ZhaoLiang

Github: https://github.com/neozhaoliang
Blog (in Chinese): https://neozhaoliang.github.io
Shadertoy: https://www.shadertoy.com/user/neozhaoliang

Last Notes

2026-05-22 03:06:49 UTC

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https://x.com/mathandcobb/status/2057490144546927046?s=20
It's interesting the configuration looks like a quascicrystal with 12-fold symmetry!
Is there any connection with the 12-fold symmetric Fadaray wave, as the figure include in this paper?
https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/abs/patterns-and-quasipatterns-in-the-faraday-experiment/8FF2B22DE046BC52D144128237B9C194
https://media.mathstodon.xyz/media_attachments/files/116/616/015/471/172/366/original/4e0ee0a2f7734be5.png

2026-05-13 09:54:50 UTC

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And here is a interactive version of the icosahedral quasicrystal:
https://neozhaoliang.github.io/demos/icosa_qc.html

2025-09-28 13:29:04 UTC

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"I've been trying to lose weight, so I've been studying the physics of negative mass.
"
Yeah, a classic John Baez–style opener—starting with nonchalant trifles, then smoothly segueing into the topic at hand.

2025-07-28 07:03:38 UTC

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Oh, @npub1nf4…nqe4 has a nice paper explains this:
https://arxiv.org/abs/1101.5690
This is basically linear algebra: it's equivalent to say, a linear operator \(f\) on a complex vector space is the complexification of some real operator \(g\) of the underlying real vector space, if and only if \(f\) commutes with some 'conjugation' \(\tau\) of the complex space. In the quaternion case, you require \(\tau^2=-1\) instead of \(\tau^2=1\) in the real case.
(finally, replace the single \(f\) with the representation of a compact/finite group)

2025-07-23 14:24:13 UTC

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Oh, I see! I shouldn’t have used the word “blog.” I agree with your reasoning! (and I wasn’t complaining!)

2025-07-23 14:13:21 UTC

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Agreed! I’m exactly the kind of reader who doesn’t understand much, but always finds something fascinating.
By the way, I also really enjoy reading Greg Egan’s blog. I think he represents the opposite extreme from you: his writing is dense, packed with insights and lot of technical details—but shows little interest in explaining things gently to the reader.
Luckily, I’m the kind of reader who’s interested enough in the topics he discusses not to be scared off!

2025-07-23 10:21:27 UTC

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I've studied your writing style and I think your articles have the following strengths:
1. Adopt a conversational style, often using informal, accessible language.
2. Start with casual remarks or interesting problems, scenarios, gradually unfolding the story — rather than throwing out theorems and proofs.
3. You make heavy use of metaphor, intuition, and imagery.
4. Frequently pose questions to guide the reader’s thinking.
5. Hide or postpone technical details that are either obscure or unimportant.
In my view, the hardest part of learning this style isn't the style itself, but rather:
**Having deep insight into the subject.**
**Writing with great passion.**
So I believe that without these two prerequisites, simply mimicking the style makes it very difficult to write articles as excellent as yours.

2025-07-23 09:29:54 UTC

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I really enjoy this Kepler series! I've decided to adopt your style when writing blog posts in the future.

2025-07-20 13:31:18 UTC

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I just bought your book "Gauge Fields, Knots, and Gravity". I'll put it in my bag and read it every day on the subway during my commute!

2025-05-27 15:20:25 UTC

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You're welcome! I tried to recreate this image because I saw lots of attempts online to reproduce it, but very few managed to capture the same aesthetic as the original (just my personal opinion!). So I gave it a try myself. It's still not the best, but for now I don't have the energy to keep experimenting. Thanks again for your wonderful blog post!

2025-05-21 14:54:37 UTC

An attempt to reproduce the image titled "Beauty of Roots", originally found on John Baez’s webpage:
https://math.ucr.edu/home/baez/roots/
Since I'm not sure how Sam Derbyshire did the coloring, I experimented many different methods and eventually found a palette that gets as close to the original effect as I could.
Source code:
https://github.com/neozhaoliang/pywonderland/blob/master/src/misc/beauty_of_roots.py
https://media.mathstodon.xyz/media_attachments/files/114/546/374/922/385/689/original/842d6a196b629608.png

2025-03-24 05:21:31 UTC

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Thank you! I found those articles published in AMS Notices under the Popularizations directory. I'm really glad to see that you're still writing. Honestly, I'm quite familiar with both your blog and Greg Egan's blog because whenever I have some spare time and feel like writing something but don't know what to write about, I often browse your and Greg Egan's websites for inspiration and fun.
What I like most about your blog is that it always starts with language that most people can understand, then gradually builds up to more advanced content. This kind of writing isn't easy because most authors, when writing such articles, tend to force themselves to be rigorous, which leads to the introduction of numerous definitions, terms, and symbols — making the content less accessible for general readers!

2025-03-24 02:04:31 UTC

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I really miss the experience of first encountering this series. I remember that my initial exploration of hyperbolic honeycombs also began with reading your articles and Roice's posts on G+. Will you continue this series?

2025-02-07 06:22:00 UTC

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deepseek r1 gives the correct result 2.

2025-01-10 07:18:41 UTC

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Your article is fantastic! Just a small suggestion: why not consider writing in Markdown and using Pandoc to convert it into HTML? This way, you can use LaTeX for mathematical formulas (mathjax). You could even have automatically numbered theorem, lemma, and proof environments, if you use some third-party filters.

2024-11-18 06:59:29 UTC

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These days the probability of contact with aliens is increasing. However, I think we humans are not prepared to face the risk. Imagine if one day we detect signs of alien life and found that their fleet will reach Earth in 100 years, I believe astronomy would immediately become the hottest in all universities!