Genius Revisited

Three years ago, I wrote two posts (post 1, post 2) about math, the media, and the genius myth, the idea that in order to be successful in math, you have to be born with some particular talent. They’re good posts, if I do say so myself, and as math hasn’t rid itself of the genius narrative in the intervening years, they’re still relevant.

“The Inspiration of Genius” by Jules-Clément Chaplain. Credit: Public domain, via the Metropolitan Museum of Art

I have been thinking about the genius myth recently because of some posts I’ve read about genius and identity in the math blogosphere. Most recently, Jim Propp’s post “Genius Box” talks about the complicated relationship he has had with the concept of genius in mathematics. Another post I’ve been thinking about this this one from Piper Harron about her objections to being labeled as a genius.

Something I have been seeing more and more in writing about the idea of genius and in neighboring discussions such as #MeToo is an acknowledgment that it’s easy to focus on the art, math, or science created by those who were able to thrive in an environment and worry that changing practices would deprive us of those things, but it’s impossible to see the art, math, or science that would have been created by the people who were pushed out of the field. That is something that I wrestle with when I read about early women and members of other groups that are underrepresented in math and which I tried to flesh out in a post last year about Sophie Germain. And of course, our loss of the products people would have created is not the chief wrong in this situation, and thinking that way risks commodifying other people. People who wanted to be mathematicians but were pushed out were deprived of the opportunity to do activities they wanted to do and thrive in a way that they were interested in thriving.

Along with the genius myth, I have been thinking about the idea of identity in math and identities as mathematicians. Last fall, UK math(s) teacher Ed Southall, author of the blog Solve My Maths, wrote about his struggle labeling himself as a mathematician. The word has baggage related to genius, speed, and tricks that made him hesitant about whether he should call himself a mathematician. I have seen this same question come up on Twitter, recently from Kate Owens.

In departmental orientation in graduate school, the then chair of the department (who later became my advisor) told us all, “You are mathematicians.” We were paid to think about and tell people about math; therefore, we were mathematicians. Today I would probably not center the role of money; the facts that we were choosing to spend our time thinking about math and had been accepted into a program where we would be trained as mathematicians and teach math to others were the salient points. Regardless, my advisor’s framing of me, a naive first-year graduate student, as a mathematician helped me view myself that way. I won’t claim I never struggled to see myself in academic math research (and I eventually stopped doing academic math research), but I did not worry that I was misusing the word mathematician by calling myself one.

Another interesting post about mathematical identity from Piper Harron asks whether we can improve the way we tell undergraduates what it is their math professors really do. Too many students don’t consider a math major because they don’t want to be primarily calculus teachers. Can we tell stories about people’s different paths into math and mathematical careers that will broaden students’ conceptions of who does math and what mathematicians do?

How do you think about genius and identity in mathematics?

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Some Math About Guns

Trying to get a clearer picture of gun violence in the US. Image courtesy of Mike Maguire via Flickr CC.

Turns out it can be really difficult to understand our collective relationship to guns, gun violence, and gun control. What seems to be obvious to some, runs completely counter to others. This was illustrated nowhere better than in the recent report out of the RAND corporation on gun policy. It studies all sorts of relationships between our attitudes about guns and our impressions of the state of gun violence in the US. An article in Vox gives a really thorough summary of the RAND report, and leaves one with two major impressions: (1) we don’t have nearly enough research on gun policy, and (2) despite the fact that there should be plenty of data about this stuff, opinions about what makes us safe seem to be totally subjective.

When faced with something like the incredibly politically divisive debate around gun violence happening in the US now – and always – it’s helpful to quantify.

Mark Reid, who writes the matching learning and statistics blog Inductio Ex Machina, recently posted some data and plots relating gun ownership to gun violence. He sourced the data form Wikipedia and wrote the plots using the statistical computing software R. A quick glance at the plot below shows that the US owns a whole lot of guns and has a whole lot of gun violence.

Gun deaths per capita versus gun ownership in OECD countries compiled by Mark Reid for Inductio Ex Machina.

Reid’s post also includes several other plots, some that incorporate the non-OECD countries, and some that differentiate between gun deaths and gun homicides. The comments section of Reid’s post is also full of alternative questions prompted by the data – like what’s up with Switzerland? – and lots of useful links for similar analyses.

Based on the same data set, Kyle Kinsburg, who writes the blog Aphyr (pronounced “AY-fur”), recently published several plots relating gun death, gun ownership and economic inequality. In particular, he compares gun homicides to Gini index, which produces a linear looking relationship. This isn’t exactly news, we’ve known for a long time that income inequality is correlated to violent crime for all sorts of reasons. Kingburg does point out that there is something interesting to be observed here about gun homicides and prevalence of guns, namely, prevalence of guns doesn’t tell the complete story. For example, Brazil and Argentina have the same prevalence of guns, but Brazil has nearly 10 times more violent crime.

Graph of gun deaths versus the Gini index complied by Kyle Kingsbury for Aphyr.

The R code for Kingbury’s plots are available on his blog, and the data for gun ownership and gun deaths is available on Wikipedia or as .csv files on Reid’s blog. As Reid points out, and I feel obliged to reiterate, this isn’t a rigorous analysis, but it’s cool that we have the tools and technology to get a reasonably quick quantified sense of the problem.

If this sort of data interests you, last year the podcast Science Vs did an episode about guns that includes a good analysis of the data surrounding guns. It is definitely worth a listen, and it draws attention to the relationship between gun ownership and suicide.

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Blind Review Review

Theoretical computer scientists have been talking about double blind peer review, and it’s an interesting discussion. The current incarnation of this discussion started when Rasmus Pagh and Suresh Venkatasubramanian used a double blind refereeing process for submissions to the ALENEX18 conference they co-chaired. Venkatasubramanian posted about their motivations and how they pulled it off in two posts on his blog, The Geomblog (post 1, post 2, post 3).

Artist’s rendition of blinded peer review. (Justice, from the Cardinal Virtues by Nicolaes de Bruyn) Credit: Public domain, via the Metropolitan Museum of Art

Why double-blind? First, it’s the standard for computer science conferences outside of the theory subdiscipline. More importantly, many people worry that single-blind peer review, where the reviewer knows the identity of the author, leads to some objectionable outcomes based on implicit and explicit biases. More famous authors or authors from more prominent institutions may have their work reviewed more favorably, and more broadly, the bias in favor of these authors combined with other biases reviewers have can continue systemic bias against women and other groups that are underrepresented in the field.

Obviously, a major change in the paper submission system is not without controversy. The discussion has continued in posts by Boaz Barak, Michael Mitzenmacher, Omer Reingold, and Lance Fortnow. In general, the conversation I have seen has been civil and thoughtful. In one post, Venkatasubramanian writes,

First up, I think it’s gratifying to see that the the basic premise: ‘single blind review has the potential for bias, especially with respect to institutional status, gender and other signifiers of in/out groups’ is granted at this point. There was a time in the not-so-distant past that I wouldn’t be able to even establish this baseline in conversations that I’d have.

“The argument therefore has moved to one of tradeoffs: does the installation of DB review introduce other kinds of harm while mitigating harms due to bias?

A few math journals—mostly in math education and undergraduate research, as far as I can tell—do use double-blind peer review. But it is not standard. One of the biggest barriers to double blind reviewing in computer science, physics, or math is the fact that so many preprints are posted on arxiv or authors’ websites before they are submitted, making it that much more difficult for a reviewer to avoid knowing who wrote the paper. (Venkatasubramanian writes about how they dealt with that problem in his posts; one point he makes is that double-blinding the process won’t necessarily prevent reviewers from being able to determine authors eventually, but it could prevent some knee-jerk reactions. He also points to a post by Regina Barzilay that delves into the issue in more depth) In some fairly narrow subdisciplines, there are few enough researchers that even without seeing the paper online, others in the field will be able to tell who wrote it anyway.

While societies and individual humans in them have biases, there will be no way to completely eliminate these biases when people (or algorithms) make decisions about paper and conference submissions. It is important for academics to look at the advantages and disadvantages of different strategies to mitigate the effects of bias. I am looking forward to seeing how this conversation evolves.

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Are Smart Cities Really That Smart?

The fun thing about a smart city is that when you watch it, it might be watching you back. Image courtesy of aotaro via FlickrCC.

Lately I’ve been reading a lot of science fiction, and also a lot of articles about smart cities. And the two seem to be converging to a single point. I’m not entirely sure what “smart city” means as a term of art, but it seems to have something to do with using technology to make a city more adaptive to its inhabitants, and thus to serve them up with a better, healthier, richer, and safer city. From what I’m reading, I’m not entirely sure this is happening.

On the one hand, increased technology has given us access to a better understanding of what humans need. One could easily argue that tracking the movement of people en masse, and studying traffic data available from smartphones should help develop better roadways and infrastructure to serve humans. And one would not be wrong. The MIT SenseableCity lab’s Global Mobility Index gives a gives cities a measure of movement that helps guide their funding towards the right resources: bike shares, car services, public transport. One could also see that knowing such granular details about where people are moving is not always in the best interests of humans. For example, look at the kind-of-hilarious-if-it-weren’t-so-scary Strava debacle of earlier this year.

Cyberpunk science fiction writer and Wired blogger Bruce Sterling says “stop saying ‘smart cities.’” Sterling argues that cities being touted as “smart”…well, they aren’t. They’re just a magnet for capital. He talks about the bygone notion that the internet boom was creating a “flat-world” where equal access to the internet would be the final and ultimate democratizer and unifier. Certainly we have seen access to wifi technology open up avenues for healthcare and create economic inroads in developing nations. But Sterling argues, that the so-called smartness is gutting cities by prioritizing the needs of big tech giants over the needs and wants of the citizens. Instead of using technology to tabulate citizen input and make decisions in accordance with their voiced wishes, they are using technology to track citizen movement and consumer habits and make decisions as their proxy (from which the big companies involved stand to profit in a big way). It seems I read a book about this once, it didn’t end well for those involved.

Sterling may be overstating the case a bit, but not by much. Already there are some mega-creepy surveillance programs being sanctioned in the smart cities of China. These programs follow people’s movements online and IRL to generate a “social credit.” Much like a traditional credit score — which BTW is already totally fraught on an Orwellian scale — will determine what sort of opportunities and freedoms a person is entitled to. And again, it seems I’ve seen a dystopian show about this somewhere. And again, it didn’t end well.

Having said that, technology can bring some good to cities. Ridesharing services, have proved to be a reasonable driver of infrastructure funding in cities. Chicago has already raised massive municipal funds by collecting a surcharge on all Uber rides, and New York is poised to do the same. Of course Uber is not without its share of gloom. A recent study out of Stanford giving some of the metrics on driving for Uber was the subject of a post on the blog TheRideShareGuy.

In my own smart-ish city of Pittsburgh — which has made it to the short list of possible new homes for Amazon’s second headquarters — I’ve seen technology bring a renewed vitality to the metropolis. The launch of the Steel City as a testing ground for self-driving cars was a mixed bag. You can consult with blogger Laura McLay on PunkRockOR on whether or not automation is really a smart choice.

For tons of spooky articles about our cyberpunk futures, The Atlantic is currently running a series on smart cities. And if you need me, I’ll be out in a field somewhere wrapping my entire body in aluminum foil.

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Gold Medal Math

For the past week and a half or so, my computer browser has been finding its way to NBC’s Olympics coverage while I’m supposed to be doing other things. I might have a different answer the next time I watch a Simone tumble through the air or shoot through the water, but right now after seeing Chloe Kim and Nathan Chen defy the laws of gravity, I’m inclined to agree with June Thomas at Slate that the winter Olympics are the best Olympics.

Credit: Jankenhoi, via Wikimedia Commons CC BY-SA 3.0

As a bonus, I can justify my short-term skate, ski, and snowboard obsession by reminding myself that winter Olympics events are exhilarating, gorgeous examples of applied math, physics, and engineering.

I wrote about the physics of figure skating jumps for Smithsonian, and I’ve enjoyed reading about the math and physics of other events as well. Jen Ouelette wrote about taking a curling expedition with a group of physicists for her blog Cocktail Party Physics. Dina Spector explained why speed skaters swing their arms back and forth for Business Insider. Larry Greenemeier at Scientific American wrote about how the U.S. skeleton team tested their equipment and body positions in a simulator at Rensselaer Polytechnic Institute. Big air snowboarding, a new Olympic sport this year, is a physics marvel, as Scientific American and Wired have explained. Teachers who want to use the Olympics in their classrooms have some suggestions from the New York Times Learning Network and the American Association of Physics Teachers.

The sports themselves are where most of the magic happens, but I have also enjoyed learning about some math and physics behind the scenes. For instance, did you know we don’t actually know why ice is slippery? F Yeah Fluid Dynamics explains some of the theories and controversies in the first post of her series about the winter Olympics. And the National Institute of Standards and Technology explores one of the most important behind-the-scenes parts of the Olympics: precision measurements. FiveThirtyEight has joined the fray with medal forecasting and data-driven stories about Olympic sports. I was particularly interested in Ella Koeze’s analysis of what might happen if men and women competed against each other in skiing events. Finally, the Olympic rings themselves have some math to them. I wrote about the topology of the connected sum of four Hopf links in the summer of 2016.

Enjoy the rest of the games!

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The NSF Gets Serious And #MeToo

We Must. Image Courtesy of Molly Adams via FlickrCC

It looks like the NSF is finally getting serious about its stance on researching funding and harassment in the sciences. Two years ago in January 2016, in an official statement, the NSF threatened to pull funding from Universities that didn’t follow Title IX mandates. They warned, “NSF encourages NSF-funded researchers and students to hold colleagues accountable to the standards and conditions set forth in Title IX.” This was a good start, if a somewhat toothless threat. Let’s just say that personally holding your colleagues accountable for their actions (while admirable) is something that only seems remotely reasonable when you’re sitting in a position of relative power and privilege.

Then the last two years happened. And things got so real.

The #MeToo movement has been picking up steam across industries and math is no exception. Stories of blatant sexism and harassment in the math and tech sector have made their way into the mainstream media, and earlier this year an anonymous crowdsourced list of Sexual Harassment in The Academy was publish by Karen Kelsky who writes The Professor is In.

As of last week, the NSF has gotten more formal in their stance about harassment on their dime. In particular, Important Notice No. 144 spells out the three major changes effective in their new policy:

  1. If a PI, co-PI or other person funded by a grant is found to have harassed, this must be reported to the NSF. Then the agency has the right to take unilateral action such as suspending the grant, killing the grant, or removing people from the grant.
  2. Organizations that are funded by the NSF are expected to have clear and formal structures in place for dealing with the reporting and investigation of harassment.
  3. The Office of Diversity and Inclusion is launching a new website to make handling these sorts of things as easy and transparent as possible.

Two things that bear mentioning. The first, is that the NSF is only made aware if there is a finding of harassment after a formal investigation or if the person being investigated is put on administrative leave as a consequence of the investigation. So, due process. Also worth pointing out, it doesn’t look like the NSF is requiring any harassment-type analogue to the disclosure of current and pending support as part of their application. These policies are only relevant to individuals who already hold NSF grants. Oh to be so blessed.

In this vein, Izabella Laba who blogs as The Accidental Mathematician recently wrote a post for the men in math who are bothered by the recent revelations (and want to do better). She tackles (brilliantly in my opinion) some of the tough questions about due process and the advocacy that women so desperately need. She clarifies the difference between a friendly touch and career-derailing harassment and the historical absence of formal structures to separate and deal with the two. This is where items 2 and 3 in the new NSF guidelines are very helpful.

The NSF Office of Diversity and Inclusion also put out their own bulletin, reminding people, “if in doubt, reach out.” This would probably be a good time to brush up on your Title IX FAQs and take a moment to remind yourself what harassment looks like. And after you do that, find someone junior to you and have a conversation letting them know how seriously you take this sort of thing.

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How to Have an Excellent E Day

A portrait of Leonhard Euler, who named the mathematical constant e, painted by Jakob Emanuel Handmann.

Tomorrow, February 7, is e Day! This year is the best year to celebrate the base of the natural logarithm because, like Pi Day 2015, the year lines up along with the month and day. Hurrah! People who prefer the day/month/year date convention can save these suggestions for July 2 or wait until January 27, 2082 and get one extra digit. (That seems like a long wait for one extra digit, but you do you.)

I wrote about the excellent number e for Slate and included some possible ways to observe e Day. In addition to putting some money in a checking account to take advantage of compound interest, I humbly suggest using a constant so tied up with change and growth to do some personal growth. Think of e Day as a second chance at my favorite holiday, New Year’s Day.

I have some other suggested e Day reads for you from around the math internet. In 2010, Math Goes Pop suggested January 27 for a yearly e Day observance that privileges the day/month convention countries the way Pi Day privileges month/day users. Wired and Mathnasium have shared e Day suggestions in the past. (For those keeping score, they posted those articles in February.)

Ben Orlin’s ABC book of e does not disappoint, with ebundant elliteration and a reminder that Euler was the wearer of one of the greatest hats in the history of mathematics.

For more on the number e itself, the MacTutor math history website has a nice overview of the history of the constant from its plucky days as the unrecognized base of the natural logarithm to the proof that it is not algebraic. John D. Cook has been making pretty pictures with sums involving complex exponential functions. You can find the exponential sum of the day here. He’s also written about why the natural logarithm is the most natural and how to live with exponential growth. (Hint: it might start slower than you think.)

An equation called Euler’s identity, eπi+1=0, has been called the “most beautiful equation.” I’m on the record as feeling kind of meh about Euler’s identity, and I’m not the only one. For one, just write eπi=-1 instead of obscuring it with a weird need to have a 0 in your formula. You can put a 0 into any formula you want! Beyond that, I love Euler’s formula e=cosθ + i sinθ. Plugging in the number π for the angle θ doesn’t do much for me. But I must say I love 3Blue1Brown’s explanation of the identity in this video. (He has since expanded on the ideas in another video.)

Update, February 7: Imaginary.org has a page where you can find your birthday in e. Anthony Bonato wrote about e Day for his blog as well, describing e as the “Jan Brady of transcendental numbers.”

How will you celebrate e Day? Growth and reflection are well and good, and I’m all for busting out a little complex analysis, but after that, I’m going out for Ethiopian food.

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On Seashells, Spirals, and Solids

Fibonacci Dodecahedron, by Rafael Araujo


Recently, a friend sent me a link to the drawing Fibonacci Dodecahedron by the Venezuelan artist Rafael Araujo. I found it quite beautiful but was immediately skeptical of the words Fibonacci and dodecahedron appearing together. It’s no secret that I am somewhat of a phi detractor. And while I respect Fibonacci, and certainly crave order in the physical universe, I know that phi is not actually everywhere. But after some quick digging, I am embarrassed to admit — but apparently not too embarrassed to publish it on a blog — that I had no idea the relationship of the golden ratio to the platonic solids and I am simultaneous soothed and pleased at this revelation and the art that exists in its name.

Feeling sufficiently chastened and impressed, I reached out to Araujo to chat with the man who harnessed the power of phi so compellingly. Araujo is trained as an architect, but has been doing technical drawing using polar geometry and classical perspective (always by hand!) since he was a teen. Much of his mathematical art is build around spirals, helices, and constructions rooted in sacred geometry, and he keeps a blog on his website where he describes some of his processes for creating the technical mathematical drawings.

Wondering how to draw a perfectly twisting seashells? Wonder no more. Curious what sort of platonic solids you can build using the principles of sacred geometry? Have a look at these. Araujo also posts time-lapse videos of his creations.

Metatron’s Cube, by Rafael Araujo

I asked Araujo what his relationship was to math as he saw it in nature, in everyday life. “I’d like to think that there are a few predictable things in life, meaning that you can calculate them,” but in the end, he says “all is prone to chaos. But, being earnest, there is a lot of math all around us, and that fascinated me.”

Many artists find themselves captivated by the order (and disorder) in the world that can be charted by mathematics. Here on this blog we’ve featured the paintings of Lun-Yi London Tsai, the prints of Tilman Zitzmann, and recently the digital art of David Whyte. Sometimes it’s not obvious to me why I consider certain art to be mathematical art and others not. I’m still trying to figure out what that geometric quality is that tickles my mathematical brain. There’s something about the structure, geometry, and consistency of mathematical art that calls out to me, the viewer. What do you consider mathematical art?

Shell Detail, by Rafael Araujo

Last year Araujo published the Golden Ratio Coloring Book, which renders his beautiful geometric designs in black and white for your doodling pleasure. If you like drawing and want to know more about how me makes these geometric sketches by hand, definitely have a look at his blog or check out Araujo’s YouTube channel, where he posts videos of his images through various stages of completion. It is truly mesmerizing.

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Math with Martin

Most teachers and students in the U.S. didn’t have math class today because of the Martin Luther King, Jr. Day holiday. But when you get back to the classroom, the online math world has some suggestions of how to incorporate ideas civil rights and justice into a math or statistics class.

Jessica Hartnett, who writes a blog about not awful and boring ideas for teaching statistics, suggests looking at public opinion polling data from the 1960s addressing attitudes towards Civil Rights protesters. (She was inspired by a Washington Post article by Elahe Izadi.) Students might be interested in comparing those attitudes to current attitudes about the Black Lives Matter movement.

The Stats Medic, a site that helps provide middle- and high-school math teachers with resources and ideas for statistics lessons, has a suggested Martin Luther King, Jr. Day lesson about poverty and educational outcomes.

Annie Perkins, a math educator in Minneapolis and author of the arbitrarily close blog, has been hosting a discussion of The New Jim Crow by Michelle Alexander as part of a #MTBoS (math Twitter blogosphere) book club. The book discusses the way the war on drugs continues the country’s shameful legacy of white supremacy and racial injustice. I read it not too long ago and can attest it is eye-opening and enraging. Perkins shared a discussion she had with some students about statistics from the book, and today she is writing an extensive Twitter thread about the book. The official discussion will take place on January 20 in person for Twin Cities residents and on Twitter for the rest of us.

Though it may be too late to incorporate any of these posts into your lesson plans for tomorrow, the good news is that any day is a good day to talk about Civil Rights history, Dr. King’s legacy, and current issues of racial justice.

King himself, in addition to well-known works such as the “I Have a Dream” speech and the Letter from a Birmingham Jail, wrote about his views on education for the Morehouse College newspaper the Maroon Tiger in 1947. His words are relevant to teachers in any subject: “The function of education, therefore, is to teach one to think intensively and to think critically. But education which stops with efficiency may prove the greatest menace to society. The most dangerous criminal may be the man gifted with reason, but with no morals.” As you ponder his writing about education or any other topic, make sure to think before co-opting his words, as math educator José Luis Vilson writes at Educolor.

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Elevating The Art Of Math(s) Communication

The 2018 Joint Meetings are just around the corner, and lots of great stuff is going on in San Diego. There will be lectures on current events in math, panels and sessions highlighting inclusion in the field and on January 11th Vi Hart and Matt Parker will be presented with the 2018 JPBM Communications Awards.

Vi Hart and Matt Parker will be receiving the JPBM Communications Awards at the 2018 JMM.

Since math communication is both the medium and raison d’être of this blog, I thought it would be nice to give a timely homage to these fantastic, inspirational, and aspirational communicators.

I first learned about Vi Hart in the way back when she first made a splash with her charmingly narrated doodly-math videos. The first I ever saw was Infinity Elephants and having just rewatched it a moment ago: it’s perfection! She takes you from hum-drum stream of consciousness math class doodling to infinite series and the sizes of infinity and you almost don’t notice it happening. It’s really mesmerizing. From her more recent submissions, I really liked Smarties in which she discusses the mathematical openability of a roll of Smarties and does some geometric Smartie constructions. Arguably one of Hart’s finest works is Twelve Tones, a doodly discourse on 12-tone musical compositions that made me lol on several occasions. Hart also keeps a blog on her website where she writes about all sorts interesting stuff.

Matt Parker, who tweets @standupmaths is a mathematical comedian, and to my knowledge still the only person to sell out a many-thousand seat comedy venue by telling math jokes. He posts his own videos to his YouTube channel. Some in which he teaches math concepts, like in What does i^i=?, others wherein he and his friend Hugh play with a thing and then do some working out, and others yet where he does incredible standup comedy about math which make me lol a whole whole lot. Parker is also a frequent guest on the very popular Numberphile video series.

The humor and levity that these two are able to inject into their conversations about math is truly a thing of beauty. I am captivated by them both, and I know that many people who consider themselves no-so-mathy have been won over by Hart and Parker. So as a fellow communicator of math, my sincerest thanks to both of you for raising the bar, elevating the art, and making math seem so stinking cool.

If you’re interested in getting on the math communication bandwagon, I’d urge you to apply for the AAAS-AMS Mass Media Fellowship. You will be embedded at a top tier news media outlet where you’re get to learn the skills of the trade and share your passion for mathin’ with the whole wide world. Both Evelyn and I are alumni of the program. Applications are due on January 15th.

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