A Mathematical Gift Guide

Some of the cherished math swag I’ve received over the years.

It’s that time of year again. The semester is winding down, mathematically rigorous 6-fold symmetric snowflakes deck the halls, and Mariah Carey is on the top of the Spotify charts. And while all Mariah wants for Christmas is YOU, finding the perfect gift for your special mathematical someone might not be so simple. But here are some suggestions to ease that gift hunting anxiety.

The best thing any mathematician can have is a good notebook and smart writing tools. I swear by the beautiful Japanese made Apica Premium C.D. Notebook, size B5, plain pages. It’s the perfect size to tote around to conferences, on trains, plains, and buses. The pages are smooth and thick enough to write with a fountain pen, but not so precious that you can’t tear one out for the occasional grocery list. To really optimize your experience I am a fan of the Lamy Safari fountain pen or, if you really want to know it, a Faber-Castell mechanical pencil.

But maybe that’s a bit too practical to really gift someone other than yourself.

The designers Christopher Hanusa and Uyen Nguyen are about to launch a new line of Riemondrian jewelry, which features pieces inspired by Riemann sums but done in the style of the artist Piet Mondrian. Hanusa, an artist and a math professor at Queens College in New York, hosts his whole collection of mathematical jewelry on his website. Nguyen, an origami artist and photographer, keeps a beautifully curated instagram page of incredible feats in paper folding.

If you’re looking for good mathematical books to buy your besties, my top pick of the last year is definitely Hello World by Hannah Fry. Also, the consistently awesome Quanta just published a collection of essays about “the biggest ideas in math” edited by Thomas Lin. If you need further inspiration, math and science writer Dana Mackenzie also has his mathematical book endorsements on Five Books.

And finally, if games are your thing, then I have some ideas for you. First up, Decrypto is a team game where opposing teams trying to encrypt and decrypt messages without being intercepted. From the reviews it sounds similar to Codenames but with a little bit extra. For the programming fiend in your friend circle, I highly recommend Roborally. The gist is that each player has to move a robot across a crowded factory floor by programming the moves using a sequence of cards without getting stopped by loops, pits, and lasers. It’s super frustrating, and super fun.

For dice of all sorts, roll on over to Maths Gear, the site where Steve Mould, Matt Parker and James Grime sell all the cool maths things you see in their videos. They also have a nice collection of games, kitchen gadgets, and Rubik’s like cubes. And don’t worry, it’s a UK site but they ship to the US. Just be sure to get your orders in early.

And if you’re really looking to impress, go for this 10.5 inch white bonded marble-cast bust of Pythagoras. My brother gave this to me several Christmases ago, and you can’t imagine the gravitas it lends my office.

While on the topic of Christmas, I have to endorse The Aperiodical’s Apriodvent Calendar. Each day in December leading up to Christmas they reveal a new mathematical curiosity, from homemade parabolic Christmas cards to mathematically non-trivial Christmas decorations, and once again I’m so darn impressed. Aperiodical editors: you are #goals.

Happy gifting and happy end of semester, and let me know @extremefriday if you get any extra special mathematical swag this year.

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A sampling of glorious snow math

Snowflake 3-D numerical model NASA

A model image incorporating key properties of melting snowflakes. Image credit: NASA

Lately, the weather has seemed to taunt me. By traveling back from my family’s Thanksgiving festivities on November 24, I narrowly missed driving through a multi-state blizzard that slowed portions of my partner’s November 25 return down to a crawl.

Our house is just minutes from Des Moines. Off-and-on for the past several days, snow flurries have intermittently skittered through the air, only to melt upon hitting the ground. Minutes later, the snowflakes have ceased falling altogether. I know it’s only a matter of time before the snow will stick, pile up and remind me that winter comes and goes on it’s own timeline, regardless of what’s safe or convenient for humans.

I’ll admit that while I’ve always lived in states with snowy winters — first New York, then Missouri, then Iowa — I rarely feel excited to welcome mounds of snow into my life. Still, for all of the inconvenience and traveling problems heavy snow accumulations often cause, I’ll admit there are some upsides to snow itself. Such as watching the beautiful dances of individual snowflakes as they glide through the air or releasing stress by creating snowballs for a fight with your kids/partner/friends or to throw for your pet. (After a hearty snowfall, my golden retriever always stares at me insistently because she wants me to throw snowballs for her, even though she never learns that whether she catches them or lets them hit the ground, they just break apart, leaving her wondering where the ball went. Yet she never seems to tire of the game.)

The topic of snow has also prompted some exciting math content. Here’s a roundup. Continue reading

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Significantly Statistical Blogs Redux

The headquarters of the Bureau of Labor Statistics in Washington DC before renovations narrowed the hallway and lowered the ceiling. Image via Wikimedia Commons.

I was just reading this article about Statscan, the Canadian warehouse for storing data and the branch of the government charged with the statistical analysis of all things Canadian, and came across this dizzyingly amazing quote about Statscan:

Its statistics are so routinely cited as fact by all parties, factions and interests that “Statscan says” is effectively a Canadianism meaning “the following is true.” It’s hard to overstate how valuable that makes this dull little agency.

It made me wonder, does the equivalent statement exists in the US? Has anyone ever said the same thing about the Bureau of Labor Statistics? The Census Bureau? Any fact ever?

We’ve posted about stats blogs here before. Evelyn first wrote about some of her favorite stats blogs in 2013 with a reprise in 2015 and a post dedicated to the much maligned — although actually useful when used correctly and honestlyp-value. Given that some time has passed, I though we were due for a reprise to the reprise. So here we go.

The Modified Bayes’ Theorem via xkcd.

I was recently reminded of the statistician, political scientist and blogger Andrew Gelman when he posted an essay on the replication crisis to the special science at 40 series for the New York Times. Gelman co-writes a blog about statistical modeling, causal inference, and social science. On the blog Gelman addresses statistical methods and then some of the not-so-obvious subtleties of election statistics and voter turnout, and a whole bunch of other statistically infused and politically adjacent topics.

Another fantastic stats blog is StatChat which is hosted out of the University of Auckland in New Zealand. I especially love blogger and biostatistician Thomas Lumley’s Briefly posts which give a roundup of recent interesting stats objects from the week, which is where I found the Statscan article that started all of this.

You should also check out Simply Statistics, a great blog written by three biostatisticians. I really enjoyed their recent post on the intricacies of gathering data for their analysis on mortality rates from the hurricane in Puerto Rico. On the slightly more technical end, I also recommend Frank Harrell’s blog Statistical Thinking.

Given my personal interests, I tend to lean towards statistics practiced in the service of social science. But if clinical and biomedical research statistics are the kind of thing that you think about in your quiet moments, then this clinical research statistical methodology free association word game — now there’s a string of words I never thought I would use in succession! — from the Swiss Medical Weekly is made for you. And if I ever order a Bud Light when Westmalle is on tap I will be sure to phone in the order to a bartender at a different bar down the street, ask him to serve it to a patron there, and have that patron call my landlord to report on the quality of the Bud Light.

Tripel blind. Get it? I’ll see myself out.

Are there any stats blogs that you really love? Have you ever heard an Americanism giving emphatic support of the Census Bureau? If so, let me know on Twitter @extremefriday.

PS on Monday November 26th the AMS is celebrating 130 years with #AMSday and offering discounts on AMS and MAA Press books, free access to mathscinet, and special perks for renewing (or starting!) an AMS membership.

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Thoughts on writing math books for kids

Eighty-eight Butterfly (Diaethria anna)

Dana McKellar wrote a kid’s book about math called “Ten Magic Butterflies.” Photo credit: Charles J. Sharp via Wikimedia Creative Commons.

Kids’ math books: I’m not talking about textbooks, but rather cheerful math-themed picture books parents might give to wide-eyed, excited kids as holiday gifts, books that take math-obsessed kids on journeys to learning thrilling new math outside the walls of the classroom, or even ones that caring adults might consider handing to kids who are struggling in math to say “You need math to succeed in life, but it’s also cool! And, you can do it!”

In a 2016 post for the AMS “Book Ends” blog, Eriko Hironaka explored the question “What makes a good math book for children?” While it’s difficult to answer that question precisely (“Is it more important that a child be left with knowledge that they can understand and retain, or a new awareness that keeps them thinking and wondering?   Is mathematics a world that one can enter and join in, or is mathematics a personal journey? Of course both sides are important, but how much weight should be put on one side or the other?” she wrote), sometimes it’s easy to spot when material written for kids is unlikely to jive with its intended audience.

I’ve never written a book about math for kids, but I have been asked to review them. That’s something I hesitate to do when the book is already published, out in the world and it’s too late to make any changes until it’s time to write a future edition. I also feel strange writing reviews of kids’ math books when I don’t have kids of my own to ask what they think.

So, instead of writing reviews, I would rather offer advice for folks who are thinking about (or have already started) writing a book about math for kids. That advice, shared below, is based on my own experience with writing in different capacities about math for kids, from online non-fiction stories aimed at middle school students to content for a series of math and science comic books for elementary school students. This isn’t meant as an exhaustive guide, but, rather, a starting point.

Continue reading

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Not Those Midterms

What our midterms need is a sensible counting tool. Like this Sharp Elsimate EL 428.

I was reminded recently of a time a few years ago when I sent my students an email on November 4, 2014 with the following addendum “P.S. Don’t forget to vote in the midterms today.” The next day I was greeted with some genuine and totally unanticipated confusion. Students asking “What do you mean? Are we voting on when our midterm happens? I thought it was going to be take home!” And I realized the majority of them had no idea what a midterm election was. And now, in retrospect, it seems quaint that there was a time so recently that midterm elections weren’t a full blown three ring circus.

Anyhow, I don’t need to remind you that we had midterm elections last week. This time I’m quite certain my students could tell there were midterms — beyond the one they took in Calculus — going on. I’m sure that even the alien probe Oumuamua could tell from outer space that we were having midterms last week.

The midterms were a big deal this year, so big, in fact, that the voting eligible percentage of the population that turned up was the highest in 50 years. And these really high turnouts meant some really long lines, many rightfully irate voters, and lots of people who were rendered unable to vote. Laura Albert, who writes the blog Punk Rock Operations Research, says, “legally, you can only vote once. But if you vote early, you can enable more than one vote to be cast.” Albert frames the process of voting in terms of queuing theory and explains the different strains on the system that can cause a blockage in the flow of voters and what can be done about them. One of the strains that can be alleviated pretty easily is the number of people entering the queue. This can be done, she says, by voting early. Lots of people took this advice, and in what was a kind of crazy — but also kind of unsurprising — turn, more people voted early in Texas this year than voted at all in 2014!

Gerrymandering has been a hot topic over the last several years. I blogged about Hacking, Cracking, and Packing last year, Fivethirtyeight did a series of podcasts for The Gerrymandering Project, and the Metric Geometry and Gerrymandering Group led by Moon Duchin and Justin Solomon has been busy looking for mathematical and computational tools to solve the redistricting problem. If you’re looking for a quick easy demo of gerrymandering, I liked this tweet from @_WTProject about creatively chopping up a 25 district city. It would be a fun starter project for students thinking about gerrymandering for the first time, and it can be generalized in all kinds of fun ways.

Once the districts have been decided and the votes have been cast the problem of counting the votes still remains. That should be easy right? lol.

I was reminded of this great article, “How to Count” from Brian Hayes that appeared in American Scientist back in 2001, a gentler time, but a time when vote counting was decidedly on our minds. He gives a nice overview of classical counting in Platonic mathematics where “chad are never hanging, and every count is full, fair and accurate. But that’s not the world we live and count in.” Hayes talks about cascading counting errors and particularly how voting machines might be vulnerable to such errors, propagating and amplifying errors in arithmetic as counts are consolidated and tabulated.

As I write this post today Sunday November 11th votes are still being counted, and hopefully the counts are error free. And while the Florida election officials tabulate the midterm results, I’ll be counting up some midterm results of my own. No, not those midterms. These midterms.

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Join In The Fun For #Noethember

Portrait of Emmy Noether

Portrait of Emmy Noether (U.S. Public Domain image)

The Inktober design challenge was created in 2009 by Jake Parker, an illustrator, writer and teacher based in Provo, Utah. Worldwide, thousands of artists participate in this endeavor, which challenges them to create ink drawings (pencil sketches under the ink are allowed) for the month of October and post them online with #Inktober. “Note: you can do it daily, or go the half-marathon route and post every other day, or just do the 5K and post once a week,” according to the challenge rules. There are also official prompts, but using those isn’t a requirement of the challenge.

This year, Constanza Rojas-Molina used Inktober as inspiration for a design challenge dubbed #Noethember after Emmy Noether. Rojas-Molina is a mathematician at the University of Düsseldorf, illustrator (under the pseudonym E. A. Casanova) and blogger at “The RAGE of the Blackboard,” which she named after the RAGE theorem. She shared her idea for #Noethember in an October 1, 2018 tweet:

“I won’t do Inktober this year, but I’m planning on doing Noethember in, of course, November, and sketch about Emmy Noether. Could I get 30 facts about Emmy Noether? Who would like to join? ,” she wrote.

Soon, Katie Steckles shared an offer to host the challenge on the Aperiodical. She wrote an October 19 post explaining the challenge. “It’s the same idea [as Inktober] – 30 days, 30 drawings, but this time each day the theme is a fact or story about the life and work of mathematician Emmy Noether.” In an October 30 post, she shared this year’s topics. For instance, the prompt for today (November 7) is “At Erlangen, Noether was one of only two women in a university of 986 students, and was only allowed to audit classes rather than participate fully. She required the permission of individual professors whose lectures she wished to attend.”

Thus far, it has been fascinating to see the varied approaches participants have used to tackle each day’s prompt. Nicholas Jackson, a mathematician at the University of Warwick in the U.K. has tweeted photos of his pencil drawings. Lele Saa, an art director, illustrator and artist based in the U.K., has chosen to depict the characters in the prompt — including Noether — as foxes. Check out Saa’s #Noethember Twitter thread here. Rojas-Molina has tweeted photos of her ink creations. Here’s an example.

Folks of all experience levels have been encouraged to participate by using the hashtag when sharing their work on Twitter or Instagram. The bloggers at the Aperiodical are retweeting their favorites and will create a roundup of some of the best creations at the end of the month.

Posted in History of Mathematics, Math Communication, Mathematics and the Arts, people in math, Recreational Mathematics | Tagged , , , , , , | 1 Comment

The New Issue Of Chalkdust Magazine

The latest issue of Chalkdust Magazine dropped last week, and it’s filled with as much mathematical goodness as a fresh unopened box of Hagoromo “Fulltouch” chalk. It’s a proper glossy magazine — also available as a PDF — featuring profiles of notable mathematicians, articles about fun mathematical concepts, puzzles, and more. There is something in there for everyone.

The cover of Chalkdust Magazine, Issue 08.

Chalkdust, the magazine, fills an interesting niche in mathematical publishing. The content is a mixture of mathematical articles and other types of mathematical curio such as games and advice columns, and it’s written (mostly) by students in the Math(s) Department at University College London. Consequently, it’s a great resource for student, or anyone who likes to read a little but of casual math on their lunch break.

The latest Issue features a fantastic profile of Eugenia Cheng written by Chris Bishop. I knew that Cheng was a mathematician, an author times two, and a YouTube star, but she is involved in so much more. It’s inspirational seeing someone like her doing such positive outreach for the field.

There are also games! This issue features Hilbert’s hotel: the boardgame, and there’s even a chance to win prizes by completing the “famously fiendish” Crossnumber Puzzle, which is exactly what you would expect, a crossword puzzle with numbers instead of words. The prize is an assortment of goodies from Maths Gear, a website you should definitely know about before the holiday season descends.

Aside from the magazine, Chalkdust is also a weekly blog. There they cover all kinds of stuff from current events in math, book reviews, and even mathematical tattoos. I do love to read about mathematical tattoos.

Content in both the magazine and the blog come from a variety of contributors. Including the students at UCL, there are also contributions from Tae-Danae Bradley, who writes the blog Math3ma, and from Colin Beveridge who writes the blog Flying Colours Math, as well as many other teachers, lecturers, professors, graduate students and mathematical people from all over.

If you or your students would like to submit an article to Chalkdust – which I think would be a very cool idea – you can do that! You can order paper issues of Chalkdust Magazine for a very fair price, or access the magazine in PDF form. You can follow the magazine on Twitter @chalkdustmag.

By the way, since I mentioned Hagoromo “Fulltouch” chalk at the outset. For the unfamiliar, Hagoromo chalk is the best chalk there ever was, gloriously smooth, like writing with a stick of butter. The original Hagoromo factory closed in 2015, but the rumor I hear – which is corroborated on this Math Overflow thread – is that the technology has been transferred to another plant, and you can still ge your chalk fix. But I’ve never actually tested the new stuff, and I can’t vouch for it. Let me know if you have on Twitter @extremefriday.

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A Tour of Robert Kaplinsky’s Online Resources

Image: US Department of Education.

Robert Kaplinsky is a math educator and presenter. He also co-founded Open Middle, a website that encourages problems which require “a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding,” according to the Open Middle website. These “open middle problems” support the Common Core standards and give students opportunities to discuss their thinking.

Kaplinsky is also the creator of #ObserveMe, according to his Twitter profile. That movement encourages teachers to observe one another and provide suggestions for improvements. In a post on his blog, he provided a template that teachers can use to list a few points they want feedback on from colleagues who observe their classrooms. Many teachers have used the hashtag to share photos of their signs on Twitter. (In a different blog post, he also shares a collection of suggestions for “Troubleshooting #ObserveMe” based on some common problems teachers have encountered after joining the movement.)

His blog has a wide range of posts that appeal to different audiences. Some are targeted towards a K-12 audience of teachers, parents and students (such as this series about the Common Core standards). Posts such as “What Do Van Halen, King Solomon And Formative Assessment Have In Common?” are framed in the context of education, but could also appeal to folks who enjoy reading engaging posts that are sprinkled with novel connections. (I won’t spoil the surprise link between King Solomon and Van Halen, but it’s a fascinating one.) Here are just a few of his other thought-provoking blog posts:

Kaplinsky’s website also offers more than 70 “real world problem-based math lessons” for grades K-8 and the subjects of algebra 1, geometry and algebra 2. The lessons, which are free to download and use with students, are centered on topics ranging from “How Can We Make Stronger Passwords?” to “How Many Soda Combos Are There On A Coke Freestyle?” At the bottom of each lesson is information about which content standard(s) the lesson relates to.

Recently, Kaplinsky offered a series of webinars on “Why We Should Reconsider Using Word Problems (And What We Should Be Doing Instead).” He created one for elementary school teachers, one for middle school teachers and one for high school teachers. You can replay them here.

Have you joined the #ObserveMe movement for your own teaching? Are there other resources for math teachers that you would like to see covered in future blog posts? Please always feel free to reach out to me in the comments, on Twitter (@writesRCrowell) or via email (RachelJCrowell@gmail.com)!

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Math Games That Make You Think

Screenshot from Nicky Case’s interactive game about networks.

In the echo chamber, social media kinda world that we’re living in, network theory is playing an increasingly important role. So I was delighted, this morning, to spend several minutes playing an interactive game by the talented Nicky Case called The Wisdom an/or Madness of Crowds. The game takes you through the steps of building a graph, connecting edges, and watching how ideas, contagions, and influences spread through networks. It’s particularly surprising how easy it is to build a network that creates the majority illusion. That’s the one where you’re connected to just the right number of people with just the right kind of beliefs that you think everyone around you thinks the same thing.

This is just another fine example of a Case curated experience that teaches, entertains, and inspires. Case keeps a blog with some behind the scenes narratives, explanations of the explorables and also some short stories. I really fell in love with the post A Way-Too-Philosophical Behind-The-Scenes Post, which gave voice to every feeling of futility I’ve ever had. In it Case riffs on several graphs of “stuff I’ve made,” plotting number of people reached vs value, wondering where the sweet spot lies. Case strips down this analysis with one nice “valuable-ness” curve.

As an academic mathematician this is a balance that makes me think, and often bums me out a lot. I spend so much time working on research papers refining arguments dealing with the emotional upheaval of the referee process and then the subsequent concern that no single human eyes will ever pass over the finished product. Compared to this blog post, which I wrote in <2 hours and at least one person (you!) is reading right now. Granted it’s not likely having any huge impact on your life. But if I have n people reading this post and learning something marginally cool from it, and m people reading my Corollary 2, what ratio of m/n am I really comfortable with? Certainly less than 1 is fine, less that 100 is ok to, but less than 1000? It’s a weird calculus to try and sort out. And then wondering…what’s it all for?

Truth, that’s what it’s all for. Well, truth and tenure. But mostly truth.

A bunch of happy polygons looking for a place to call home.

I first became acquainted with Nicky Case’s work when I encountered Parable of the Polygons. This interactive post, co-created by Vi Hart, is based on a paper by the Nobel Prize winning game theorist Thomas Schelling. By dragging around little polygons you learn how a small amount of racism can easily result in hugely segregated neighborhoods. It’s a great interactive for young brains because it gives such a concrete demonstration of a pretty fundamental concept in game theory and social science. Also it’s just fun to play.

If you want to hear Case talk about this project, check out the episode of The Other Half on Racism and Segregation (forgive the blatant logrolling, but I just think Case has a lot of interesting things to say!)

You can support Nicky Case and this incredibly fun work through their Patreon page and following Case on Twitter at @ncasenmare. And if I find anything you might like on the internet this week, I’ll tweet at at you @extremefriday.

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On Michael Atiyah and the Riemann Hypothesis


Riemann has been back in the news lately, thanks to an announcement that his nearly 160 year old hypothesis might be solved.
Public domain image courtesy of Wikimedia CC.

At the 2018 Heidelberg Laureate Forum (HLF), Sir Michael Atiyah gave a lecture in which he claimed to have found a proof for the Riemann hypothesis. If Atiyah’s proof holds up, then the nearly 160 year problem concerning the distribution of primes will finally have a solution.  It’s on the Clay Mathematics Institute’s list of seven Millennium Prize Problems and just one of those — the Poincaré Conjecture — is listed as solved on the institute’s website. However, the $1 million prize for a proof of the Riemann hypothesis is yet to be awarded, and some folks doubt that the long-open problem is finally solved.

It’s unsurprising that the world is watching Atiyah — and waiting to hear the verdict about the proof he proposed. Atiyah received a Fields Medal in 1966. In 2004, he and Isadore Singer were jointly awarded the Abel Prize for their discovery and proof of the Atiyah-Singer index theorem. Yet many other supposed proofs for the Riemann hypothesis have been proposed, only to fall apart under further scrutiny.

The Clay Mathematics Institute’s “Official Problem Description” for the Riemann hypothesis is 11 pages long (with nearly two full pages of references), while Atiyah’s current write-up of the proof is five pages long. “Atiyah attributes much of the theoretical work that underpins the proof to a paper of his own that has been submitted to the Proceedings of the Royal Society A,” Frankie Schembri wrote for Science. “That paper has yet to be published,” she added. In fact, Atiyah’s list of references includes just three works: the aforementioned unpublished paper, his 2018 Abel lecture at the ICM in Rio de Janeiro and Friedrich Hirzebruch’s 1966 Topological Methods in Geometry.

News of Atiyah’s claim has reached far and wide since his announcement. Articles about the development appeared in Science News, Gizmodo, Popular ScienceNBCNews.com, the Irish Times and more. Bloggers also covered the announcement, including Katie Steckles and Christian Lawson-Perfect for the Aperiodical, John D. Cook for his consulting blog, as well as Dick Lipton and Ken Regan for Gödel’s Lost Letter and P=NP.

John Baez also wrote a lengthy thread about Atiyah’s claimed proof on Twitter, starting on September 23 (the day before Atiyah’s lecture at the HLF). He wrote “I bet that Atiyah’s claimed proof…will not convince experts. In 2017 he claimed to have a 12-page proof of the Feit-Thompson theorem, which usually takes 255 pages: https://www.maths.ed.ac.uk/~v1ranick/atiyahtimes2017.pdf. He showed it to experts, and… silence.” What’s more, “In 2016 Atiyah put a paper on the arXiv claiming to have solved a famous problem in differential geometry. The argument was full of big holes: So, I’m not holding my breath this time. But of course I’d be happy to be wrong,” Baez added.

Steven Strogatz tweeted “Uh oh. I have a bad feeling about this. Famed mathematician Michael Atiyah claims proof of Riemann hypothesis,” along with a link to the September 21 New Scientist article about Atiyah’s claimed proof. When asked by Twitter user Jonathan Horrocks “Why bad? I take anything Atiyah says very seriously,” Strogatz responded “I take him seriously too. It’s the same bad feeling I have when a diver attempts an extremely difficult dive: afraid, yet hoping for success.”

The skepticism surrounding the claimed proof doesn’t appear to faze Atiyah. “Nobody believes any proof of the Riemann hypothesis, let alone a proof by someone who’s 90,” he said to Gilead Amit​, author of the New Scientist article. “People say ‘we know mathematicians do all their best work before they’re 40,'” Atiyah said, adding “I’m trying to show them that they’re wrong. That I can do something when I’m 90.”

Regardless of whether Atiyah’s proof holds, he has already done something phenomenal: reignited a worldwide conversation about the Riemann hypothesis. That alone is something to celebrate.

What do you think? Share your thoughts in the comments below or reach out to me on Twitter @writesRCrowell! As always, I’m also happy to hear ideas for future blog posts.

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