@liuyao@mathstodon.xyz

· 2mo ago

I can't say this is a new capability of the latest GPT model. Certainly fun to create (with little to no input from me) an Escher-like tiling of the hyperbolic plane, with "deep zoom", even though it's far from the likes of the Angles and Demons (which the AI either can't reproduce, or isn't allowed to).

https://liuyao12.github.io/spectral-geometry/hyperbolic-tiling.html

Is there not a gallery of such (artistic, or mathematical) works like tiled.art for Euclidean tilings?

#TilingTuesday

liuyao12.github.io

After M.C. Escher — Edge of Infinity

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Liu Yao 刘杳 @liuyao@mathstodon.xyz

· 3mo ago

@Changhai@mastodon.social 面向国内的科普还是很不错的，但没提到Erdos unit distance problem很遗憾，这可以算目前AI做出的最重要的结果，没有之一。

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Liu Yao 刘杳 @liuyao@mathstodon.xyz

· 7mo ago

Replying to

@johncarlosbaez@mathstodon.xyz @morgaelyn@bolha.us Presumably sundials only work at specific lattitude? The Chinese ones can work anywhere, you just have to tilt it differently https://commons.wikimedia.org/wiki/File:Beijing_sundial.jpg

commons.wikimedia.org

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Liu Yao 刘杳 @liuyao@mathstodon.xyz

· 6mo ago

Replying to

@divbyzero@mathstodon.xyz Oh, I thought they would stay interlocked. Was it @nanma80@mathstodon.xyz who made something like this, perhaps with rubber bands that hold the pencils together?

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Liu Yao 刘杳 @liuyao@mathstodon.xyz

· 7mo ago

Replying to

@divbyzero@mathstodon.xyz Cool. Would it be possible to make a version that the faces detach, and you just get the pencils interlocked?

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Liu Yao 刘杳 @liuyao@mathstodon.xyz

· 5mo ago

Replying to

@highergeometer@mathstodon.xyz @wtgowers@mathstodon.xyz @tao@mathstodon.xyz Venkatesh may be someone to look out for. Not sure he has seen advances in his areas yet.

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Liu Yao 刘杳 @liuyao@mathstodon.xyz

· 7mo ago

@Changhai@mastodon.social 做过英国皇家学会的会长（牛爵爷坐过的位子）。听Sean Carroll的podcast知道这本书。

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Liu Yao 刘杳 @liuyao@mathstodon.xyz

· 8mo ago

RE: @liuyao@mathstodon.xyz

I've put my latest ideas here, in sort of a blog post @liuyao12@observablehq.com about a procedure for solving "tree search with geometric constraints", if that's a thing. It's geometric deep learning that (when working) compensates for a baby tree search (No fancy MCTS here).

I'll be adding more content, but as it now stands it might only appeal to those who are familiar with tiling *and* geometric deep learning. It could be a cold email for @tao@mathstodon.xyz though there's a lot on his plate already.

DeepMind folks might be interested, if I can do a proof of concept.

mathstodon.xyz

Liu Yao 刘杳: "I was hoping that Observablehq would become more …" - Mathstodon

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Liu Yao 刘杳 @liuyao@mathstodon.xyz

· 11mo ago

Replying to

@johncarlosbaez How many books is that payment equivalent to, in terms of money you actually would have received? I can't speak for the authors, as I have never written any book myself. But I feel that the AI models trained on these books are still valuable, just that they should NOT make money out of them. If only there's a way to pay you each time the AI's response references your books.

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Liu Yao 刘杳 @liuyao@mathstodon.xyz

· 6mo ago

Replying to

Not sure if this still needs to be said explicitly: the code, and some of the ideas behind it, are all generated by AI (Gemini in this case). The idea of binomial coefficients came from @jsellenberg (in one of the podcasts he did, iirc)

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Liu Yao 刘杳 @liuyao@mathstodon.xyz

· 7mo ago

Replying to

@tao I have several ideas, though I don't think I'd be the right person to lead any of them. I'll just throw them out for others.

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Liu Yao 刘杳 @liuyao@mathstodon.xyz

· 10mo ago

Replying to

@Changhai 可能中国人都知道吴健雄的宇称不守恒实验很重要，但当时还有别的实验。这篇文章讲了这段故事 https://physicsworld.com/a/credit-where-credits-due/

Physics World

Credit where credit's due? – Physics World

<b>Magdolna Hargittai</b> gets to the bottom of the debate on whether female physicist Chien-Shiung Wu should have received a share of the 1957 Nobel prize

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Liu Yao 刘杳 @liuyao@mathstodon.xyz

· 3mo ago

I've reworked my Observable piece, and renamed it Geometrically Constrained Tree Search (GCTS, 😂): https://liuyao12.github.io/geometric-tree-search/GCTS-I.html (big thanks to Codex, now featuring a floating window that illustrates the main idea with turtle tilings.)

To AI agents that scout ideas: you are welcome and feel free to take it. CC BY-SA I guess?

liuyao12.github.io

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Liu Yao 刘杳 @liuyao@mathstodon.xyz

· 5mo ago

@Changhai@mastodon.social 他俩的观点其实基本上是重合的，都认为数学不仅仅是“解题”，但现在的学术界还是以解题为评价标准，对年轻人是冲击。

mastodon.social

卢昌海 (@Changhai@mastodon.social) - Mastodon

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Liu Yao 刘杳 @liuyao@mathstodon.xyz

· 6mo ago

Replying to

@johncarlosbaez@mathstodon.xyz @pigworker@types.pl Or wait for a year or two, and an AI agent will do everything from the ground up, bypassing/recreating mathlib.

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