Topology in the Limelight

Topology is having a moment. Maybe not as much as this never-ending election season or this Pringles “ringle” with 40,000 retweets and counting (seriously, you should go look—it’s a self-supporting ring of potato chips, need I say more?), but it’s been getting more recognition than usual for a field of theoretical math. Somewhat ironically, it’s all because of the Nobel prize, and there’s not even a Nobel for math. (And no, it’s not because a mathematician had an affair with Nobel’s wife; he was a bachelor.) Earlier this month, the Nobel prize in physics went to three physicists for their work on topological phase transitions and topological phases of matter.

Delicious topology. Image: Dave Crosby, via Flickr. CC BY-SA 2.0

Delicious topology. Image: Dave Crosby, via Flickr. CC BY-SA 2.0

As science news editors across the globe sighed and shelved their pre-written explainers about LIGO and gravitational waves, they got to work figuring out how to talk about the work that actually won the prize this year. The easiest part of the prize to explain ends up being the most off-putting word, topology, so the bagels and coffee cups were at the ready.

Nobel Committee member Thor Hans Hansson had an adorable illustration of the basic idea of a topological property, in this case genus. But his explanation and some of the other ones I saw sometimes gave people the impression that the physicists were studying literal, if miniature, bagel- and pretzel-shaped objects floating around in superconducting materials. That’s not quite right. I tried to make it a bit clearer in an article I wrote for Scientific American. I can also recommend Kevin Knudson’s article about it for The Conversation and Brian Handwerk’s piece for Smithsonian. Vasudevan Mukunth also has a nice article on The Wire reminding us that the value of these physics discoveries is not necessarily in their utility or applications.

For me, one of the most fun things to come out of the Nobel’s mathematical connection is a series of interviews Rachael Boyd did on the blog Picture This Maths. (I wrote about Picture This Maths this past July.) One of the interviewees, Ruben Verresen, complains about the usual description of topology so many of us give of topology, which tends to be of the donut-coffee mug variety. “The issue is that they seem very arbitrary: what’s so special about holes?” Even if a reader or listener understands what you’re describing, he thinks it’s not all that interesting. He writes, “if I explain topology by comparing a donut to a coffee mug, I can just see my listener slowly turning off.” Instead, he thinks we should emphasize the difference between properties that are local and those that aren’t. Local properties even include things like height, anything that can be assessed by looking at the property in a small region and then combining those observations over the entire object. He says that emphasizing this distinction can make it more clear why someone should care about topology in the first place.

Boyd’s interviews also made me aware that someone’s been writing a comic strip about topology and nobody told me! The strip, by Tom Hockenhall, is in Chalkdust Magazine.

I’ve seen topology around a few other places recently, so this post comes with a dessert course. Mathematician Jean-Luc Thiffeault used ideas from topology to analyze taffy-pullers, both modern and old-timey, and I was ON IT for Smithsonian. Candy and math? Yes, please. Then there’s this Nature News Q&A with Microsoft researcher Alex Bocharov about why Microsoft is investing to heavily in building a topological quantum computer. One of the most interesting things I learned when I was writing about the physics Nobel prize was that physicists are trying to figure out how to use topology to build a quantum computer. Once you’ve heard it, it makes sense: topological properties are more robust to small perturbations than other properties, so in theory, information would be less prone to degradation from outside noise.

Finally, behold the ultradonut topology of the nuclear envelope, a real paper title from the Proceedings of the National Academy of Sciences. Mmm, ultradonut.

Posted in Applied Math, Theoretical Mathematics | Tagged , , | Leave a comment

How Polling Works…Or Doesn’t Work

From the perpetual pit in my stomach, to the sleepless nights, to the eyes bloodshot from peering at endless forecast models and polling predictions, only one thing can be true: the election is nigh upon us. In a time of uncertainty, where opinions and gut feelings seem to dominate, the mathematician in me craves the concreteness of numbers. And polling does just that. It gives me a quantified sense of what the future will look like. And sure, it’s something cozy to wrap myself up in. But what do those numbers mean? What am I really looking at when I see election forecasting?

First, there’s the question of the act of polling itself. Like anytime you gather data for statistical analyses, there’s always a chance for sampling bias. Since it’s impossible to contact every single person in the country, pollsters need to find some representative subset. That is, polls need to use a small number of opinions to extrapolate the national opinion. National polls are typically conducted by phone, and Pew Research reports that — largely due to the disappearance of land lines over the past 20 years — response rates have gone from 36% in 1997 to 9% in 2012. Since landlines can be autodialed while cell phones must be dialed by hand, calling land lines is still the best way to reach the largest swath of people as fast as possible.

This of course brings with it some problem of bias, since the set of all land line owners in the United States is a very particular demographic, not necessarily representative of the country as a whole. But the Pew Research Center says that through careful weighting of poll responses they are able to overcome these biases. So a single poll, which already contains thousands of responses is weighted to correct biases and massaged to give the most accurate picture of national opinion.

But typically the poll results that you see on popular news sites don’t just reflect a single poll, they are often aggregates of the top 5 state and national polls in some cases, to several thousands of polls in other cases. And then the thousands of polls — some of which are more reliable than others — are weighted to reflect their reliability, sample size, and representative regional demographics.

And finally an aggregation of polls becomes and mathematical model when a few more factors are added into the mix. Depending on the agency doing the modeling they will factor in effects like the convention bounce, the shape of the economy, and accuracy in prediction in certain states in past elections. All of these factors come together to build a robust mathematical model to forecast the election.

As one example, The New York Times maintains an active “Who Will Be President?” Scoreboard, comparing their aggregate model will several of the other top forecasts like fivethirtyeight, Daily Kos, HuffPost, and Princeton Election Consortium. And to game things out even further they also have an interactive chart weighing out the probabilities of each candidates path to the presidency based on electoral votes and states that have determined election outcomes in the past.

And then there’s this dimly lit corner of election forecasting that doesn’t rely on polls at all. These are places like the Cook Political Report which produces forecasts based more on reporting trends and expert opinions, or PredictWise which bases its forecasting on a combination of polls and betting markets.

There are a host of quantitative ways to deal with the election right now — and some slightly more qualitative ways as well — but I find the best thing to do is light some aromatherapy candles, immerse yourself in a warm bath of polls and forecasting, breathe deep cleansing breaths, and wait for November 8th.

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Celebrating Latin@s and Hispanics in Mathematics

September 15-October 15 is Hispanic Heritage Month in the U.S. (In case you were wondering, it starts on September 15 to coincide with the Independence Days of several Latin American countries.) The new website helps us in the math community celebrate by sharing a photo and brief biography of a Latina, Latino, or Hispanic mathematician every day during this month. I’ve seen a few familiar names and faces and a lot of new people to learn about.

Ten of the Latina, Latino, and Hispanic mathematicians featured for Hispanic Heritage Month on the website. For full image credits, click here.

Ten of the Latina, Latino, and Hispanic mathematicians featured this month on the website. Image from the AMS Notices article about LathismsFor full image credit information, click here.

Alexander Diaz-Lopez, Pamela Harris, Alicia Prieto Langarica, and Gabriel Sosa are the mathematicians behind Lathisms. Harris and Sosa were gracious enough to chat with me last week about what inspired them to create Lathisms and why they think it’s an important project. Below is an abridged transcript of our conversation. (Note: This is an AMS blog, and the AMS has been supportive of Lathisms, but the AMS was not involved in my decision to write about the site.)

Evelyn Lamb: What inspired the creation of Lathisms?

Gabriel Sosa: It was during February, it was Black History month. I was asking people whether we knew of a poster featuring prominent African American mathematicians. The AMS has this really nice poster about women in math. When I started in grad school, I was like, how many famous women mathematicians have there been? If you look back in time there were not that many. Of course it’s because women were not allowed to do math back then. But there are so many examples, so many amazing people on this poster. I thought, what a wonderful thing. Maybe there should be one for African Americans too. And Pam said there isn’t one for Latinos. So she said, “Let’s do one!” [Editor’s note: I published a roundup of resources for learning about African American mathematicians on this blog in February.]

Pamela Harris: It’s one of those things that sort of happened over Facebook. Alicia, Gabriel, Alexander, and I have met each other at multiple different conferences, and we work together amongst ourselves doing research. It became this natural thing, another project we could do. I think what was really beautiful about it was that without even intending it to be this way, we found two Hispanic women and two Hispanic men to do this project. It was this idea that sprung up from having Gabriel ask this question, does such a poster exist?

EL: So will there be a poster at the end, or will it all be online?

PH: The original idea was for us to get information out as soon as possible. Alexander has a connection at the AMS. He has written for the Graduate Student Blog, and he is an editor for Notices of the AMS. Immediately we knew that Alexander was somebody who had a nice connection and good rapport with the AMS. We knew that maybe we could write a short article featuring some mathematicians.

The AMS was extremely supportive of this endeavor from the start. It was pretty incredible. We found out that the cover October issue of Notices has always been reserved to feature the city of JMM. This year, they put part of our collage of photos there. The fact that they went above and beyond to feature the Latinos and Hispanics in our community this year has been an extremely positive experience. They really stepped up and made this be something that adds value to the community. We are extremely thankful for them for their support.

GS: I was pleasantly surprised. I never expected that the moment we asked to do an article, they would say, oh, go ahead. They replied back that same day two hours later.

EL: I haven’t gone through carefully. Are the people you feature all working in the US?

PH: That was the idea. The reason for that is not that we are trying to not feature other mathematicians, but the idea for Hispanic Heritage Month is really to celebrate the culture and accomplishments and contributions of US-based Latinos and Hispanics. Solely for that purpose, and because we organized it for that particular month, we focused on featuring US-based mathematicians.

EL: I saw some discussion on Facebook about this, so I have a burning question: how do you pronounce the website name?

GS: Lat-isms. The “h” is silent in Spanish.

EL: What are your goals for the project this year? Are you going to do something similar next year? How will that evolve?

PH: The goal for this project to begin with was for us to inspire a new generation of students and junior faculty while being able to honor those who have come before and have done a phenomenal amount of research and a phenomenal amount of mentoring and service in the math community and specifically for underrepresented mathematicians and students. That was really the goal for us, to have this platform on which we could feature these mathematicians and their contributions to this community.

For next year the goal is to continue working on this. It is a pretty extensive time requirement to put this together. The plan is moving forward to maybe not every year feature this many mathematicians but for sure to have some subset of the month covered by mathematicians, and possibly bring in some more junior up-and-coming leaders in the field. There are a lot of phenomenal junior mathematicians that are maybe not getting the amount of press that they deserve for whatever reason. We thought that moving forward that’s something we want to provide.

EL: Have you gotten much feedback from people on it?

PH: Absolutely. Through the website there is a contact us link. We’ve gotten numerous emails. One of the most recent ones was a math professor who mentioned that they love our website, they wish that this had existed before, that he actually has been looking for a poster that features more diverse mathematicians.

Most of the comments have been complete support for the project, very thankful that we spent time doing this. That’s great. We never did this in order to be thanked. In my opinion it was a project that I needed. At this point in my career, I need to be reminded that I can achieve the goals I have set for myself, that there are people that look like me that have had similar life experiences as mine that are serving as great role models. Not only was it for us to share these mathematicians, it was very fulfilling for us to learn about the phenomenal work that our mentors are doing.

GS: To add to that, the person who sent this email mentioned that Juan Meza visited his institution at one point. He said it was life changing because they have a 25% Latino student body. For them to see him and hear his personal story, besides his research, was something that changed the way they thought about it.

EL: When you were in undergrad and grad school, did you have Hispanic and Latino mathematicians to look up to?

PH: Gabriel and I had very, very different experiences. I did my undergraduate in Milwaukee, Wisconsin. The first time I actually met a Latina or Latino who had a Ph.D., it was a dear friend of mine, Alejandra Alvarado. I met her five years ago. I was at a women’s conference. I was presenting a poster on my research, and she came up to me and said, “Are you Latina?” I said, “I’m Mexican.” She said, “So am I.” I was like, “You have a math Ph.D.? There’s more of us? There’s more of us!” From there it really became like this small avalanche. I met Alejandra, then I met Maria Vega, who has also become a dear friend of mine. Then I met Erika Camacho, then Alicia and Gabriel and Alexander. it’s amazing how many phenomenal people we have. But it really did take a long time for me, being US-based, to have met some of my peers and some of my mentors. It was very late in my career.

GS: I think it’s a very big difference because Pam did her Ph.D. here and immigrated to the US very young. In the case of Alicia and me, we came here after undergrad, so obviously all our professors had been Latinos, so we knew it was achievable. For instance, I ended up here because one of my professors got his Ph.D. from Purdue. He said, “You should consider that place because I was Latino and I succeeded there. We know that you have everything that you need there to have a support system.” I’m always like, “Pam, how did you do it?” To me it’s hard to even imagine what would have happened if I had not had these people before telling me I should go there and do this.

PH: I did have mentors, they just did not happen to be Hispanic or Latino. My mentors were phenomenal, and clearly they pushed me in the right direction. Otherwise I would not have continued in mathematics. But in addition to having a good mentor, being able to see yourself in someone is extremely important. It’s something that I missed for a very long time. Having a community of peers and collaborators and colleagues that are members of underrepresented groups has really helped me grow not only as a mathematician, but also as a person.

It does give me a lot of pride, that even though I missed having Hispanic mentors I was able to succeed. But I think that’s the reason why we needed to do this kind of program. I don’t think it’s fair for someone to be as old as I was and not have known about Carlos Castillo-Chavez, or Erika Camacho. Featuring these mathematicians on this platform, what we’re doing is we’re reaching people at a much earlier age.

EL: Do you have recommendations of other resources for people to learn about Hispanic and Latino and Latina mathematicians, or resources for students in those groups?

PH: Alicia, myself, and Marco Martinez put together a list through the MAA. We have a page on their website solely dedicated to resources for students coming from underrepresented groups and faculty who work with those students. [Editor’s note: Find their list here.]

For me SACNAS [Society for Advancements of Chicanos/Hispanics and Native Americans in Science] has been a phenomenal organization that has always provided a great balance between diversity and pushing the boundaries of science. They really blend beautifully the idea that we can be proud of our culture and continue our traditions and love our heritage, but we can also be amazing leaders in science. Anytime I meet students I make sure they know about SACNAS.

GS: I was a member of SACNAS, and when I went to the annual conference for the first time my mind was blown. All of these amazing things are happening. You can still be you and still be amazing.

PH: For me that’s the best thing. You do not understand the amount of community building you make at a conference like that, how close you feel to people that are geographically thousands of miles away.  That amount of community building is something that SACNAS provides that I’ve never experienced anywhere else.

EL: Sometimes as a woman in math, you feel like have to act like a man, or try to hide your femininity to blend in with a more dominant culture. I’d imagine that happens for other groups as well. And not having to do that must be a really important thing.

PH: It’s very true. Sadly, I’ve had very negative experiences given that my name is Pamela Harris. Really, my name is not Pamela, it’s Pamela. Having immigrated to the United States at a very early age and the fact that maybe I don’t have much of an accent when I speak English, it’s very easy for people, when they talk to me on the phone or when they haven’t yet met me, not to realize that I’m not who they might imagine I am. I’ve had very negative experiences in job interviews. I show up and people’s jaws drop because I don’t embody in their mind what somebody with my name should look like. It is something that’s difficult. Also as a woman, we know there’s discrimination based on our name and our assumed gender. Having SACNAS to be able to go the annual conference and to not ever think about that is really refreshing, it’s freeing. And it allows us to build community, but also to focus on why we’re there, which is the science.

EL: I’d imagine this project helped you all meet new people and make more connections too.

PH: When we started thinking about this project and who we wanted to feature, of course prominent people come to mind: Erika Camacho, Carlos Castillo-Chavez, Ricardo Cortez, Richard Tapia, among many others. At the same time, what we wanted to do, and what we ended up doing, was reaching out to a large group of Hispanic mathematicians for them to give us input on who we should feature this year. We basically crowd-sourced.

Having a diverse group of people really provides us so many more learning opportunities. We should take advantage of that. We’re educators, we’re mathematicians, we’re scientists. It’s something I’m quite proud of our group for doing.

I think the greatest joy is to finally see the end product and get such positive feedback and such interest from the community at large about what we have done. It’s just been a very happy experience overall.

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The Mathematical Tweet Beat

Twitter Architecture Icon

I was a twitter skeptic for a very long time. And now my love affair with twitter is so deep, it’s hard to even remember what my reservations were in the first place. I first joined in 2013, compelled by my hard-tweeting cohort of the AAAS Mass Media Fellowship. And what I discovered was the most pleasant online community of mathematicians and educators chatting all day about…well, math and education!

I get some of my best lesson plan ideas from Twitter, I learn about new math research papers, I get links to every possible math blog in the universe, and perhaps most relevant to you, I get all of my ideas for this blog. So I wanted to take this week to tell you about some of my favorite math tweeters and hashtags.

So first things first, a few hashtags to get you on your way.

This week the MAA hosted the #loveyourmath challenge. Tweeters posted on a different topic each day of the week, including, favorite math puzzles, proudest math moments, and mathematical arts and crafts. I didn’t find the challenge itself particularly inspiring, but if you’re new to the medium, it’s a good introduction to the mathematical twittersphere.

When I’m looking for fun problems and puzzles, I love to peruse the tweets on #mathchat. It tends to skew more towards K-12 teachers, but there are fantastic videos and links to technology and lesson ideas that I would never otherwise find.

Now on to people. At the very least, you can follow the big mathematical societies. I frequently check in with the AMS, the MAA and the AWM to see what they’ve found on the internet in a given week.

If you’ll forgive the blatant log rolling, my co-blogger Evelyn Lamb maintains a highly entertaining twitter account. She also wrote about her favorite mathy ladies on twitter for her blog at Scientific American several years about.

Mathematicians and tweeters John Allen Paulos and Marcus du Sautoy were listed among Science Magazine’s top 50 science stars of twitter. Other top mathematicians who tweet are Steven Strogatz, Laura Albert McLay, Matt Parker and Hannah Fry, to name just a few.

Some of my favorite math tweets over the years have also come from the collective hive mind behind The Aperiodical: Christian Perfect, Peter Rowlett, and Katie Steckles.

Finally, there are accounts that are dedicated to spitting out intermitted math facts just when you need them most. Like Algebra Fact, Prime Numbers and the not exactly mathematical but still fun in a mathy sort of way, Wolfram|Alpha Can’t.

So here are just a few ideas to get your started. Happy tweeting!

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In Praise of People Who Tell Us How to Play with New Toys

I’ve been thinking about getting a 3D printer for a long time but haven’t taken the plunge yet. Aside from the money, space, and inevitable proliferation of small plastic things to step on, part of me is worried I wouldn’t know what to do when I got it. I think of myself as a creative person, but I feel most comfortable being creative when I have a little scaffolding to hang onto, like a recipe to modify or commercial sewing pattern to alter. This post is a tribute to the people who help give the rest of us that boost we need to figure out how to play with new toys.

A pile of Lego bricks

Image: Curtis McHale, via Flickr. CC BY-SA 2.0

When it comes to 3D printing, Henry Segerman and Laura Taalman are two of my inspirations. I wrote about Taalman’s MakerHome blog a couple years ago, and now she posts at Hacktastic, a blog about “design, math, and failure,” in her words. Segerman’s book Visualizing Mathematics with 3D Printing was published recently. I had the privilege of reading it early and blurbing it, and of course I recommend it. As a mathematician, of course I want to print mathematical objects, but something I appreciate about both of them is getting an idea of what 3D printing can do that other visualization media often can’t, like knots and links printed in place without seams and hinged negatively curved surfaces. People like Segerman, Taalman, and Mike Lawler, who has been basing some of his math lessons with his kids on their work, help me understand how I can put that 3D printer to good use if I ever decide to get one.

Another emerging technology is virtual reality. Recently I’ve been admiring the way Emily Eifler, Vi Hart, and Andrea Hawksley of eleVR are helping me think about how to play with virtual and augmented reality. I’ve never been particularly gung-ho about VR. It’s always felt like something for a certain type of tech geek or gamer whose interests and mine are not terribly aligned. But a series of blog posts and videos they’ve made recently have broadened the way I think about what you can do with VR.

They’ve posted about room makeovers, VR makeup, multi-person activities and games you can play with a VR headset and brush for drawing, and experiments in combining VR with real physics. They also have a guest post from artist Evelyn Eastmond about using VR to enhance the experience of meeting people online, and I enjoyed Eifler’s meditation on context in VR and the way you can use this technology to change and enhance people’s experiences in the world.

More immediately mathematically, they have teamed up with Segerman and Mike Stay to create Hyperbolic VR, which immerses the user in hyperbolic 3-space. I also recently saw a video and blog post about a VR app called Hypercube that allows the user to manipulate 3D shadows of 4D objects using VR equipment.

The eleVR team’s social VR experiments remind me a little of one of my favorite podcasts, Flash Forward by Rose Eveleth. In each episode she imagines a possible future scenario—meat is outlawed, the Earth acquires a second moon—and talks about what might actually happen to cause that scenario. On the last episode of the recently concluded second season, she had an algorithm write the script for the fictional future scenario part of the show and then tried to figure out what the scenario would be and how to interpret it. I’ve seen some funny stuff come from Markov chains and neural networks, but this was a new level of creativity and interactivity for the listener, and it got me thinking about how else the techniques could be used.

Thank you to the brave explorers who help the rest of us tap into our creativity!

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More To Math and Art Than Just Phi

Image courtesy of Lun-Yi Tsai.

Image courtesy of Lun-Yi Tsai.

I recently became aware of the mathematical artist Lun-Yi London Tsai. Tsai has a master’s degree in math, and it is clear that he has studied a great deal of math in his life. His mathematical paintings and drawings are like a snapshot of chalkboard right at the end of a brilliantly delivered lecture. There’s a chaotic energy, a blend of math symbols as art, surfaces and shapes common to mathematics as well as the artists own interpretation of the concepts and processes.

Image Courtesy of Lun-Yi Tsai.

Image Courtesy of Lun-Yi Tsai.

I really like Tsai’s work because, as a mathematician, I always have these strange ideas in my head of what certain math concepts look like. Not the numbers and notation, but the actual carrying out of infinite processes. There’s such a beauty and order to it all. And I’m no artist, but I often find myself doodling tangent planes, manifolds and chain complexes when I’m sitting in meetings.

And there’s nothing quite like the gobsmacked feeling you get when you walk in on a chalkboard covered with really intense looking math. There are several tumblr dedicated to precisely this art, and in fact the photographer Alejandro Guijarro recently traveled the world photographing the chalkboards of quantum physicists for his art exhibit Momentum. And in a very cool way, I feel like Tsai’s art — particularly the charcoal drawings — recreate that sensation.

Image courtesy of Lun-Yi Tsai.

Image courtesy of Lun-Yi Tsai.

Here is Tsai in an excerpt from from an interview for Germany’s Jahr der Mathematik.

I don’t actually have a favorite number. When people find out I do art and math, they guess that my favorite number must be Phi, the golden section. But I actually don’t like that number much, because I think it limits people’s concept of what math and art is about—there’s so much more to math and art than just the golden ratio! I’ve only made one painting of this number and I called it “Goodbye, Golden Ratio.”

It’s always nice to recall that bridge between the theoretical and the visual, and I’m always excited to find new mathematical artists. Are there mathematical objects that you love to draw, professionally or just for fun? Are there mathematical processes for which you have a distinctly visual interpretation? Tweet it at me @extremefriday.

Posted in Mathematics and the Arts, Uncategorized | Tagged , , , , , | 2 Comments

Happy Birthday, Dear arXiv

On August 14, the beloved preprint server turned 25. For many mathematicians, including me, it’s almost impossible to imagine doing or reading research without it or the over a million papers it lovingly collects and stores for us.

Happy birthday, arXiv! I made and devoured a delicious cake for you. Image: Evelyn Lamb

Happy birthday, arXiv! I made and devoured a delicious cake for you. Image: Evelyn Lamb

Physicist Paul Ginsparg started arXiv while he was a researcher at Los Alamos National Laboratory, and now it lives at the Cornell University library, where Oya Rieger is the program director. In recent years arXiv has been concerned with funding and has launched a membership model where university libraries and the Simons Foundation (disclosure: I have written for the Simons Foundation) contribute to help maintain the site. (Perhaps surprisingly, arXiv does not receive funding from the NSF, even though it is a vital component of research for many mathematicians, physicists, and computer scientists.)

This year, in honor of its 25th anniversary and as part of an upcoming site overhaul, arXiv conducted a survey to see how they might better serve their users. The most divisive issue seemed to be comments sections. In an arXiv paper about the survey, Rieger writes that people were hesitant about the idea, and even people in favor noted that implementation of a good comment system would be tricky. Like Izabella Laba, I think internet comments sections are often not worth the pixels they’re printed with, and I share her concerns about women being subject to unnecessary scrutiny about their credentials or even abuse.

But on to more important things, by which I mean trivial questions about the scientific/mathematical vernacular. Earlier this summer I set up a highly non-scientific online survey to address a burning question: what do we call the preprint repository with the web address The official arXiv preference is to refer to it without the definite article, but I usually hear people saying “the arXiv” when they talk about posting things there. I this post I’m following my policy of referring to people (or in this case entities) the way they wish to be referred to, but it sounds weird to me without the definite article, and I’m curious about what the rest of you say.

So far 65% of survey respondents say they tend to use the definite article when referring to the website with the address The answers so far do not appear to correlate with respondents’ scientific fields, native languages, or status as arXiv volunteers. Some respondents wonder if “the” might be a marker of unhipness: “Older folks talk about ‘the Google’; maybe folks younger and cooler than me drop the ‘the’ from ‘the arXiv’?” So far, age does not seem to correlate with direct article use, but perhaps in 10 or 20 years it will only be backwards Millennials and older who will be saying “the arXiv.” I did not think to ask about people’s geographical location, but another respondent notes that Northern and Southern Californians have different customs when it comes to highways: “people from northern Cali call a freeway by its number: “take 80 to 580″ while SoCal people say, take the 405 to the 5.” If you would like to chime in with your responses, theories, or silly comments (“people should not be taking the Christ out of”), the survey is still open and will be until September 30. I’ll update this post with the final results then.

How should you celebrate arXiv’s birthday? By reading open-access math papers, obviously! (Or physics, computer science, or whatever your favorite arXiv-using discipline is.) You might consider Grigori Perelman’s papers solving the Poincaré conjecture, which are only available on arXiv, Paul Ginsparg’s reflections from five years ago on the occasion of arXiv’s 20th birthday, or if you’re feeling whimsical, an economic analysis of the ramifications of destroying Death Stars. If you want to go all-out, you could submit a paper to arXiv or one of the overlay journals such as Discrete Analysis that have sprung up recently. You could even surf over to bioRxiv, a biology preprint server, sociology’s SocarXiv,  or another discipline-specific preprint server, or take a walk on the wild side with viXra.

For a hit of nostalgia, try partying like it’s 1991. The Billboard number-one hit song in August 1991 was (Everything I Do) I Do It For You by Bryan Adams, big hair was in, and Star Trek: The Next Generation had just finished its fourth season. That sure sounds like a party to me.

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Don’t Worry, Math Is Still Everywhere

Last week Michael J. Barany — a mathematical historian — published a blog post in Scientific American titled Mathematicians Are Overselling the Idea That “Math Is Everywhere.” We can talk about whether or not the main arguments of his article have merit in a moment, but first, let’s start by dismissing the title as little more than an editorial blunder. It gives the impression that Barany intends to argue that math actually isn’t everywhere, despite what all those mathematically enthusiastic look-around-you-math-is-hidden-in-the-fabric-of-our-lives media types would have you believe.

This is not the point of Barany’s post at all, in fact it’s barely even mentioned beyond the title and a passing dig at mention of Jordan Ellenberg. Instead, what it seems Barany is endeavoring to establish is that mathematicians are not everywhere. And this, he says, should be considered when making policy decisions concerning public support of advanced mathematics.

Barany discusses the role of mathematics in society and culture from the Babylonian times through post-World War II.The ancients, he says used math as “a trick of the trade rather than a public good,” adding, “for millennia, advanced math remained the concern of the well-off, as either a philosophical pastime or a means to assert special authority.” Historically, Barany explains, math was the domain of the elite, it was a source of power that was only available to the highest born. Mathematicians inhabited a rarefied domain, they were acting as advisors to heads of state and maintained an untouchable air of the occult.

This otherness and elite status meant that math wasn’t available to all people, and Barany argues that this has bled through to mathematics today. And I completely agree. Anecdotally — since I can’t find an actual demographics survey to back this up — advanced math is largely occupied by people who come from the economically advantaged side of things. But here’s where Barany’s argument starts to lose some strength: isn’t that the case for any course of advanced study? Attending graduate school at all is a tremendous luxury, whether studying math, science, language, or art, it’s a pretty brazen thing to want to sit around for 4-6 years to get paid very little to think about things.

And some historians, most notably the blogger Thony Christie, even take exception with the picture Barany paints of math and society. Christie suggests that Barany may her oversold the elitism and “otherness” of mathematicians, pointing out that math played a huge role in the scientific revolution of the seventeenth century. Confirming what I suspect, which is that math isn’t all that different from the other sciences in terms of its growth and expansion over the last several centuries.

In a conversation on twitter, Barany defends his position to Steven Strogatz — legendary bringer of math to the people — saying there are two core questions that people try to answer with “math is everywhere” namely, (1) why should the public support advanced math, and (2) why should the public learn basic math? Barney contends that “math is everywhere” is not an appropriate answer to either. I disagree.

I think math being everywhere is exactly the antidote to the ancient rhetoric of “when will I ever use this?” Math is everywhere just as much as anything is everywhere. Science is everywhere, art is everywhere, language is everywhere, and for some reason in those cases, being everywhere is sufficient to convince folks that they will use the subjects. It is everywhere, and therefore knowing it will help you understand everything. So I think a good dose of “math is everywhere” is a great way to motivate why the public should learn basic math. And I think we can mostly agree that learning basic math is a good and important thing.

And since the best way to help your kids develop good habits is to set a positive example, I obviously think policymakers should opt in favor of supporting advanced math, just as they would support any advanced science research. Because even though it often seems pointless, basic research is the provenance of great discovery.

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It’s Not a Trick, It’s an Illusion

I’ve stumbled on the Best Illusion of the Year Contest a few times, but this is the first year I’ve thought about the illusions mathematically.

Dave Richeson wrote two posts about this illusion by Kokichi Sugihara, one of the top illusions from this year. In it, (topological) cylinders appear to have either square or circular cross-sections depending on what angle you view them from. He used Geogebra to show how to derive a curve that has the requisite properties and made a template so you can put your own deceptive cylinder together.

Naturally, Richeson’s posts led me down an illusive, illusory, illustrative, or perhaps just illusional, rabbit-hole. The illusions on the contest website highlight various perceptual habits most people’s brains share—our preference for right angles, the way we infer motion from changes in light, and the importance of context in identifying shade—but not so many of them have obvious mathematical connections. Then I got to a color illusion that really grabbed me.

In June, Vi Hart, mathemusician and virtual reality researcher, posted a long, interesting rabbit-hole of a post about color perception on the eleVR blog. It starts with that late-night dorm room question “is my red your red?” and considers how our color perception might influenced or be influenced by virtual reality. What color effects will we be able to learn about and play with as VR gets better and more widespread?

The mathematics of color is fascinating and perplexing to me. I was strongly indoctrinated into the red-blue-yellow primary paint color paradigm as a child, and it’s been hard to unlearn that enough to understand how we actually see color in light. Nick Higham, applied mathematician at the University of Manchester, has a post about mathematics and color that explains some of the nuances.

To me, the most astonishing thing about these illusions is that even when you know the mathematical and perceptual reasons you see what you do, you can’t help but see it. Right now I’m stuck on these drifting Gabors.

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Carnival of Mathematics 137

Welcome to the 137th Carnival of Mathematics! Let me begin with a story about pizza. I was at one of my favorite pizzerias in New Haven recently where they have the craziest method for slicing pizza: start with a standard round pie, then just go at it with a pizza roller like a maniac, hacking it up willy-nilly. First, this is actually a really great way to slice a pie, because pizza is way better when you don’t have to commit to an entire slice. Second, it struck me as a risky move, since it’s really hard to guarantee that each customer is getting the same number of slices. Sure, they slice it the same number of times, but depending where their roller goes on any given day, you could end up with a different number of slices.

Here a lazy pizza cutter only got 9 pieces out of 4 cuts when he could have gotten 11.  Shame.

Here a lazy pizza cutter only got 9 pieces out of 4 cuts when he could have gotten 11. Shame.

And this brings us to the number 137, which is the 16th lazy caterer number. It’s the maximum number of pieces that you can get from cutting a circular pizza straight through 16 times — so really they should call it the 16th smart pizzeria number. In general the nth lazy caterer number is given by the equation n^2+n+22, and together they form the lazy caterer sequence

1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154,…

of which 137 is the 16th term (assuming we call 1 the 0th term). So those pizza cutters at my pizzeria should go on doing exactly what they’re doing, but always be sure to aim for the nth lazy caterer number when they start slicing, y’know, just to make things fair.

Now, on to the main dish of this carnival: the posts of the month!

  • I really liked this piece from Brian Hayes about the derivation of wire gauging. Seriously, before today I had spent approximately 0 minutes of my life talking about gauged wires, but this post is so much fun I just made my poor mother listen to me explain to her all about 36 gauge wire and the 39th root of 92. Trust me, just go read it.
  • Kevin Knudson sent us a great piece about visualizing music mathematically. He describes a software that interprets the different tonal and percussive qualities of music to plot out a multidimensional character profile. I can’t get the real time video to load, but the still photos are already really cool. Plus, Michael Jackson.
  • On the more technical end of things, a post from Mark Dominus explores how to decompose a function into its odd and even parts. It would be a fun discussion to have in an algebra or calculus class someday, I also like that Mark explains one piece of his discussion by saying “…as you can verify algebraically or just by thinking about it.” Ah, the old proof by just thinking about it trick.
  • Gonzalo Ciruelos explains an algorithm for determining the roundest country. Harder than it sounds, and also, geez, the island nation of Nauru is really round. Check out the post for a ranking of the roundest countries.
  • In case you’re wondering what’s going on with the ABC conjecture, this post from David Castelvecchi gives us a nice plain English update on what the key players in the fight to verify Mochizuki’s proof are up to these days.
  • And for the crafty maker types, Nancy Yi Liang submitted this how-to guide for an incredible laser cut dress. The dress is a graphical visualization of some arcsin functions, and it’s custom made to fit!

Thank you for so many wonderful submissions! You can check information on past and future carnivals at The Aperiodical.

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