## That Time Terence Tao Won $500 From Paul Erdős A 10 year old Terence Tao hard at work with Paul Erdős in 1985. Couresty of Wikimedia Commons. Suppose you have some arbitrary sequence of 1 and -1, something like this 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, …. And suppose you start plucking entries from fixed intervals and adding them together. For example, if I just pick every third entry from the sequence, and add them all together, I would get -1 + 1 + 1 + -1 + … If I carry on doing that for some finite amount of time, will that sum get as big (positive or negative) as I want? Very simply, this is the idea behind the Erdős Discrepancy Problem, which claims that for any arbitrary sequence {x1, x2, x3, …} where the xi are either 1 or -1, and for any constant C, it is possible to find positive numbers k and n so that xk + x2k + x3k + … + xnk > C. Sounds easy enough, right? Not quite. And indeed this problem perplexed the great Paul Erdős to such an extent that he offered a$500 reward for a solution in the 1950s. And let’s hope that the late Erdős left a stack of cash lying around, because as of last week the problem has been solved by Terence Tao and the contributors to Polymath5.

In his blog, Tao gives a series of technical explanations of how he and the people of Polymath5 solved the famous problem. He explains how the key to cracking open the Discrepancy Problem was actually solving a totally different problem called the Elliot conjecture. This is such a common occurrence in math (and all fields, I suppose) that solving a really hard problem turns out the be just solving another really hard (but maybe a wee bit easier) problem.

The Polymath project — whose most well-known result to date is the tightening of the prime gap bounds of Maynard and Zhang — is a crowd-sourcing effort to drive mathematical breakthroughs. Mathematician Timothy Gowers, over on his webblog, gives a great commentary on the collaborative nature of this result. Although Tao was admittedly the one to put bring the whole thing to a culminating result, the terrain of the foundation would have looked much different without the crowd-sourced contributions. Gowers comments,

“My own experience of polymath projects is that they often provoke me to have thoughts I wouldn’t have had otherwise, even if the relationship between those thoughts and what other people have written is very hard to pin down — it can be a bit like those moments where someone says A, and then you think of B, which appears to have nothing to do with A, but then you manage to reconstruct your daydreamy thought processes to see that A made you think of C, which made you think of D, which made you think of B.”

This result is a marked victory for polymath, speaking to the impressive power of collaboration in mathematics, and an exciting success for Tao. And Tao will not be spending his well-deserved $500 on high-priced journal fees, since he will be publishing his paper in the new Arxiv overlay journal Discrete Analysis. ## Blogs for an IBL Novice This semester, I’m teaching complex analysis using an inquiry-based learning approach. I kind of jumped into the deep end: it’s my first time to teach the subject and my first time to use this teaching method. I’m getting used to the view from the back of the classroom this semester. Image: Derek Bruff, via Flickr. Although I’m new to teaching using IBL, I’m not new to IBL. The class that made me want to be a mathematician was taught using an IBL model where students presented all theorems and proofs. The class structure was perfect for me, but it turns out my experience as a cocky college student in the class isn’t very helpful for me now that I’m a less cocky teacher trying to run the class. Luckily, between my facebook friends and math blogs, I do have a lot of places to go for guidance. There are many different ways to implement IBL. I decided to emphasize student presentations of material. I give them notes with definitions, theorems, and exercises, and they supply the proofs in class. The notes I’m using are by Richard Spindler, and I found them in the Journal of Inquiry-Based Learning in Mathematics. I am of course making some modifications, but it’s been incredibly helpful to have a base to work from. I follow more IBL-ers than I can mention here, but for course structure, I am probably most indebted to Dana Ernst. I borrowed heavily from his past syllabuses when I was setting mine up. I have also benefitted from reading Dave Richeson’s posts, especially the one about his inquiry-based topology class. While I was preparing for the first few weeks of class, I found Carol Schumacher’s Instructor’s Resource Manual (pdf) invaluable. It is designed to be a guide to use with her abstract mathematics textbook Chapter Zero, but the first 30 pages are about course organization and strategies for various types of active learning in the classroom, and her advice in those pages applies to many different math subjects. There’s a new IBL blog on the block that has also been interesting for me: the Novice IBL Blog. It’s a joint blog by David Failing of Quincy University, Liza Cope of Delta State University, and Nick Long of Stephen F. Austin State University that’s been running for about a month, the same length of time as my class. It’s nice to feel like there are a few other people with some of the same questions I have, and reading about their experiences. For example, I am currently not entirely satisfied with the quality of course presentations and of my assessment of them, so I am grateful that Cope has written about the way she evaluates presentations. I also keep an eye on Stan Yoshinobu’s IBL blog. I’m trying to incorporate more of his tips for positive coaching into the way I give feedback. I’m not going to pretend things have gone entirely smoothly for me so far. I had more students drop the class at the beginning of the semester than I expected, and the drop rate for women was higher than it was for men. One of the reasons I decided to go for IBL was that many people believe that IBL and other active learning techniques are more fair to people who aren’t well-off white men. (See for example this recent New York Times article about whether lectures are unfair.) Of course I could not do exit interviews of students who dropped (they tend to ghost), so I don’t know why they left, but I am disappointed that my class has not retained women as well as men. If I set up a similar course in the future, I need to think carefully about how to get better student buy-in and assuage students’ fears that they are not prepared for the class. So far, my semester has been a bit of a roller coaster, but I’m glad I’m trying something new. And I’m extra glad to be teaching complex analysis. For never was a math topic of more whoa than this of complex differentiation and its lovely Cau…chy-Riemann equations. (With apologies to Shakespeare and all people of good taste.) Posted in Math Education | | 2 Comments ## A Cheap Alternative To Pricey Journals I’ve written before about the Elsevier boycott and the current shift in community feelings about the traditional journal model. Namely, that it stinks. The traditional journal model, that is. This morning while perusing my Monday morning blogroll I found something that piqued my interest. To quickly recap, academic journals are ridiculously expensive to administer, subscribe to, and even publish in. This is all so crazy when you imagine that I, as a junior faculty looking towards tenure, am required by my institution to publish in the leading journals. So I submit a paper, the fruits of months of my own labor and hand it over to the Journal of Whatever and Such-and-Such. If it is accepted, I’m then given the option: publish it open-access for a cost of upwards of$1,500 (typically paid by the university, I guess, to be honest I’ve never picked this option) or publish it normally, in which case the only people who can read it are those who pay the — some huge amount of money — per year subscription fee to the journal. And in the age of the internet, what is it that you’re really paying for? Official journal typesetting, a meager 200 KB of server space to host the paper, and a whole bunch of pointless overhead.

But as long as you can use LaTex, the official typesetting really isn’t all that important. Reach some minimum baseline aesthetic and your paper is more than readable. And I can think of a place where you can upload all the KB of paper you want: the ArXiv. So really, all you’re paying for is the pointless overhead part. Enter Tim Gowers, host of the great Gowers’s Weblog, and the editorial team of the new journal Discrete Analysis.

What they are launching is called an ArXiv overlay journal. What this means is, from the editorial standpoint it looks exactly like a traditional journal. The editorial board deals with submissions, sending them out to be peer-reviewed by appropriate reviewers, and managing the quality of content of the journal. Accepted papers are edited and the typesetting is cleaned up, per the referee’s suggestions, and uploaded to the ArXiv. Then Discrete Analysis hosts a page of ArXiv links with abstracts. Your paper has gone through all of the rigors of the traditional peer-review process, and it will even get a special Discrete Analysis stylized bibtex entry, but you’ve saved everyone a lot of time and money.

I think it’s an interesting model. I mean, we all want to do math, we want to publish math, and we want to read math. It makes sense to keep the process as close to the mathematicians as possible. Right now the electronic end of the journal is being run on a relatively cheap platform that costs \$10 per submission. That’s currently covered by a grant, but when that runs up, Gowers points out, “the absolute worst that could happen is that in a few years’ time, we will have to ask people to pay an amount roughly equal to the cost of a couple of beers to submit a paper, but it is unlikely that we will ever have to charge anything.”

Gowers, who won the Fields Medal in 1998, gives a great point-by-point explanation of every facet of the publishing process, and whether you agree with the feasibility of the model or not, I think it’s a worthwhile read.

Posted in Publishing in Math, Uncategorized | Tagged , , | 2 Comments

Last month, researchers Casey Mann, Jennifer McLoud, and David Von Derau at the University of Washington Bothell found a new pentagon that tiles the plane, and the crowd went wild. It’s tough for a piece of research mathematics to get news coverage, but this plucky little pentagon was the perfect media-friendly story. Everyone likes shapes, and they can understand what it means to tile the plane. The problem also has an interesting history, and it’s a good way to show people how mathematicians think: once we answer a question in one context, say for regular polygons, we see what changes when we change the context.

Representatives of the 15 types of pentagons that tile the plane. The newest one is in the bottom right corner. Image: Ed Pegg Jr, via Wikimedia Commons.

Several good math writers covered the story of the little pentagon that could. Alex Bellos wrote about it for the Guardian, NPR had a nice article by Eyder Peralta, Kevin Knudson wrote a post about it in his recently-launched Forbes column, Katie Steckles covered it for the Aperiodical, and Robbie Gonzalez wrote a short post for io9.

Lost in some of the news coverage was the fact that most of the pentagonal tilings are not individual pentagons that work but infinite families of pentagons, so there are infinitely many pentagon tilings, not just 15. It’s a subtle point but one that has caused a bit of confusion. Luckily, Wolfram has an interactive demonstration of the different types of tilings that helps clear things up. Reshan Richards also has a pentagonal tiling module on his Explain Everything app. (I do not have Explain Everything, so my mention of it here is not an endorsement or review.)

The question of pentagonal tilings is two questions in one: what pentagons can tile the plane, and how can they tile the plane? In other words, this is the distinction between tiles and tilings. The current discovery is of a new tile, a different shape that tiles the plane. Frank Morgan has a post about the other question: how can tiles be arranged into tilings? Specifically, he has mentored undergraduate students who are studying tilings involving two of the different pentagonal tiles. The post is full of pictures of these two tiles in all sorts of different tiling patterns with names like Christmas Tree, Toothy Smile, and Space Pills. His group’s AMS article about their work (pdf) has even more illustrations.

I first learned about the history of pentagonal tilings when Math Munch wrote about Marjorie Rice in 2013. Rice, one of the big names in pentagonal tiles, was not a mathematician but learned about the problem from a Martin Gardner article in Scientific American. It is rare that true amateurs make breakthroughs in research mathematics, but she discovered four new classes of pentagons that tile the plane, and her story is heartwarming and inspirational. Ivars Peterson, the Mathematical Tourist, has a post about her and the tiling of the MAA’s entryway.

While I was researching this post, I ran across another article from Peterson about pentagons and tilings. This one is about the seemingly paradoxical Biosphère dome in Montreal. It is a dome, hence spherical rather than flat, but it appears to be tiled with regular hexagons. “Where does the curvature come from?” Peterson asks. “I know the pentagons are there, and I have tried to find them, but I have had very little success in locating even one.”

I wonder if we’ve now found all the pentagonal tiles, or if someone else will have success locating another one.

## Long Live The Blank Slate

It’s the first day of school. I always loved this feeling as a kid. You’ve got your shiny new notebooks, freshly sharpened pencils, and your first day outfit all ironed and ready to go. Nothing can really compete will that feeling of having a totally blank slate, a reset, a fresh start. This will be the year you go home and copy all your notes after class, this will be the year you ask thoughtful questions. This will be the year you finish your homework ahead of schedule. This will be the year that you dazzle the academe with your brilliance.

Unsurprisingly, as a professor I still experience many of those feelings. A new batch of classes, a fresh crop of students, I’m bristly with ideas about alternative assessment strategies and non-traditional classroom models. On the first days we feel each other out, as we jointly embark on this magical journey into the unknown.

Of course in our modern day the unknown quality of the journey is slightly compromised. The omnipresence of social media and anonymous online forums steal some of the mystery. And then there’s the greatest blight of them all: RateMyProfessor.com.

This is a site that collects brief narrative reviews of thousands of professors by their students. Some reviews are helpful “definitely buy the textbook, it helps a lot,” to lewd and ridiculous “her class was ok but mostly I just stared at her butt.” I’ve often wondered about some of the biases that appear in these reviews, for example, do butts come up more often in reviews of female faculty? Luckily for me Ben Schmidt swooped in this year with his blog Gendered Language in Teaching Reviews. Schmidt scraped the data from 14 million RateMyProfessor reviews to study the occurrences of particular words across genders and disciplines.

As reported on NPR earlier this year, men are far more likely to be “brilliant,” especially when they are philosophers, while women are more likely to be rated as “friendly.” In mathematics, we see some really egregious (although unsurprising) gender splits with the words “genius” and “funny.”

It looks like physics, chemistry, and math professors are most likely to be “too smart,” unless they’re women.

But don’t worry, not everyone thinks we’re too smart, math professors also have the highest incidence of the word “stupid,” with it showing up 160 times per million words of text regardless of gender.

And if you’re curious, the word butt doesn’t really seem to follow a distinct gender pattern, but mathematicians seem to rank quite low as compared to the other lab sciences.

## Promoting Diversity and Respect in the Classroom

For a lot of us, the new school year is just around the corner. We’re getting ready for new classes and a new group of students. We have plenty of learning goals for our students and subject-specific material to think about, but we also need the classroom to be a place where all our students are welcome and are treated fairly.

A mosaic of pictures from people using the #ILookLikeAnEngineer hashtag on Twitter to combat sexist and racist assumptions in engineering. Image: Emma Pierson. Click to go to high-resolution, zoom-able version.

David Kung, math professor at St. Mary’s College of Maryland and director of Project NExT, gave an inspiring keynote address at the Legacy of RL Moore Conference in July. It’s a must-watch. I’ll wait.

In the talk, Kung calls on us to be honest about the current state of affairs, which is not good when it comes to representation of women and some minority groups in most STEM fields, and reminds us that math classes are sometimes gatekeepers for the rest of STEM. Our actions in the classroom can affect whether people become physicists, doctors, or engineers.

Kung’s talk is just one of the things I’ve seen recently about the intersection of math, teaching, and bias. Adriana Salerno of Bates College, in one of her last posts for PhD+Epsilon, writes about her desire for the classroom to be “structured in a way that empowers students or that makes them capable of resisting oppression and changing power structures.” Like her, I am tempted to think math is neutral and pure, not sullied by society’s prejudices, and I appreciate reading her ruminations on how to shake that idea off.

Both Kung and Salerno are critical of the way organizations that promote IBL use R. L. Moore in their branding. I was until recently unaware of his appalling treatment of black students. Raymond Johnson, the first African American to earn a degree from my grad school alma mater, Rice, writes about his undergraduate experience with Moore at UT:

Moore, his method and his work are highly thought of in the mathematical world. When he died, there was a laudatory article in the Math Monthly, a publication of the Mathematical Association of America. There is also a major MAA project on the legacy of R. L. Moore. The image of R. L. Moore in my eyes, however, is that of a mathematician who went to a topology lecture given by a student of R. H. Bing. Bing was a student of Moore. The speaker was what we refer to as Moore’s mathematical grandson. When Moore discovered that the student was black, he walked out of the lecture.

One person’s shortcomings in one area do not erase good things they do in another, but the pain and bitterness in Johnson’s writing made me think about the fact that attaching this person’s name to a pedagogy can be one of those little things that makes people feel unwelcome. Moore was not racist in some abstract way; he clearly and deliberately made it harder for some individuals to succeed than others, and those individuals have faces, names, and stories. They remember their treatment by this person others hold in such esteem.

Darryl Yong, mathematician at Harvey Mudd and the school’s associate dean for diversity, has re-launched his blog with a post about radical inclusivity. He writes, “My message to all educators: not attending to diversity and inclusion concerns in the classroom is the same as allowing your classroom to continue propagating the discrimination and bias that exists in our society. We have to actively combat discrimination and bias in our work as educators.”

None of us want to feel like we’re racist, sexist or anything else-ist, but we all have implicit biases. It hurts to be told or to admit to ourselves that we have these biases, but it hurts more to have your education and progress impeded as a result of these biases. These biases often don’t manifest themselves in overt racist or sexist actions, but small differences in how we treat different groups of students can accumulate into a force that pushes some students forward in math and some students out. And being a member of an underrepresented group does not mean you can’t be biased against that group. Last year, a story about sexism in hiring made a big splash. “John” got hired more often and with a higher salary than “Jennifer” did, even though they had the same resumés. One of the takeaways of the study was that both men and women on hiring committees were biased against Jennifer. That is a bit demoralizing, but it has a silver lining. No one needs to feel like they’re being singled out when we call on people to examine their biases. We can all fall prey to them, and we should all think about how we can do better.

If you’re reading this, I’m sure you would never tell a woman she shouldn’t be majoring in math because she’s a woman. (If you would, hi, nice to meet you, now stop saying that crap.) But you probably have some implicit biases that cause you to treat women a little differently from men and black people a little differently from white people. I don’t know how to stop doing that, but I honestly believe that being aware of our cognitive biases instead of soothing ourselves with the comfortable reassurance that we aren’t racist or sexist is a huge first step. Whether I am grading, having a class discussion, or writing a recommendation letter, I try to ask myself fairly frequently whether I would act or feel the same way if the student were a different gender or race. I hope that the small step of asking the question keeps me from unthinkingly slipping into biased behavior.

It’s all well and good for me to think about my actions in the classroom, but I also want my students to think about diversity and respect. Yong’s post about being welcoming on day 1 has gotten me thinking about how I should address the issue of diversity in my syllabus and on the first day of class. The fact is, in some ways this discussion is purely academic for me. I teach in Utah, and the demographics of my classroom reflect the (very white) demographics of the state. I can’t make my school more racially diverse, but in addition to striving to treat the few underrepresented minority students I do have equally, I can explicitly encourage my students to think about diversity and respect in my classroom and other aspects of their lives.

How are you promoting diversity and respect in your classroom?

Posted in Math Education | | 2 Comments

## Math Fought The Law, And The Law Won

Photo courtesy of stock monkeys.com

Math is full of laws: group laws in abstract algebra, the law of sines in trigonometry, and De Morgan’s law in set theory, to name a few. And occasionally, the law is full of math. That was the certainly the case in recent patent dispute at the London Court of Appeals, as covered by The Independent.

Here’s the TLDR: two drug companies were arguing over a patent. Company A has a patent for a solution containing between 1 and 25 percent of a certain compound. Now company B has manufactured a very similar solution, containing .95 percent of the compound in question. But everybody knows that .95<1 so company B is obviously in the clear, right?

Wrong. The judge eventually decided that any number larger than .5 is actually the same as 1, since we can round .5 up to 1, and apparently this judge has no love for non-integers.

My immediate reaction as a mathematician is that this could all have been avoided if Company A had just used interval and set builder notation. A quick recap in case it's been awhile since you've seen interval notation. There are two types of intervals, closed and open. The closed ones have square brackets, like [1,25], and the open ones have round brackets, like (1,25). The first contains all numbers between 1 and 25 including 1 and 25, and the second contains all numbers between 1 and 25 excluding 1 and 25.

The whole point of interval notation (in my mind) is that it takes away any and all possibility for ambiguity. If I say that my solution contains m percent of some compound, where m is in the interval [1,25], I truly mean that the smallest possible value for m is 1 and the largest value is 25. For example, the number 0.9999…9. (that’s just some long string of nines), which by any convention of rounding would round to 1, is still, itself, smaller than 1 and therefore not part of the interval [1,25]. Because of course, significant digits aside, you can round and truncate wherever you please. So to say that anything larger than .5 is really the same as 1 is a bit arbitrary, why not say anything larger than .49 or even .499, you get the idea.

So I guess the upshot is this: when making large business deals, use the most rigorous language possible to describe numbers, because you can’t count on some guy in a powdered wig to do it for you.

Correction: I initially said that .9999… repeating nines forever was less than 1, but as several apt commenters pointed out, if it really goes on forever forever, that’s just 1 — a true but unsettling controversial fact the internet loves to argue about! So let’s say it’s .999…9 for some really long but finite amount of nines, then we’re ok.

Posted in Uncategorized | Tagged , | 8 Comments

## Dimensions of Flavor

We talk a lot about visualizing mathematics, and we can even listen to it sometimes. But it can be hard to get the other senses involved, especially taste. Last year, I was delighted with Andrea Hawksley’s tasty and attractive Fibonacci Lemonade, which makes the Fibonacci numbers and golden ratio tastable. Her post about Fibonacci lemonade starts like this: “How would one make mathematical cuisine? Not just food that looks mathematical (like math cookies), but something that you truly have to eat and taste in order to experience its mathematical nature.”

A collection of points in beerspace is called a “flight.” Image: Quinn, Dombrowski, via Flickr.

I recently ran across a similar idea from Nathan Yau at Flowing Data. “Data plus beer. Multivariate beer.” (By the way, if you don’t already follow Flowing Data, you probably want to rectify that immediately.) Fibonacci lemonade has two variables: lemon juice and sugar. Beer has a few more degrees of freedom in the types and amounts of grains, hops, and malt.

Many of Yau’s data visualizations involve maps and demographics, so it’s not a surprise that for his first foray into mathematical libations, he chose to make beer recipes based on statistics such as the ethnic makeup, population density, and education levels of different counties. In the end, he brewed batches that represented Aroostook, Maine; Arlington, Virginia; Bronx, New York; and Marin, California. He writes:

Here’s what I eventually settled on.
1. Population density translates to total amount of hops. The more people in a county, the hoppier the beer tastes.
2. Race percentages translate to the type of hops used. For example, a higher rate of white people means a higher percentage of the total hops (determined by population density) that are Cascade hops.
3. Percentage of people with at least a bachelor’s degree translates to amount of Carapils grain, which contributes to head retention.
4. Percentage of people with healthcare coverage translates to amount of rye, which adds a distinct spicy flavor.
5. Median household income translates to amount of Crystal malt, which adds body and some color.

Did it work? Yau didn’t run a randomized control trial, but he says the beers definitely tasted different, and he had some tasting notes notes relating to the population density, healthcare coverage, and median income of the counties the beers represent.

I am coming to this idea from the point of view of a mathematician rather than a data journalist, so something I love about the idea of multivariate beer, Hanna Kang-Brown’s census spices, and other data gastronomification, as Tom Levine calls it, is that it is a natural way to explore the idea of dimension without going the Flatland route. (Flatland is great, don’t get me wrong, but it’s good to have extra tools at our fingertips.) It seems that most practitioners are interested in the way such concoctions can help people understand real-world data, but I like the potential for use in the strictly mathematical realm. Who knows? Flavors that represent shapes or polytopes? Could you taste the prime factorization of a number?

Yau says he is out of the multivariate brewing game, but if anyone is interested in doing an experiment in mathematical flavor, I’m a willing and able taste tester.

## In Praise of Teamwork

Left to Right: John Jones, Rachel Davis, and Christelle Vincent work on the LMFDB.

Part of what makes math blogging so interesting is that it helps to build connections between the people creating math and those consuming math. The evolution in math blogging and blossoming of math on twitter has done a great deal to dispel the crazy myth of math as a solitary pursuit, or worse yet, of mathematicians as weirdo loners. Mathematicians, just like other scientists (or humans for that matter), like to work together.

This sort of working-togetherness and community mathematics can come in many shapes: collaborative research, math blogging, and open source software initiatives, to name a few. I was first inspired to think about this by a wonderful portrait of Terrence Tao in The New York Times this week, calling attention to some of Tao’s exceptional work in collaborative math and mathemematical outreach.

But then those feelings were further amplified when this week found me at the LMFDB workshop in Corvallis, Oregon where I am sitting directly at the heart-center of an incredibly cool community math project. So, being here as I am on the front lines, I wanted to share a bit about the process. I’ve written about the LMFDB before, but to recap, it’s an online database of L-functions and “friends.” The database is open source, edited mostly through github and the kind and selfless hearts of so many contributors.

So here we are, 33 mathematicians, 33 laptops, 7 days and an unlimited desire to classify and sort things. On the first day, David Farmer, one of the LMFDB founding fathers asked that we begin by sorting ourselves according to what we felt we could contribute. He then recommended that we start by “pair programming.” Yes, this is when you sit next to someone and write code together on one laptop. Farmer said, “you might think this would cut productivity in half, but on the contrary, it doubles it since fewer errors are made.” So you see: teamwork.

This is how we spend our days, small groups clustered around tables pair programming whatever pieces of the LMFDB has sparked our interest. Some people are adding new sections to the database, perhaps a whole new wing dedicated to modular forms of half integral weight. Other people are working on the exposition of the database, writing concise descriptions of the objects for non-experts nested in knowls on the page. Some people are skimming the database for typos and html errors to make the whole thing more good-looking — seriously, nobody wants to get the L-functions from an ugly website, right?

After spending the entire day making changes and building new things and all the while programming in pairs, we have an end-of-day report. This is when the collaboration really kicks off. Each small group gives a brief recap of what they’ve done, and it is submitted to the jury of 33 for approval. Everything that goes into this database has passed before the community and been the subject of some intense and thoughtful scrutiny, from small changes (like, maybe these query boxes should be left aligned?) to huge ones (like, do you think we should change our entire labeling scheme?) gets a full-blown conversation. So you see: community.

I think the LMFDB project is an interesting example of extreme community collaboration in mathematics, but it is certainly not unique; this sort of community exists around lots of open source software initiatives. And of course this type of intense collaboration can also exist around the good old fashioned doing of mathematics.

Ok, I know what you’re thinking, “why are you telling me all this on a blog about math blogs?” Because, dear reader, I think this is the point of it all. Blogging abut math, and blogging about math blogs, or even blogging about blogging about math blogs (like I’m doing right this second), is all about brining the community together. So while writing about the LMFDB conference is not directly writing about a math blog, it feels like a friend of math blogging. And I think it’s important to remember why we blog about math.

## PCMI Blog Roundup

Earlier this month, I had the opportunity to give a cross-program talk at PCMI, the Park City Mathematics Institute. I talked about how doing math online can help us reach others in the math community, building bridges between teachers, researchers, and recreational math enthusiasts and reach those who think math isn’t for them. I talked about both social media and blogs as places where online math happens and some suggestions for how to talk about math so other people will listen.

PCMI’ers march in the Park City July 4th (Dimension) Parade. Image: Wendy Menard.

PCMI is really several programs in one. There is a research program with a graduate summer school, a secondary school teachers program, a program for faculty at undergraduate teaching-focused institutions, and an undergraduate summer school. (There might be more, but I think those are the groups I’ve encountered. It is large. It contains multitudes.) When I attended in the past, the instinct was for people to associate with others in their group, but some gentle nudges towards cross-program socialization led to some interesting and fruitful conversations. I think it’s easy to have tunnel vision as a participant in any of the programs, so those nudges really help people make connections and think about the broader math community they belong to. Incidentally, these are two of the things I find most gratifying about doing math online. Programs like PCMI are rare and short; the Internet, for better or worse, is always there. I’d never cross paths with math teachers who live thousands of miles away if I didn’t do it online.

With all that online math talk, I thought it would be nice to share some of the blogs written by this year’s PCMI participants. It turns out the teacher program is one step ahead of me: they keep a list of participants’ blogs here. So I’ll just include a few blogs by the people I met either in person or online during my brief trip up into the mountains.

I was happy to see that my AMS blogging pal Adriana Salerno, who writes PhD Plus Epsilon, was at PCMI this year. She was even kind enough to include my talk in her week one roundup post. While I didn’t get to meet him, I also heard about Dagan Karp, AMS blogger, Harvey Mudd math professor, and leader of the Undergraduate Faculty Program at PCMI.

I got to meet one of my online math pals, Ashli, known to me on Twitter as @mythagon and the author of Learning to Fold. I had lunch with her, Wendy Menard, who writes Her Mathness, and Dylan Kane of Five Twelve Thirteen. Both Menard and Kane blogged about the PCMI teacher program this year. Kane posted about a short talk he gave on the #MTBoS (math twitter blog-o-sphere), a cool online conglomeration of people blogging and tweeting about math and teaching. Later, I met Anne Paoletti Bayna on Twitter, where she shared her math Tumblr, paomaths. Menard and Bayna both blogged/tumbl’d about making conic sections with piles of salt. I’ve never done that before, but there’s a PCMI page about it (pdf). I’ll have to try it.

I really wish I had been able to stay and talk more with other math bloggers at PCMI (and of course see Henry Segerman’s talk on 3D printed geometry the day after mine). If I missed any PCMI blogs, please leave a note in the comments or find me on Twitter. I’d love to connect online, even if we didn’t get to meet face-to-face.