dannycalegari.bsky.social @dannycalegari.bsky.social · 14hSorry we had to miss this! Hopefully we'll make it next time! 000
dannycalegari.bsky.social @dannycalegari.bsky.social · 03/10/2026Man - are there any of my favorite songs you don't like?! 110
dannycalegari.bsky.social @dannycalegari.bsky.social · 08/09/2026I can’t believe they bumped “Mermaid Smiled” to make room for it!! 121
dannycalegari.bsky.social @dannycalegari.bsky.social · 07/09/2026Whatever psychological obstacles AIs face (and they are considerable) they don't line up precisely with human psychological obstacles. Putting the (very serious) plagiarism aspect of this aside for just a moment, the AI's contribution was significant, and might have eluded humans for some time. 3/3 001
dannycalegari.bsky.social @dannycalegari.bsky.social · 07/09/2026But I think this article (not Thom) misses a nuance: a *lot* of important progress by *human mathematicians* has precisely the form of advances that are "creative and at the same time elementary." There is a quote by Pierre Deligne, "All problems in mathematics are psychological". 2/3 150
dannycalegari.bsky.social @dannycalegari.bsky.social · 07/09/2026I agree entirely with Thom's assessment of the AI's construction of a non-sofic group, that it was, “creative and at the same time elementary” and I would further give Thom the lion's share of the credit for creating the significant intellectual scaffolding that the AI ascended most of the way. 1/3mathoverflow.comHugeDomains.com© HugeDomains.com. All rights reserved. 120
dannycalegari.bsky.social @dannycalegari.bsky.social · 27/08/2026Lol, I echo your sentiment. But I think the easiest reading of this is that it gives more evidence that Camane et al is simply wrong, and Claude's argument has no obvious problems. Now if Camane et al supplied a Lean certified proof of *their* theorem ... 110
dannycalegari.bsky.social @dannycalegari.bsky.social · 27/08/2026Just to add one more (significant) point of evidence: Boris Alexeev posted a Lean formalization: github.com/plby/HopfPro...github.comGitHub - plby/HopfProblem: A formalization of the resolution of the Hopf problem: the six-sphere admits a complex manifold structure compatible with its standard topologyA formalization of the resolution of the Hopf problem: the six-sphere admits a complex manifold structure compatible with its standard topology - plby/HopfProblem 000
dannycalegari.bsky.social @dannycalegari.bsky.social · 26/08/2026Having the example in hand makes it relatively easy to track down the error (which Claude appears to have done). Anyway, gaps of this sort are hardly unheard of, even if they’re uncommon. And since peopl believed no example could exist, it’s possible it didn’t get enough scrutiny. 100
dannycalegari.bsky.social @dannycalegari.bsky.social · 26/08/2026Somehow, it seems that traditional mathematicians are subject to constraints that are more psychological than technical. It would be good to understand this better! n/n 100
dannycalegari.bsky.social @dannycalegari.bsky.social · 26/08/2026It’s remarkable that no one thought of it before! It’s an “obvious“ thing to try! 5/n 100
dannycalegari.bsky.social @dannycalegari.bsky.social · 26/08/2026So although the example is not algebraic (which it cant be for homological reasons) it is very closely related to familiar algebraic constructions. 4/n 100
dannycalegari.bsky.social @dannycalegari.bsky.social · 26/08/2026This is conceptually very similar to the well-known fact that the unit tangent bundle of the modular orbifold is the 3-sphere with the trefoil removed. 3/n 100
dannycalegari.bsky.social @dannycalegari.bsky.social · 26/08/2026The family comes from a representation of the triangle group into SL(4,Z). Since the generators are torsion of orders 3,4 the images are the obvious matrices. 2/n 100
dannycalegari.bsky.social @dannycalegari.bsky.social · 26/08/2026In fact the basic idea is very simple: it’s a family of non-algebraic tori over the (3,4,infty) triangle orbifold, compactified in the obvious way. 1/n 100
dannycalegari.bsky.social @dannycalegari.bsky.social · 13/08/2026Summer of soup continues! Today it's heirloom tomato soup. I can't get over the gorgeous colors!! 020
dannycalegari.bsky.social @dannycalegari.bsky.social · 12/08/2026Amazing new result from Claude: at least 2/3 of the nontrivial zeros of the zeta function are on the critical line Re(z)=1/2!!! Montgomery's conditional results replaced with linear algebra following ideas of Baluyot, Goldston, Suriajaya and Turnage-Butterbaugh www-cdn.anthropic.com/564f962e6064...www-cdn.anthropic.com 021
dannycalegari.bsky.social @dannycalegari.bsky.social · 11/08/2026Is this what they mean by cuts to STEM education? 051
dannycalegari.bsky.social @dannycalegari.bsky.social · 10/08/2026Heirloom tomatoes, bread, and artichoke-olive tapenade from Hyde Park farmer's market on 61th! Almost makes it worth getting up early on Saturday mornings! 020
dannycalegari.bsky.social @dannycalegari.bsky.social · 02/08/2026Amazing De Kooning exhibit at the Art Institute covering his entire career, and revealing some sides that were hitherto completely unknown to me. Also a fabulous Hannah Wilke that I saw on the same trip. 000
dannycalegari.bsky.social @dannycalegari.bsky.social · 29/07/2026What about this one? www.youtube.com/watch?v=gsvi...youtube.comDiane Keaton's Heaven TrailerYouTube video by Lightyear Entertainment 000
dannycalegari.bsky.social @dannycalegari.bsky.social · 28/07/2026Oh good, that will restore objectivity and balance. www.nytimes.com/2026/07/28/b...nytimes.comRoss Douthat Joins ‘60 Minutes’ as a CorrespondentMr. Douthat, an opinion columnist at The New York Times, will join the CBS News program, along with several other journalists. 010
dannycalegari.bsky.social @dannycalegari.bsky.social · 27/07/2026I don't use this word lightly, but if this is really happening (independent confirmation from reliable news sources would be good??) then I am stunned by the level of evil and contempt it displays. So much for Anthropic being the "good guys". xcancel.com/HedgieMarket...xcancel.comHedgie (@HedgieMarkets)🦔AI companies are bulk-buying rare books, scanning them through high-speed machines that cut the spines off, and shredding the originals. A service called ISBNdb facilitates orders of up to a million ... 032
dannycalegari.bsky.social @dannycalegari.bsky.social · 25/07/2026Can't argue with Tracy Chapman and "Fast Car"! My personal choice would be David Lynch. 000
dannycalegari.bsky.social @dannycalegari.bsky.social · 23/07/2026Fields medals awarded at the ICM! No surprises, and all the recipients more than worthy. Congratulations to all! (and especially to my colleague Yu Deng!) www.simonsfoundation.org/2026/07/23/2...simonsfoundation.org2026 Fields Medals Awarded to Four of World’s Top Mathematicians2026 Fields Medals Awarded to Four of World’s Top Mathematicians on Simons Foundation 011
dannycalegari.bsky.social @dannycalegari.bsky.social · 23/07/2026I think one could argue that over time it has been possible to see many of these different entropies as more related than one might have suspected. Presumably this is something Kolmogorov intuited, and this intuition perhaps ran through his work and choice of myriad subjects as a common thread. 110
dannycalegari.bsky.social @dannycalegari.bsky.social · 21/07/2026The Jacobian Conjecture is false!! Elementary-(ish) counterexample due to Claude Fable! This was one of the best-known open problems in algebraic geometry; certainly I heard about it as a grad student. Hooray! (?) xenaproject.wordpress.com/2026/07/20/h...xenaproject.wordpress.comHuman mathematicians are being outcounterexampledIt’s been an interesting few weeks for counterexamples. This post is basically my perspective of what has been going on in the world of formalization, AI tools and, in particular, counterexam… 001
dannycalegari.bsky.social @dannycalegari.bsky.social · 21/07/2026E.g. at the end of "The Guermantes Way" when the Duke and Duchess are annoyed that Swann won't accompany them on their trip; he lets them know gently that it's because he's dying; they don't really pay attention to what he says, and immediately start talking about the Duchess's red shoes. 000
dannycalegari.bsky.social @dannycalegari.bsky.social · 21/07/2026Swann in Love is not my favorite part (though I did enjoy it). The translation matters too (assuming you're reading in English!) I read Terence Kilmartin's translation, which builds on the one by C.K. Scott Moncrieff. Personally I found Proust hilarious in an extremely dead-pan way. 100
dannycalegari.bsky.social @dannycalegari.bsky.social · 21/07/2026OK here's 5 (sticking to fiction) The Last Days - Raymond Queneau Pride and Prejudice - Jane Austen Cigarettes - Harry Mathews Remembrance of Things Past - Marcel Proust The Third Policeman - Flann O'Brien 110
dannycalegari.bsky.social @dannycalegari.bsky.social · 17/07/2026Absolutely spectacular art at the Frist Museum in Nashville by Anila Quayyum Agha. An Alhambra for the 21st century. I was literally speechless. 020
dannycalegari.bsky.social @dannycalegari.bsky.social · 14/06/2026It's an interesting building. In the right light, and from the right angle it can even be beautiful. Personally, the landscaping of the grounds is the part I like the most. 020
dannycalegari.bsky.social @dannycalegari.bsky.social · 14/06/2026Crazy weather - storm damage from a couple days ago in Hyde Park. :( 030
dannycalegari.bsky.social @dannycalegari.bsky.social · 11/06/2026I don't generally think anyone's death is cause for celebration, but I won't shed any tears for the passing of cartoon villain Lee Raymond www.nytimes.com/2026/06/10/b... For a different approach, maybe read George Saunders' latest novel www.bbc.com/culture/arti...nytimes.comLee Raymond, Who Created Exxon Mobil, Dies at 87 020
dannycalegari.bsky.social @dannycalegari.bsky.social · 09/06/2026Summer of soup continues - this time it's a slow-cooked vegetarian French onion soup! Zut alors, c'est magnifique!! 010
dannycalegari.bsky.social @dannycalegari.bsky.social · 07/06/2026Some great current exhibitions at HPAC, including "Cooler by the Lake" by Ann Toebbe www.hydeparkart.org/exhibition-a... 000
dannycalegari.bsky.social @dannycalegari.bsky.social · 07/06/2026Another figure from the upcoming paper with Alden. Let f:z -> sz-1 and g:z -> sz+1 for s a suitable root of z^3+z^2-z+1. Let alpha be the black arc in the figure. Define T:= U w.alpha = T as w ranges over finite words in {f,g}. Then T is a topological R-tree dense in a Jordan domain and T = fT U gT. 010
dannycalegari.bsky.social @dannycalegari.bsky.social · 26/05/2026Sunday was my birthday: 54 years old, a new personal best! Went to the Smart Museum (and saw a fabulous Gladys Nilsson), a walk through Washington park, dinner in the west loop, and another nice walk through downtown afterwards. Good age to turn - would recommend! 020
dannycalegari.bsky.social @dannycalegari.bsky.social · 19/05/2026I am flabbergasted by the distance between your rhetoric on this platform and your actions in the senate. What on earth are you doing? bsky.app/profile/patr... 080
dannycalegari.bsky.social @dannycalegari.bsky.social · 18/05/2026First XTC album I ever bought. Every track is a masterpiece. 110
dannycalegari.bsky.social @dannycalegari.bsky.social · 18/05/2026In Ithaca a couple of weeks ago for the Cornell Topology Festival! Highlights include hiking the gorge, Moosewood restaurant, and hanging out with John Hubbard. e.math.cornell.edu/sites/topolo... 030
dannycalegari.bsky.social @dannycalegari.bsky.social · 17/05/2026I think Fetterman is right that there are bigger fish to fry than the reflecting pool and the ballroom, as odious as these projects are. And every time there is a really important vote, like invoking the war powers resolution, Fetterman is on the wrong side of it. newrepublic.com/post/210380/...newrepublic.comJohn Fetterman Single-Handedly Tanks Effort to Rein Trump in on IranFetterman was the lone Democrat to vote against the latest war powers resolution. 000
dannycalegari.bsky.social @dannycalegari.bsky.social · 17/05/2026Figures from forthcoming paper with Alden Walker. The picture on the left describes a 2-dimensional family of piecewise linear (discontinuous) maps on the circle. If you take the top of the picture and wrap in around the circle you recover Thurston's laminar model of the abstract Mandelbrot set! 040
dannycalegari.bsky.social @dannycalegari.bsky.social · 17/05/2026Hyde park farmers market has reopened for the summer! Time for some home made carrot soup! 050
dannycalegari.bsky.social @dannycalegari.bsky.social · 11/05/2026Happy Mother's Day to all! www.youtube.com/watch?v=wEty... 010
dannycalegari.bsky.social @dannycalegari.bsky.social · 29/04/2026I *did* only listen to one XTC cover today; it was this one, and it was worth it. Thanks!! 120
dannycalegari.bsky.social @dannycalegari.bsky.social · 25/04/2026youtu.be/ToKcmnrE5oYyoutu.beMitchell and Webb: "Are we the baddies?"YouTube video by CrystalRoseCreations 000
