Liu Yao 刘杳
@liuyao12.bsky.social
AI ⋉ Math. Blogs at Observable on interactive math.
Education
20%
Business
19%
Liu Yao 刘杳
@liuyao12.bsky.social
· Apr 29
Zhong-Peng Zhou: The inter-universal Teichm\"uller theory and new Diophantine results over the rational numbers. I https://arxiv.org/abs/2503.14510 https://arxiv.org/pdf/2503.14510 https://arxiv.org/html/2503.14510
How likely will this hold up? And will that be formalized before @xenaproject.bsky.social finished with his?
Reposted by Liu Yao
Zhong-Peng Zhou: The inter-universal Teichm\"uller theory and new Diophantine results over the rational numbers. I https://arxiv.org/abs/2503.14510 https://arxiv.org/pdf/2503.14510 https://arxiv.org/html/2503.14510
Liu Yao 刘杳
@liuyao12.bsky.social
· Mar 5
Ignorance, as you said, not stupid (but we often conflate the two). But if he imposes his own opinion (business "intuition") in something he has no expertise in, what do we call it?
I hope that's not the obviously wrong reason you referred to.
I hope that's not the obviously wrong reason you referred to.
Liu Yao 刘杳
@liuyao12.bsky.social
· Mar 5
He thinks it's a win. He thinks trade deficits between countries are just like losses for a company, and tariff is the only way to fix it (either directly as revenue, or making companies move back to US). Plus he thinks he knows better than everyone else, and kicks out anyone who tries to explain.
Liu Yao 刘杳
@liuyao12.bsky.social
· Mar 3
He isn't asking, he goes in and takes billions.
Liu Yao 刘杳
@liuyao12.bsky.social
· Feb 24
Star Wars也差不多，古罗马式的元老院就要被皇帝取代了。本来是想给孩子看些科幻的，凡尔纳的潜艇现代版就应该是宇宙飞船，结果还是肉搏（反正孩子看着开心）。这方面的确《三体》更好，虽然有很多其他问题。
Liu Yao 刘杳
@liuyao12.bsky.social
· Feb 7
One can probably allege the same towards photography vs oil painting. Will AI make oil painting great again (but cheap)?
Liu Yao 刘杳
@liuyao12.bsky.social
· Jan 9
Will? It’s already happening.
Liu Yao 刘杳
@liuyao12.bsky.social
· Jan 9
Are ambulances private? and ER visits come with big bills, but at least they can't refuse treatment.
God help us if insurance companies get involved in fire fighting.
God help us if insurance companies get involved in fire fighting.
Liu Yao 刘杳
@liuyao12.bsky.social
· Dec 13
还有这种情况？Good to know!
Liu Yao 刘杳
@liuyao12.bsky.social
· Dec 12
本身学术书很多是大学出版社出的，去大学书店可能更靠谱。
Liu Yao 刘杳
@liuyao12.bsky.social
· Dec 8
great to see that inclusion of the Chinese original has become the norm
Liu Yao 刘杳
@liuyao12.bsky.social
· Dec 4
I love that it's not just "turtles all the way down", but turtles all the way up, down, left and right, filling up the entire plane.
It was also soon discovered that you can decorate the tiles with stripes that line up. (The reflected turtles get three stripes, as they are where three lines meet.)
It was also soon discovered that you can decorate the tiles with stripes that line up. (The reflected turtles get three stripes, as they are where three lines meet.)
Liu Yao 刘杳
@liuyao12.bsky.social
· Dec 4
They noticed early on that they needed to use reflected hats, and they'd see a long stack of hats that go through those reflected ones.
If they had used turtles, the stacks would be more straight. With such clues, they found that the tiles do follow some pattern, not translational but hierarchical.
If they had used turtles, the stacks would be more straight. With such clues, they found that the tiles do follow some pattern, not translational but hierarchical.
Liu Yao 刘杳
@liuyao12.bsky.social
· Dec 4
It’s a shape Jim, but not as we know it
Thanks to the super human effort of Craig Kaplan, Joseph Myers and Chaim Goodman-Strauss, the hat and turtle polykites have finally arrived on the scene… This article is intended to be a temp…
hedraweb.wordpress.com
It has become known as the "ein stein" problem (German for "one stone").
In late 2022, David Smith, a "shape hobbyist" as he describes himself, first set his eyes on the hat. It's wonderful to read his own account, up to the release of the paper by the team of four in March 2023.
In late 2022, David Smith, a "shape hobbyist" as he describes himself, first set his eyes on the hat. It's wonderful to read his own account, up to the release of the paper by the team of four in March 2023.
Liu Yao 刘杳
@liuyao12.bsky.social
· Dec 4
The Infinite Pattern That Never Repeats
YouTube video by Veritasium
youtu.be
Moreover, the ONLY ways to tile the plane with the Penrose tiles — if we enforce some matching rules, or add jigsaw notches on the edges — are aperiodic. Check out this great video by @veritasium-science.bsky.social
The obvious question is: Can we do it with one shape?
The obvious question is: Can we do it with one shape?
Liu Yao 刘杳
@liuyao12.bsky.social
· Dec 4
For background, aperiodic tilings are tilings of the plane (no gaps, no overlaps) that do NOT follow a translational (i.e. periodic) pattern. The most famous are the Penrose tilings with a five-fold rotational symmetry, made up of two base tiles (either two "rhombs", or a kite and a dart).
Liu Yao 刘杳
@liuyao12.bsky.social
· Dec 4
An aperiodic monotile
cs.uwaterloo.ca
As the hat was the first one discovered, the paper and the Internet are filled with hats; and when the special property of the spectre was revealed in a second paper, it too got a lot of publicity. However, I think the turtle deserves more love, so this thread is for the less-celebrated 🐢.
Liu Yao 刘杳
@liuyao12.bsky.social
· Dec 4
In 2023, David Smith, Joseph Myers, Craig Kaplan, and Chaim Goodman-Strauss shocked the world with the discovery of the first aperiodic monotiles, the so-named hat, the turtle, and (a bit later) the spectre.
In fact there is a continuum of 13-sided polygons, with all the angles multiples of 30°.
In fact there is a continuum of 13-sided polygons, with all the angles multiples of 30°.
Liu Yao 刘杳
@liuyao12.bsky.social
· Nov 27
Seems more appropriate for the CDC. Let someone without a doctorate lead (i.e., destroy) the NIH!
Liu Yao 刘杳
@liuyao12.bsky.social
· Nov 23
Hello World!
Now that AI for Math is becoming a distinctive field, why would one write "AI ⋉ Math", a semidirect product?
1. It's a larger group constructed from the two groups.
2. It depends on an "action" or transformation of Math by AI.
That's all.
Now that AI for Math is becoming a distinctive field, why would one write "AI ⋉ Math", a semidirect product?
1. It's a larger group constructed from the two groups.
2. It depends on an "action" or transformation of Math by AI.
That's all.
Liu Yao 刘杳
@liuyao12.bsky.social
· Nov 14
If you are plotting the points like this, you may as well connect them (or perhaps only the ones from tangents, i.e., 1, 2, 4, 8... multiples of the generator).