We know it has limitations, but if university courses can be conducted online and at massive scale with the assurance of comparable student outcomes, I don’t see why a video conferencing solution couldn’t be appropriate for some purposes. I think part of the solution here could be purely technical. Humans have been organizing traditional conferences for decades so the mechanics are both familiar and highly-developed, while video conferencing is still (in my experience) often clumsy and frustrating. If someone would design a slick and reliable platform for organizing video conferences, I could see this becoming a thing. Imagine one portal with all the conference abstracts, schedule, relevant chatrooms, etc., and then you could easily enter and leave sessions at your leisure… say, if I don’t get a job due to my lack of conference attendance, maybe I could start this business…

One study found that CO2 emissions due to travel for the purpose of presenting scientific papers accounted for only 0.003 % of the annual total, somewhere between the transportation emissions of Geneva and Barcelona. This sounds maybe not that bad. But I think what sets the climate crisis apart from other challenges is that

it requires action on all fronts. We won’t achieve our goals on reducing carbon emissions by singling out individual sectors that need reform. We need to create a culture which considers the impact of all of our personal and professional activities on the environment, and as scientists, high priests of this secular era, we are responsible for leading the cultural shift. If we aren’t going to stop flying to conferences (and we aren’t, I guess) we need to start thinking of ways to offset this activity. We need climate-consciousness to be baked into the process of conference organizing. I don’t know of any math conferences that are explicitly trying to address their environmental impacts, but I would like to.

To be clear, I’m not calling for any sort of a heroic abandonment of all air travel by the scientific community or advocating the use of sanctimonious hashtags (see #istayontheground). I’m sure I will fly again for a conference, and probably even use a paper cup or two for coffee when I have forgotten my reusable mug. I just want to point out that the path of minimizing the consequences of our own actions is too tempting for a community that should be taking leadership, and that this path is made even easier by the fact that individualistic resource consumption and accumulation is still de rigeur in this country in general. Non-conformity might initially require a little bit of courage, but I think it’ll be a bit easier for the rest of society, and result in less political strife, if scientists act first.

*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.

*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 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 third quarter as a math Ph.D. student at Oregon State University, along with some thoughts that stay with me from that time.*

I lived every term of my first year of grad school desperately hoping things would get easier. I still remember my first term as the most bitterly difficult of them all, but the truth is that each one of them — as my mentors warned me would happen — were approximately equally difficult (I recently thought maybe I should just turn this series into a memoir about the entirety of graduate school, since this past term, my fourth at Oregon State and the first of my second year, was busy as all heck and I felt like I’d stepped out of first year into a fire). I started spring quarter with the hopeful energy with which I had started every other quarter: with a determination to excel in my courses and return to my peak mental performance.

Winter quarter ended with the knowledge that my first attempt at Ph.D. qualifying exams was about ten days in the future. By this time, I understood that this attempt would be my practice run: I had been so completely overwhelmed during the past two terms that I hadn’t had the ability to study as much as is necessary for these exhausting tests, so I was intent on studying as much as I could throughout spring break and giving it an “honorable effort.”

The analysis exam went better than I thought it would, but that’s hardly surprising, since analysis is my field of study. Linear algebra, on the other hand, went absolutely terrible — I left the exam early, knowing without a doubt that I’d failed because I couldn’t get much more than one problem out of four solved. Two weeks later, I received the predictable news that I had failed both exams. In my head, I tried to tell myself I didn’t care, but failing those exams only made that little voice whisper more persistently, *You are a failure. You don’t deserve to be here. You don’t work hard enough. You didn’t deserve to be a Provost Scholar.*

Spring quarter, my course load was Real Analysis III (focused on general measure theory), Complex Analysis, and Partial Differential Equations III (largely bent toward applied mathematics; the last four weeks or so we discussed important topics in fluid mechanics). The beginning of the term, I was so excited about working really hard in complex analysis: we had reading assignments and problems to solve for each class day, as well as the typical set of four or five problems to hand in at the end of each week. Unfortunately, these daily assignments didn’t work out quite the way I expected. I hoped they’d be fairly simple: instead, they would often consume two or three hours of my time if I wanted to actually, really understand (they were graded on completion). As a result, I was left little time to work on the weekly homework, which was graded extremely carefully for correctness. The class I was excited to do well in quickly became the class for which I pulled multiple all-nighters, rarely managed to finish the homework, and was convinced I’d fail.

I could compare the three or so years prior to the beginning of May 2019 to being encapsulated in the deflector shields Droideka wear in *Star Wars*. Inside the deflector shield was math, math, and more math. Sure, being inside the deflector shield wasn’t a cakewalk, and the shield temporarily shut down in January 2018 when I learned that the only grandparent I had been very close to, my last surviving grandparent, had passed away. But it went back up again, shutting me inside with my math and not much else of the world.

Around the beginning of May, the deflector shield had sustained too much damage to protect me, and it burst. I started experiencing wretched allergies (did you know that Linn County, Oregon is the grass seed capital of the world?) and had to go to the health clinic three or four different times to try to (unsuccessfully) combat symptoms of allergies which left me with about 50% of my normal hearing. I randomly got heat exhaustion, even after drinking many fluids, after volunteering at a math outreach event in Eugene for the afternoon and then going on a bike ride in a Corvallis heat wave. I later learned that the random nausea was likely to be attributed to my new medication, the only side effect of which I had yet experienced was annoying itchiness on my extremities. Completely unexpectedly, I experienced a few weeks of relationship turmoil and confusion — the romance ended as suddenly and dramatically as it had begun, but the turmoil and confusion consumed my mind for months after. Then I received the news during one of my four recitations that my business calc class’s primary instructor was going on unforeseen leave; the next day I was asked to consider taking over a 100-person lecture, which I imminently decided to do, since it would give fellow grad students the opportunity to receive a teaching assistantship for the remainder of the academic year. I found a new apartment and my car got towed, and partly as a result of those two things experienced my first bout of the financial trouble grad students notoriously face.

All of this happened over the space of about two weeks. I said the deflector shield burst, didn’t I?

Having written almost three of these memoir-ish posts by now, one would think I would know how to end them. Do I discuss what I learned from that time, what I advise others to do? But I am a candid person; I have learned that honesty, even when it is brutal, is the best course of action; I have learned that lack of vulnerability is one of the tremendous weaknesses of humankind. So I’m afraid I will never be the one to wrap up a post like this with a nice little bow and make it pretty enough to put under a Christmas tree.

Perhaps what I think of when I think about the chaos and emotional toll spring term took on me, I am most thankful for the growth I see in myself — and not only the growth, but the evidence I gave myself that I am brave. It was not easy to know that I had to stop seeing someone I really enjoyed being around, but I did have to for the sake of multiple people involved, and so I did. It was not easy to keep showing up to teach a class where attendance on Fridays was around 15%, but I had to because I said I would, and I did. It was not easy to witness the subsequent strife in the mathematics department and feel that I was its cause, but I stood equally for both sides of the argument, knowing that I had made a decision and that I had to stand by it, so I did. It was not easy to read insulting student evaluations at the end of the term, knowing that I had poured so much time and energy into this body of students and into being as clear and precise as possible, but I knew I had to take their insults with a measure of salt, so I did. I did not know I could be strong, but I was, and I can be, and I am.

And you? You are strong too. Unfortunately, it is not the case that merely because we are human beings sequestered in learning the most beautiful field of study (I admit to being biased), we do not have to experience the pain of real life along with the pain of learning. I say this not to be pessimistic, but rather to tell you that I am aware that it is hard, and that showing up is hard, and that if you are showing up, you are standing strong in a hard battle. Don’t give up! I’m rooting for 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.

After a while I started a conversation with a couple of people about our jobs and what we enjoy about it. I told them about the research and teaching aspects of my graduate program. This semester I was a teaching assistant for a lower-division *Linear Algebra and Differential Equations* course. I find this course to be quite fun to teach, because I get to help students develop a geometric intuition for abstract mathematics and point to wonderful applications of that abstraction.

As it turned out, one of the people in our group was a graphics design student. He told me about a project involving linear algebra, and how he wished that he had taken more math courses. He also mentioned using the *Bézier curves* in his classes. I had never heard of that name, so I wrote a note to look into it later. This conversation reminded me of something I had read in Jordan Ellenberg pitch for Outward-Facing Mathematics:

“Those of us who teach spend a lot of hours talking about math in front of students who have been forced to be there. That makes it easy to forget that people out in the world generally admire math and are excited to learn about it, if we give them a way in!”

Back at home, I looked up *Bézier curves*, which lead me down a delightful rabbit hole of computer fonts and automobile design^{2}, and in the process I learned new math. In this post (and hopefully others) I am going to write about the wonderful mathematics that I learn inspired by people in other professions.

Geometry. Even the most basic illustrations involve lines and areas. To design the fancy $\LaTeX$ fonts used for mathematical symbols, for instance, each glyph is pieced together by many curves enclosing a shaded region.

This might sound like a trivial fact, like answering a toddler who asks “how are words written?” or at best something that typographers, not mathematicians, would find interesting. In that case, you might be surprised to hear that in the late 70’s and 80’s the AMS formed an advisory Standing Committee on Composition Technology^{3} and helped work on a then up-and-coming software by Donald Knuth called $\TeX$.

Stay with me and I will explain why I find this mathematically interesting.

Euclid postulated that given any two points, we can draw a straight line passing through them.

**Question:** in how many different ways can the statement above be generalized?

Here are a few I can think of:

- given three points, when can we draw a straight line passing through them? How about a circle or a conic section?
- given three points, what is the lowest degree polynomial $y=P(x)$ passing through them?
- given two lines in the space, when can we find a unique plane passing through them?

Each of these are interesting problems, typically studied by algebraic geometers. There are also others, but for now let’s consider the following:

- given two points and two lines passing through them, is there a cubic polynomial tangent to the given lines at the respective points?

This is referred to as spline interpolation.

The idea here boils down to finding a special basis $H_0(x)$, $H_1(x)$, $H_2(x)$, and $H_3(x)$ for the space of cubic polynomials in one variable so that given $y_0$,$y_1$,$m_0$, and $m_1$, we can quickly find the cubic polynomial we wanted by computing $P(x) = y_0 H_0(x)$ $+ y_1 H_1(x)$ $+ m_0 H_2(x)$ $+ m_1 H_3(x)$. Here is the idea:

Consider $P(x) = ax^3+bx^2+cx+d$, so $\tfrac{dP}{dx}(x) = 3ax^2+2bx+c$. Plugging in our initial conditions gives:

$$

\begin{aligned}

y_0 = P(0) &= d \\\

y_1 = P(1) &= a + b + c + d \\\

m_0 = \tfrac{dP}{dx}(0) &= c \\\

m_1 = \tfrac{dP}{dx}(1) &= 3a + 2b + c

\end{aligned}

$$

This is a system of linear equations:

$$

\begin{pmatrix} y_0 \\\ y_1 \\\ m_0 \\\ m_1 \end{pmatrix} =

\begin{pmatrix} P(0) \\\ P(1) \\\ P'(0) \\\ P'(1) \end{pmatrix} =

\begin{pmatrix}

0 & 0 & 0 & 1 \\\

1 & 1 & 1 & 1 \\\

0 & 0 & 1 & 0 \\\

3 & 2 & 1 & 0 \\\

\end{pmatrix}

\begin{pmatrix} a \\\ b \\\ c \\\ d \end{pmatrix}

$$

Since this matrix is invertible, we can find:

$$

\begin{pmatrix} a \\\ b \\\ c \\\ d \end{pmatrix} =

\begin{pmatrix}

0 & 0 & 0 & 1 \\\

1 & 1 & 1 & 1 \\\

0 & 0 & 1 & 0 \\\

3 & 2 & 1 & 0 \\\

\end{pmatrix}^{-1}

\begin{pmatrix} y_0 \\\ y_1 \\\ m_0 \\\ m_1 \end{pmatrix}

$$

Now we can go back to $P(x)$:

$$

\begin{aligned}

P(x)

&= \begin{pmatrix} x^3 \\\ x^2 \\\ x \\\ 1 \end{pmatrix}^T

\begin{pmatrix} a \\\ b \\\ c \\\ d \end{pmatrix} \\\

&= \begin{pmatrix} x^3 \\\ x^2 \\\ x \\\ 1 \end{pmatrix}^T

\begin{pmatrix}

0 & 0 & 0 & 1 \\\

1 & 1 & 1 & 1 \\\

0 & 0 & 1 & 0 \\\

3 & 2 & 1 & 0 \\\

\end{pmatrix}^{-1}

\begin{pmatrix} y_0 \\\ y_1 \\\ m_0 \\\ m_1 \end{pmatrix} \\\

&= \begin{pmatrix} x^3 \\\ x^2 \\\ x \\\ 1 \end{pmatrix}^T

\begin{pmatrix}

2 & -2 & 1 & 1 \\\

-3 & 3 & -2 & -1 \\\

0 & 0 & 1 & 0 \\\

1 & 0 & 0 & 0 \\\

\end{pmatrix}

\begin{pmatrix} y_0 \\\ y_1 \\\ m_0 \\\ m_1 \end{pmatrix} \\\

&= \begin{pmatrix} 2x^3-3x^2+1 \\\ -2x^3+3x^2 \\\ x^3-2x^2+x \\\ x^3-x^2 \end{pmatrix}^T

\begin{pmatrix} y_0 \\\ y_1 \\\ m_0 \\\ m_1 \end{pmatrix} \\\

&= \begin{pmatrix} H_0(x) \\\ H_1(x) \\\ H_2(x) \\\ H_3(x) \end{pmatrix}^T

\begin{pmatrix} y_0 \\\ y_1 \\\ m_0 \\\ m_1 \end{pmatrix} \\\

&= y_0 H_0(x) + y_1 H_1(x) + m_0 H_2(x) + m_1 H_3(x)

\end{aligned}

$$

These polynomials are the cubic Hermite splines.

Interpolating piece-wise cubic curves certainly is not the end of the story. As studied by algebraic geometers, multivariate spline theory and geometric modeling of curves and especially algebraic surfaces of higher degree is an active area of research. Even more, we can consider complex analytic functions and arrive at periodic designs. All of that also for another time.

From here it is a short walk to define Bézier curves. To keep this post short I will point to two references instead^{5}, but if you are interested to explore, there are many connections to numerical analysis and even a constructive proof of the Stone–Weierstrass approximation theorem.

If you are interested in the computations, you can experiment with cubic and quadratic Bézier curves or learn more about modern fonts and create one or make an animation instead.

To close, I want to give a nod to David Austin’s essay in which he suggests that “the singular value decomposition should be a central part of an undergraduate mathematics major’s linear algebra curriculum.” The book used in the course I am teaching stops at simple applications to physics, but perhaps introducing applications from other areas like computer science or the arts, even for students taking lower-division mathematics courses, would encourage people (including mathematicians) to view the subject in a more approachable light.

Notes and footnotes:

- The animations above are created by the Manim engine, as seen in 3Blue1Brown videos. I am confident that somewhere deep inside the Python libraries used in Manim, there are Bézier curves smoothing the transitions.

- In case anyone found my costume scary, I was ready to recite the quote by Gauss that “mathematics is the queen of sciences,” so technically I was wearing a princess costume! ︎
- If you haven’t heard yet, the new Tesla Cybertruck has decided to buck the trend of using smooth surfaces for vehicles in favor of low-poly designs. Oh well. ︎
- I couldn’t find much on this committee beyond an invitation by them to join the $\TeX$ user’s group in Knuth’s 1979 book “$\TeX$ and METAFONT,” published by the AMS. ︎
- These polynomials are not the same as Hermite polynomials
*a la*the quantum harmonic oscillator, but they’re both named after the same Charles Hermite. ︎ - Bill Casselman’s feature column From Bézier to Bernstein and these slides from a Computer Graphics and Imaging course at UC Berkeley are good places to read 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.

Before I dive into the gist of Professor Thompson’s argument, I think it is important to reiterate why diversity matters in mathematics. Here, I risk making Professor Thompson into a strawman; she’s not asserting diversity in mathematics is unwelcome, just that diversity statements should be removed from hiring. But humor me so I can climb on this soapbox.

First, creating a more equitable society and correcting past injustices that have disadvantaged underrepresented minorities is the most obvious reason diversity should matter. Of course, I have heard the rebuttal, “Yes, but why is it a responsibility of mathematicians to facilitate this change in our field?” Well, mathematicians have the power to enact substantial change by incorporating diversity initiatives into hiring, extracurricular programs, and candid reassessments of the academic climate. Sure, mathematicians may not cause systemic change in society at large, but undoubtedly academics have the power to influence climate and advocate for their values at their own universities.

More selfishly, collaborative environments benefit from diversity. A Tufts study on collaboration efforts of mock jurors found that diverse groups “deliberated longer, raised more facts about the case, and conducted broader deliberations” (6). While the Tufts study focused only on racial diversity, it is emblematic of a larger trend in social psychology which has demonstrated positive effects of diversity in a variety of collaborative environments (7). Crucially, mathematics is more collaborative now than it has ever been and, unfortunately, is not much more diverse (5). Through this lens, if we care about the advancement of our field, we should value diversity for its practical use in addition to its moral imperative.

Now, to the substance of Professor Thompson’s argument:

One of Thompson’s major planks is that a diversity statement is “a political test with teeth.” Thompson likens diversity statements to McCarthy-era loyalty oaths (back in the 1950s, the UC system forced faculty to sign pledges that they were loyal to America and not the Communist party, infamously firing those who refused to comply). Gently put, this is an odd comparison. Even if we accept Thompson’s claim that diversity statements are “political,” they hardly seem comparable to McCarthy-era extremism with respect to harm and disruptiveness. People didn’t sign the loyalty oath, likely because it aimed to exclude, isolate, or punish individuals for their political beliefs. A diversity statement’s entire purpose is to include historically excluded, silenced, or isolated minorities and allow them space in the academic community.

Moreover, is assessing whether job candidates treat people as individuals really a political statement as Thompson asserts? A person’s background influences the way they interact with most things–the classroom is no exception. Consider a student who can’t afford school supplies. Likely, that student will encounter challenges many others won’t: working a job outside class, distracting financial concerns, or even how to take notes each day. I’m not arguing that the instructor should give preferential treatment to this student; just that an inclusive instructor should strive to work with each student to help them realize their academic goals, being sensitive to the backgrounds different students bring into the classroom.

Studies also support the notion that individual identity influences performance in the classroom. For instance, two different studies (one conducted in Florida, one in Tennessee) found that having a teacher of the same race contributed positively to academic success (1, 2). Other studies reiterate that representation matters and that even math classrooms aren’t immune from the effect one’s background brings. For instance, a University of Massachusetts Amherst study found that “increasing the visibility of female scientists, engineers and mathematicians […] profoundly benefits [young women’s] self perception in STEM” (8).

While I agree with Thompson that treating people as individuals is an assertion of how society “ought to be organized,” I believe characterizing this sentiment as “political” misconstrues the meaning by associating it with partisan politics.

All of this is to say: it’s not political to treat people as individuals. It’s human and it’s logical.

Then, Professor Thompson criticizes the fact that “the diversity ‘score’ is becoming central in the hiring process.” Thompson’s language implies that other factors like caliber of research take a backseat to diversity which, when looking at the faculty of any R1 University, seems misleading. The New York Times rebutts this point best:

“The ethos [of mathematics] is characterized as meritocracy [and] is often wielded as a seemingly unassailable excuse for screening out promising minority job candidates who lack a name-brand alma mater or an illustrious mentor. Hiring committees that reflect the mostly white and Asian makeup of most math departments say they are compelled to “choose the ‘best’” […] even though there’s no guideline about what ‘best’ is.”

To paraphrase, hiring committees are just like the rest of us: subject to implicit bias. Certainly, the diversity statement plays a crucial role in patching “the leaky pipeline.”

Moreover, the diversity statement also communicates to underrepresented minorities that a math program cares about creating an inclusive research community. The University of Michigan recently conducted a study on academic attrition and found that, for underrepresented minorities, academic climate was a major factor in their decision to leave (4). In other words, stressing a department’s belief in the value of diversity helps positively shape department norms and combat attrition. The same Times article wrote about Edray Goins, a black mathematician who left a “better” position in a hostile academic environment for a department which emphasized inclusivity (3). Fortunately, Professor Goins chose to remain in academia, but his story is the exception, not the rule.

To her credit, Thompson ends by asserting that “mathematics must be open and welcoming to everyone, to those who have traditionally been excluded, and to those holding unpopular viewpoints.” Unfortunately, the substance of her previous argument makes these words feel empty.

If we truly care about increasing diverse representation in mathematics, we should pursue every available avenue. Diversity statements are only one piece of the puzzle, but they are important nonetheless.

1. Long Run Impacts of Same Race Teachers: https://www.nber.org/papers/w25254

2. Representation in the classroom: the effect of own race teachers on student achievement: https://www.sciencedirect.com/science/article/abs/pii/S0272775715000084

3. For a black mathematician, what it’s like to be the only one: https://www.nytimes.com/2019/02/18/us/edray-goins-black-mathematicians.html

4. Exit Interview Study: Executive Summary, University of Michigan: https://advance.umich.edu/wp-content/uploads/2018/09/UM-Exit-Interview-Study-2014-Report-executive-final.pdf

5. Women, Minorities, and Persons with Disabilities in Science and Engineering: https://www.nsf.gov/statistics/2017/nsf17310/digest/fod-women/mathematics-and-statistics.cfm

6. Racial diversity improves group decision making in unexpected ways: https://www.sciencedaily.com/releases/2006/04/060410162259.htm

7. More sources on the value of diversity in performance: https://blog.capterra.com/7-studies-that-prove-the-value-of-diversity-in-the-workplace/

8. Female Scientists Act like a Social Vaccine to Protect Young Women’s Interest and Motivation in the Sciences, UMass Amherst Study Shows: https://www.umass.edu/newsoffice/article/female-scientists-act-social-vaccine-protect-young-women%E2%80%99s-interest-and-motivation-sciences

*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.

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.

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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.