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.]https://bsky.app/profile/divbyzero.bsky.socialhttps://bsky.app/profile/divbyzero.bsky.social/post/3mvilceyjp22nOver 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.14 Sep 2026 16:56 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mvilceyjp22nhttps://bsky.app/profile/divbyzero.bsky.social/post/3mvbejpdlr222Friday afternoon print: lightning/thunder cloud impossible object. 🌧️⛈️🌧️11 Sep 2026 20:06 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mvbejpdlr222https://bsky.app/profile/divbyzero.bsky.social/post/3mvakj2ctu222This 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. 😂 [contains quote post or other embedded content]11 Sep 2026 12:21 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mvakj2ctu222https://bsky.app/profile/divbyzero.bsky.social/post/3mv6zan4wpk2s"What's the Steelers' logo?" https://www.youtube.com/shorts/NwQg8nuyrNk10 Sep 2026 21:39 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mv6zan4wpk2shttps://bsky.app/profile/divbyzero.bsky.social/post/3mv6ubwe4p22jHere's a thoughtful blog post about math and AI by Matt Baker. https://mattbaker.blog/2026/09/10/some-late-night-thoughts-on-ai-and-the-future-of-research-in-mathematics/10 Sep 2026 20:10 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mv6ubwe4p22jhttps://bsky.app/profile/divbyzero.bsky.social/post/3mv3hh74pu22eWow! So cool! [contains quote post or other embedded content]09 Sep 2026 11:42 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mv3hh74pu22ehttps://bsky.app/profile/divbyzero.bsky.social/post/3mux5c74ivc2iI 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. https://divisbyzero.github.io/isothermgenerator/ [contains quote post or other embedded content]07 Sep 2026 18:30 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mux5c74ivc2ihttps://bsky.app/profile/divbyzero.bsky.social/post/3muwl6wa2i22cWhenever 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. https://divisbyzero.github.io/impossible-objects/07 Sep 2026 13:06 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3muwl6wa2i22chttps://bsky.app/profile/divbyzero.bsky.social/post/3muwjl3n23k2yWhat 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. https://www.nytimes.com/2026/09/06/science/92-year-old-mathematician-apprentice.html07 Sep 2026 12:37 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3muwjl3n23k2yhttps://bsky.app/profile/divbyzero.bsky.social/post/3murqhbkhg22tA sword and a shield. The shape of the object is pretty crazy! 05 Sep 2026 14:57 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3murqhbkhg22thttps://bsky.app/profile/divbyzero.bsky.social/post/3muozmkqea22iI'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 the04 Sep 2026 13:03 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3muozmkqea22ihttps://bsky.app/profile/divbyzero.bsky.social/post/3munqpmdy3222The 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. https://www.quantamagazine.org/live-from-icm-2026-what-is-math-for-in-the-age-of-ai-20260903/04 Sep 2026 00:51 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3munqpmdy3222https://bsky.app/profile/divbyzero.bsky.social/post/3mun6vgekdc2qI thought this was an interesting math ed article about the ideas of "concept image" and "concept definition" in the most recent American Mathematical Monthly. https://www.tandfonline.com/doi/full/10.1080/00029890.2026.266370503 Sep 2026 19:32 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mun6vgekdc2qhttps://bsky.app/profile/divbyzero.bsky.social/post/3muijmdacxs26A hyperbolic one-handed clock. You can see hours, minutes, and seconds. https://jpivarski.github.io/hyperbolic-map/clock.html01 Sep 2026 23:01 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3muijmdacxs26https://bsky.app/profile/divbyzero.bsky.social/post/3muezeyuoxs2tSo 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!31 Aug 2026 13:32 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3muezeyuoxs2thttps://bsky.app/profile/divbyzero.bsky.social/post/3mubaeyox3k2tThumbs up or thumbs down?30 Aug 2026 01:27 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mubaeyox3k2thttps://bsky.app/profile/divbyzero.bsky.social/post/3mu4bmkkbck2kSince the semester starts in a few days, I thought I'd share a link to the web app I've been working on: https://divisbyzero.github.io/impossible-objects/. 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 a28 Aug 2026 02:06 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mu4bmkkbck2khttps://bsky.app/profile/divbyzero.bsky.social/post/3mtygnhcnsc2lThank 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!26 Aug 2026 13:25 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mtygnhcnsc2lhttps://bsky.app/profile/divbyzero.bsky.social/post/3mtyg2st4zc2lAI 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 forget26 Aug 2026 13:14 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mtyg2st4zc2lhttps://bsky.app/profile/divbyzero.bsky.social/post/3mtx32pcmu22vOk. One more. Two circles or three?26 Aug 2026 00:25 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mtx32pcmu22vhttps://bsky.app/profile/divbyzero.bsky.social/post/3mtu4563bbs2nHere are a few more impossible objects: the duck/rabbit illusion and the hand/foot illusion.24 Aug 2026 20:06 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mtu4563bbs2nhttps://bsky.app/profile/divbyzero.bsky.social/post/3mttub3cywk2lOrigami artist Robert Lang talks about life after the California fires destroyed his work. https://www.youtube.com/watch?v=XOWMsXSsYKE24 Aug 2026 17:45 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mttub3cywk2lhttps://bsky.app/profile/divbyzero.bsky.social/post/3mtr2mxri3s2oI 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. 23 Aug 2026 15:01 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mtr2mxri3s2ohttps://bsky.app/profile/divbyzero.bsky.social/post/3mtpdsooo622uHere is another impossible arrow. It occurred to me that you can get the same effect by putting it on a mirror! 22 Aug 2026 22:40 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mtpdsooo622uhttps://bsky.app/profile/divbyzero.bsky.social/post/3mtp4iqxzvs2uMore impossible arrows 22 Aug 2026 20:29 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mtp4iqxzvs2uhttps://bsky.app/profile/divbyzero.bsky.social/post/3mteygi3yv22mThe "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.18 Aug 2026 19:50 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mteygi3yv22mhttps://bsky.app/profile/divbyzero.bsky.social/post/3mtce2k22ms2cWe 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."17 Aug 2026 18:40 +0000at://did:plc:u3jwk5o7g7l3ivgc33m25b6f/app.bsky.feed.post/3mtce2k22ms2c