dannycalegari.bsky.social

I gave a math talk about my collaborations with Claude creating software for the visualization of geometric objects. I thought it would be interesting to have Claude write the slides, saying what it looked like from their perspective. This is the result. www.youtube.com/watch?v=jj7c...

Stochastic gradient descent is great and all, but I think the single best improvement you could make to Claude would be to give it a visual cortex and train it on a huge corpus of pictures via attention, so that it learns to generate key-query pairs that encode how to "think" about visual images.

Rather psychedelic figure from my NSF proposal (a prize to whoever can figure out the mathematical meaning of it just from the figure). Also in the proposal: a plan to do a series of blog posts (at lamington.wordpress.com) on the mathematical content, co-blogged with Claude.

Summer of soup continues! Today it's heirloom tomato soup. I can't get over the gorgeous colors!!

Amazing 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...

Is this what they mean by cuts to STEM education?

Heirloom tomatoes, bread, and artichoke-olive tapenade from Hyde Park farmer's market on 61th! Almost makes it worth getting up early on Saturday mornings!

Amazing 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.

Oh good, that will restore objectivity and balance. www.nytimes.com/2026/07/28/b...

I 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...

Fields 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...

The 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...

Absolutely spectacular art at the Frist Museum in Nashville by Anila Quayyum Agha. An Alhambra for the 21st century. I was literally speechless.

Crazy weather - storm damage from a couple days ago in Hyde Park. :(

I 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...

Summer of soup continues - this time it's a slow-cooked vegetarian French onion soup! Zut alors, c'est magnifique!!

Some great current exhibitions at HPAC, including "Cooler by the Lake" by Ann Toebbe www.hydeparkart.org/exhibition-a...

Another 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.

Sunday 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!

In 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...

Figures 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!

Hyde park farmers market has reopened for the summer! Time for some home made carrot soup!

Happy Mother's Day to all! www.youtube.com/watch?v=wEty...

More cherry blossoms in Hyde Park! Last week was mostly pink, this week they're white. Also featured: the (almost complete) Obama center.

Cherry blossoms in Hyde Park! Probably the peak will be next weekend.

Origami curve on the sphere - it's possible to fold the sphere over itself in such a way that this curve folds up over itself at the same time!

The greatest player in snooker history just got a little bit greater: www.bbc.com/sport/snooke...

This is one of the more evil proposals I have ever read. Where is the outrage on this? Where are my senators? Dick Durbin? Hello?? www.nytimes.com/2026/03/16/h...

Voted early in Chicago for Juliana Stratton (Senate) and Robert Peters (IL-02). Appalled to see all the crypto dark money propping up their opponents in the Democratic primary.

"But late Friday .. OpenAI said it had reached its own agreement with the Pentagon to provide its A.I. for classified systems. OpenAI said it had found a way to put safeguards into its technologies that would somehow prevent the systems from being used in ways that it does not want them to be." 2/2

"Sam Altman, the chief executive of OpenAI, said in a memo to employees this week that “we have long believed that A.I. should not be used for mass surveillance or autonomous lethal weapons,” which is the same stance as Anthropic’s." 1/2

You know if you fold a piece of paper and make a cut and unfold it you get a cool shape? What if you do the same fold 10 times before you make the cut?

Deleted my Facebook and Instagram accounts, canceled my Amazon prime account, boycotted Amazon and Whole Foods since the inauguration. Was never on X and never will be. Never subscribed to any paid AI service. But I can and should do more, and so should you. www.resistandunsubscribe.com

Article about the speed with which China is rushing past the US in every aspect of their economy, including (especially) tech. Tracks with my own experiences in Beijing in 2025 seeing the unbelievable depth of talent in the math department at Peking University. www.nytimes.com/2026/02/10/o...

Remarkably sane analysis from a conservative economist. www.nytimes.com/2026/02/06/o...

Ironically, this pro-crypto website is a great resource to identify politicians who want to properly regulate crypto so that you can give them your support. www.standwithcrypto.org/politicians (2/2)

www.nytimes.com/2026/01/15/t... Crypto - the currency of choice for criminals and nitwits. The good news is that Republicans and Democrats are united in their regulatory response to this lawless behemoth. The bad news is that they both embrace it. (1/2)

Credit: David Smead; excerpted from www.jstor.org/stable/25678...

Interesting new blog post by Jordan Ellenberg using ML to find large coefficients of Kazhdan-Lusztig polynomials (and along the way creating a fun new variant of Sudoku): quomodocumque.wordpress.com/2026/01/12/b...

Article on Venezuela by someone who has actually spent some time there, and seems to care about the lives of the people who live there: www.nytimes.com/2026/01/04/o...

So I have been boycotting everything Bezos since January; thus when I bought some technical math books recently I got them from AbeBooks ... which turns out to be a subsidiary of Amazon :/ What are better online options (when bricks and mortar -which is my first option - fails)?

Mince tarts made from scratch! (first time ever) The oven smoked a bit, and the fire alarm did go off, but that's the price of haute cuisine ...

As a grumpy old man who grew up on Pascal and C++, I am finally getting around to learning Python, and I am flabbergasted at how awesome it is. Here's a random spanning tree of a map of Australia!

Excellent concert yesterday by Ukrainian folk group Kurbasy!

Chicago No Kings Protest!! Biggest crowds I've ever seen.

Inbox zero!!! It has to be close to a decade since the last time! *sobs*

Just saw Paul Thomas Anderson's masterful documentary excuse me film "One Battle After Another" in the cinema. A masterpiece. I hope all the Christmas Adventure Club types on the right see it and wonder how PTA snuck a hidden camera into their country clubs. www.nytimes.com/2025/09/25/m...

www.nytimes.com/2025/06/29/n... Good. Nice to hear some politician say it. By any measure, the existence of billionaires is a massive failure of economics and tax policy. Not even counting their corrosive effect on democracy, and Caligula-levels of personal crassness.

🚨🚨The White House is pissed off about this ad so you know what to do, share it everywhere! ICE is disappearing people just because of the color of their skin! No Warrant! No Due Process! This is not who we are as Americans! #MAGAKidnappers want an all white America, fuck that‼️