Dave Richeson
@divbyzero.bsky.social
Mathematician. John J. & Ann Curley Chair in Liberal Arts at Dickinson College. Author of Tales of Impossibility and Euler's Gem. Coffee drinker. [Everything in the timeline before October 2024 was imported from my Twitter/X feed 2008-24.]
So... I just saw there's a film about the Unabomber coming out tomorrow... And it stars John Nash... I mean, Russell Crowe. www.imdb.com/title/tt6933... In all seriousness, I was in grad school at Northwestern when the Unabomber was caught, and Northwestern math professor Don Saari pointed said
imdb.com
I was just reminded of this surprising fact: one pound of dimes, one pound of quarters, and one pound of half-dollars are each worth $20. So, if you grabbed a mixed assortment of these coins that weighed one pound, you'd have $20. (This doesn't apply to pennies or nickels.)
I had a student ask the other day why we don't multiply vectors in the expected way (component-wise). So, <a,b,c>⊙<d,e,f>=<ad,be,cf>. My gut response was that we could, but it isn't as useful as the dot product or the cross product. But I decided to think about it and see if I could come up with 1/6
Here are a few more impossible objects. This time, I printed the stand in black and the object in another color. It adds a lot of print time, but I like the final version better.
Today in Multivariable Calc, I mentioned the connection between the cross product and quaternions. So I showed them a photo of me with the Hamilton plaque in Dublin from this summer!
Over the weekend, I had an idea: what if, instead of the objects appearing to sit horizontally in front of you, I modified them to appear vertically? Here are four test attempts.
Friday afternoon print: lightning/thunder cloud impossible object. 🌧️⛈️🌧️
This post got one like in 14 hours. I probably should have hinted at the math content: This is probably the first time the word hypocycloid has appeared in a humorous rap song on a late-night TV program. 😂
Dave Richeson@divbyzero.bsky.social · 3w ago"What's the Steelers' logo?" www.youtube.com/shorts/NwQg8...
Here's a thoughtful blog post about math and AI by Matt Baker. mattbaker.blog/2026/09/10/s...
Some late-night thoughts on AI and the future of research in mathematics
Every time I’ve organized my thoughts sufficiently to finally write a proper blog post about the impact of AI on mathematical research, something massive happens which causes me to delay. I w…
mattbaker.blog
The 254th Carnival of Mathematics is posted! Check out all the cool math we collated from the internet in August. @CarnivalOfMath @aperiodical.bsky.social #CarnivalOfMath #iTeachMath #MathSky #MathsToday karendcampe.wordpress.com/2026/09/07/c...
Carnival Of Mathematics
Welcome to the 254th installment of the Carnival of Mathematics, a roundup of interesting mathematics content from August 2026. The Carnival is a monthly post hosted by a different blog each month.…
karendcampe.wordpress.com
I just updated this web app I made last summer—it lets you design your own US weather maps for use in Multivariable Calculus classes. Now you can add cities to the map and save map settings for later. I also improved the UI. divisbyzero.github.io/isothermgene...
Isotherm Generator
divisbyzero.github.io
Dave Richeson@divbyzero.bsky.social · last yr.I participated in a two-day workshop on AI this week. One thing I did was create (by "vibe coding") a way of generating fake weather maps. I like to use these when discussing level curves, the gradient, directional derivative, etc. But looking for real weather maps with precisely the features I want
My hot takes: standard dominoes (individually) are only 1-dimensional. These are 2-dimensional.
Whenever I had a few minutes over the last few days, I created a new shape for my "impossible objects" library. Want to make a cactus/cowboy boot shape? You can now. I also implemented a visual picker to replace the drop-down menu. I plan to keep adding to it. divisbyzero.github.io/impossible-o...
What a lovely article about Joan Birman's seven-year mentorship of a teenage neighbor and the results they proved in braid theory. Joan Birman is now 99, and her neighbor is starting graduate school at Princeton. www.nytimes.com/2026/09/06/s...
The 92-Year-Old Mathematician and the Teenage Apprentice
Joan Birman thought her major discoveries were behind her. Then came an email from a young neighbor — a girl who knew little but wanted to learn.
nytimes.com
A sword and a shield. The shape of the object is pretty crazy! 
I've been thinking about how to best display and view my impossible objects. Here's what I've come up with so far. The feet fit into the spinner to line up the object. The spinner turns 180°. The window forces the viewer to look down at a 45° angle. And the mirror has a slot to hold it at the
The most recent Joy of Why podcast features a discussion about math and AI with moderators Janna Levin and Steven Strogatz and panelists Akshay Venkatesh, Ravi Vakil, and Alex Kontorovich. www.quantamagazine.org/live-from-ic...
Live from ICM 2026: What Is Math For in the Age of AI? | Quanta Magazine
In this special live recording from the International Congress of Mathematicians in Philadelphia, July 2026, the central question discussed was what do mathematicians really value about doing mathemat...
quantamagazine.org
I thought this was an interesting math ed article about the ideas of "concept image" and "concept definition" in the most recent American Mathematical Monthly. www.tandfonline.com/doi/full/10....
Surprises from mathematics education research: Student (mis)use of mathematical definitions
Published in The American Mathematical Monthly (Vol. 133, No. 7, 2026)
tandfonline.com
A hyperbolic one-handed clock. You can see hours, minutes, and seconds. jpivarski.github.io/hyperbolic-m...
One-handed clock — hyperbolic-map
jpivarski.github.io
So far, every student email I've received this semester has had late-teens/20-something grammar, punctuation, formatting, and enthusiasm. I never knew how much I would appreciate those traits in personal communication until I started receiving perfectly bland GenAI-written emails!
Since the semester starts in a few days, I thought I'd share a link to the web app I've been working on: divisbyzero.github.io/impossible-o.... It lets you design your own impossible objects! Anyone can view and rotate them in a browser, but you can also download the OpenSCAD file to generate a
Thank you, @moduality.bsky.social for pointing out the weird shadows of my impossible objects. That got me to think of yet another way to show how weird they are. Here, a light is shining down from behind at a 45° angle!
AI chatbots remind me of my mom. When I was a kid, I said I liked angel food cake with fresh strawberries. Now, many many decades later, my mom still thinks that angel food cake with fresh strawberries is my favorite dessert. Likewise, I want to say to my chatbot, "Will you forget
Here are a few more impossible objects: the duck/rabbit illusion and the hand/foot illusion.
