iiinova — where your digital self keeps evolving

Dave Richeson @divbyzero.bsky.social · 25/09/2026

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

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Dave Richeson @divbyzero.bsky.social · 20/09/2026

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.)

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Dave Richeson @divbyzero.bsky.social · 18/09/2026

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

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Dave Richeson @divbyzero.bsky.social · 18/09/2026

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.

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Dave Richeson @divbyzero.bsky.social · 17/09/2026

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!

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Dave Richeson @divbyzero.bsky.social · 14/09/2026

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.

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Dave Richeson @divbyzero.bsky.social · 11/09/2026

Friday afternoon print: lightning/thunder cloud impossible object. 🌧️⛈️🌧️

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Dave Richeson @divbyzero.bsky.social · 11/09/2026

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. 😂

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Dave Richeson @divbyzero.bsky.social · 07/09/2026

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...

divisbyzero.github.io

Isotherm Generator

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Reposted by Dave Richeson

Chris Staecker @chrisstaecker.bsky.social · 07/09/2026

My hot takes: standard dominoes (individually) are only 1-dimensional. These are 2-dimensional.

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Dave Richeson @divbyzero.bsky.social · 07/09/2026

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...

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Dave Richeson @divbyzero.bsky.social · 07/09/2026

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...

nytimes.com

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.

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Dave Richeson @divbyzero.bsky.social · 05/09/2026

A sword and a shield. The shape of the object is pretty crazy!

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Dave Richeson @divbyzero.bsky.social · 04/09/2026

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

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Dave Richeson @divbyzero.bsky.social · 04/09/2026

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...

quantamagazine.org

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...

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Dave Richeson @divbyzero.bsky.social · 03/09/2026

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....

tandfonline.com

Surprises from mathematics education research: Student (mis)use of mathematical definitions

Published in The American Mathematical Monthly (Vol. 133, No. 7, 2026)

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Dave Richeson @divbyzero.bsky.social · 02/09/2026

A hyperbolic one-handed clock. You can see hours, minutes, and seconds. jpivarski.github.io/hyperbolic-m...

jpivarski.github.io

One-handed clock — hyperbolic-map

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Dave Richeson @divbyzero.bsky.social · 31/08/2026

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!

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Dave Richeson @divbyzero.bsky.social · 28/08/2026

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

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Dave Richeson @divbyzero.bsky.social · 26/08/2026

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!

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Dave Richeson @divbyzero.bsky.social · 26/08/2026

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

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Dave Richeson @divbyzero.bsky.social · 26/08/2026

Ok. One more. Two circles or three?

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Dave Richeson @divbyzero.bsky.social · 24/08/2026

Here are a few more impossible objects: the duck/rabbit illusion and the hand/foot illusion.

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Dave Richeson @divbyzero.bsky.social · 24/08/2026

Origami artist Robert Lang talks about life after the California fires destroyed his work. www.youtube.com/watch?v=XOWM...

youtube.com

From the ashes arise origami koi

YouTube video by CBS Sunday Morning

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Dave Richeson @divbyzero.bsky.social · 23/08/2026

I am thinking about having my students (~35) design their own impossible objects this semester. That would mean I would have to print quite a few of these. This little guy took about 27 minutes, and it is pretty sturdy. If I put multiple on the build plate, this might be reasonable.

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Dave Richeson @divbyzero.bsky.social · 22/08/2026

Here is another impossible arrow. It occurred to me that you can get the same effect by putting it on a mirror!

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Reposted by Dave Richeson

Andrew Stacey @mathforge.org · 22/08/2026

Optimist: the glass is half full. Pessimist: the glass is half empty. Topologist: the glass is a disc, and what's that wet patch on the floor?

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Dave Richeson @divbyzero.bsky.social · 18/08/2026

The "impossible objects" that I've been posting look a little better when the mirror is tipped forward slightly. To look down at a 5 cm object from about 60 cm away and in a mirror 10 cm behind the object, the mirror should be at an angle of approximately 86° to get two 45° views of the object.

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Dave Richeson @divbyzero.bsky.social · 17/08/2026

We got a rental minivan to take our daughter to college. Look at what I found in the footwell under the seats that fold down. 😮😮😮 The Enterprise guy said the previous renters knew they'd lost a hermit crab but couldn't find it. He said he'd try to contact them. "Otherwise, I'll keep it as a pet."

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Dave Richeson @divbyzero.bsky.social · 16/08/2026

Partly because it makes my daughter laugh at my mathematical ridiculousness, I like to take pictures of wallpaper, tiles, and carpet patterns. Here's some wallpaper we saw yesterday. It got a 🤦 from her. I haven't looked at it long enough to see the repeating pattern.

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Dave Richeson @divbyzero.bsky.social · 16/08/2026

When we were in Ireland, trying to drive carefully on the left-hand side of the road, our daughter played this Family Guy clip for us. It quickly became our catchphrase. "I turn now. Good luck, everybody else!" www.youtube.com/watch?v=yCdG...

youtube.com

Family Guy - Changing lanes

YouTube video by Driver Ed - DW

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Reposted by Dave Richeson

Jaap Scherphuis @jaapsch.net · 13/08/2026

I think the original instructions are more precise, something like: Assemble these pieces to fit within a 3x3x3 box. It is a brilliant puzzle.

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Dave Richeson @divbyzero.bsky.social · 13/08/2026

Here's a fun puzzle that @cardcolm.bsky.social shared with me: The Bucolic Cube, designed by Yasuhiro Hashimoto. Assemble these identical pieces to obtain a 3x3x3 cube.

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Dave Richeson @divbyzero.bsky.social · 11/08/2026

At Bridges, @quiteclare.bsky.social spoke about Oliver Byrne and his version of Euclid's Elements. She mentioned that Byrne's last known work (unpublished but in the archives at Trinity College Dublin) was "The Trinal Calculus," which was his attempt to put calculus on a rigorous

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Dave Richeson @divbyzero.bsky.social · 11/08/2026

Recently, I've seen a bunch of "Gen Z translation" videos explaining the slang of today's youth. Those videos remind me of the prank pulled on the NY Times in 1992, when they wrote about grunge, Seattle, and local slang. These terms were all made up by a record label employee.

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Dave Richeson @divbyzero.bsky.social · 10/08/2026

At Bridges, I gave a talk about how to make "impossible objects" from curves defined in terms of functions of x, parametric, polar, and implicit equations. @standupmaths.bsky.social asked if a similar technique could be used for a curve given by an SVG file. Yes! Here are some proofs of concept.

A chicken that has an egg-shaped reflection

An egg that has a chicken-shaped reflection

A sneaker that has a car-shaped reflection

A car that has a sneaker-shaped reflection

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Dave Richeson @divbyzero.bsky.social · 10/08/2026

I left my car in an outdoor parking lot near Washington Dulles Airport for 11 days while traveling. It must have been warm. A sealed seltzer can exploded, and the melatonin gummies melted into one massive gummy.

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Dave Richeson @divbyzero.bsky.social · 08/08/2026

At family day at Bridges I volunteered to help Nick Sayers with his giant pantograph. Trace the outline of the person, and a small copy is drawn by the pen. It was fun for kids and adults of all ages. Here is @ayliean.bsky.social as a model and an artist.

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Dave Richeson @divbyzero.bsky.social · 07/08/2026

I saw this lovely design on the sidewalk in Galway. According to Google, it is a water main stopcock cover. The inscription "uisce" means "water" in Irish, and "WSC-R" stands for Water Service Control - Road.

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Dave Richeson @divbyzero.bsky.social · 07/08/2026

A fun free coordinated motion puzzle from George Bell and Nan Ma.

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Dave Richeson @divbyzero.bsky.social · 07/08/2026

Euclid illustrator Oliver Byrne married someone with last name Rugg. So her married name was the unfortunate Rugg Byrne.

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