Research : Formal Math ∩ Algorithms ∩ Lean ∩ Hardware
Some advice:
1. Lean can’t read your mind or the bot’s.
2. Good lean proofs improve exposition. Drastically.
3. Learn lean to use it properly.
If you are formalizing anything in lean and you are not a foundations expert, please avoid using axioms at all costs.
A formalization with axioms is almost always fatally flawed. At that point it is a net negative for the community.
#Algorithms#AlgorithmsTheory#Lean4
I think Tom Hales's guest post on "What's new" might have overstated the issue with lean kernel bugs: You are orders of magnitude more likely to have a bug in your informal proof or lean statements than end up exploiting a kernel bug in lean (+ other ITPs). #Mathsky#AlgorithmsTheory#CSTheory
“The companies developing these sociotechnical systems aim to establish a private monopoly over cognition and knowledge, built on the plunder of the entirety of humanity’s cultural, textual, and visual output.”
The math dump’s main “purpose is to produce an effect of propaganda and stupefaction, relying on scientific illiteracy and on its uncritical amplification by the media echo chamber. To produce its propaganda effect, it erases…hundreds of researchers…”
europeanreviewofbooks.com/the-spectacl...
In the end I didn't get to solve the problem, but at least I formalized a full solution by combining all the ingredients (including an idelic construction of narrow ray class fields for real quadratic fields... 😎). Have a look at my repo if you find this stuff interesting!
github.com/marozols/SIC...
New fraud dropped: arxiv.org/abs/2610.10072
> The result is also contained in a paper released by OpenAI on October 6, 2026, in which the proof strategy and specific choices of notation are identical to a preliminary version of the present paper that was uploaded to ChatGPT on September 8, 2026.
Me: Ahh! new “almost-linear time matching algorithm” … can we implement it?
Codex: No. It just uses a normal algorithm for anything with less than ~10^(30000000000000000000000) vertices.
Me: Oh, my graphs aren’t that big.
Me: Ahh! new “almost-linear time matching algorithm” … can we implement it?
Codex: No. It just uses a normal algorithm for anything with less than ~10^(30000000000000000000000) vertices.
Me: Oh, my graphs aren’t that big.
I am sort of constantly baffled by critics (which I am, more than not!) who don't feel like they have to stay apprised of what these things can actually do. not least you're going to come off like a fool, but also it's not at all like knowing what they can do obviates the criticisms of them?
I am not sure how to feel about this. One the one hand, if Anthropic is asking researchers to look at their pdfs then yeah compensation seems justified
By the way, even as I work through this paper, this little tucked-away paragraph didn't escape me. I'm not a fan of AI companies now trying to launder their proofs through humans.
I fear this is going to taint the result, which is a shame given the otherwise-stellar reputation of the human authors.
If you are formalizing anything in lean and you are not a foundations expert, please avoid using axioms at all costs.
A formalization with axioms is almost always fatally flawed. At that point it is a net negative for the community.
#Algorithms#AlgorithmsTheory#Lean4
A group of 25 Fields Medalists, including myself, have made a joint declaration on Math and AI: mathandai.org . We welcome additional signatories. See also this article in the Economist announcing the declaration: www.economist.com/science-and-...
As the possibly apocryphal quote from pioneering computer scientist Edsger Dijkstra goes: Computer science is no more about computers than astronomy is about telescopes. In this week’s Qualia column, writer Ben Brubaker goes deep on whether it’s fair. www.quantamagazine.org/does-compute...
"We're all worried," as what it means to do research (in my field, Theoretical CS) seems to be shifting, and shifting fast. What to do?
Senior researchers must lead by example, knowing that not everything will pan out. What I'm suggesting below may not work everywhere, but here's my own advice:
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On the topic of online resources, worth spreading the word again about Ryan O'Donnell's "CS Theory Toolkit" course: "Covers a large number of the math/CS topics that you need to know for reading and doing research in Computer Science Theory"
youtube.com/playlist?lis...@booleananalysis.bsky.social
I just gave a tutorial on Design Templates for Dynamic Graph Algorithms at IISc in Bangalore.
The kindest words I received were "best tutorial I have listened to in the last 10 years." Hope it interests you.
Video: www.youtube.com/live/L8ev24g...
Slides: tinyurl.com/yetx3vxu
Open Printer: an open-source inkjet printer with no DRM, no subscriptions, and repairable parts.
Sometimes the best innovation is just making things work the way they should have all along.
You likely have a world model running inside your skull right now — it’s how you know not to step in front of a moving train without needing to run the experiment first. So far, AI lacks such a scaled-down representation of the environment.
"The day the paper was published should have been a moment of pride. Instead, it felt like a quiet erasure." #ScienceWorkingLifehttps://scim.ag/4p3eH5g
To all the people mocking LLMs because it's "just matrix multiplication (linear algebra):"
Careful there! You're going to piss off the quantum physicists
After 3 1/2 years of work my course on quantum computing is finally finished — the "Director's Cut" of Understanding Quantum Information and Computation is now available.
arxiv.org/abs/2507.11536
This lecture provides a gentle introduction to amortized analysis.
For experts: At the end, I explained Hollow Heaps, an optimal heap like Fibonacci heaps, but simpler! Surprisingly, I have not seen video lectures on this before.
www.youtube.com/watch?v=8mHa...
Markus Himmel has written a blog post about how to write a simple imperative program in Lean and then how to verify that the program is bug-free.
markushimmel.de/blog/my-firs...
📣 We're excited to share the new lean-lang.org!
Relaunching our website was a key deliverable in our Year 2 roadmap to provide "improved navigation and access to valuable content, resources, and tools." We hope you like it!
#LeanLang#LeanProver
Graph theorist Maria Chudnovsky proved the strong perfect graph theorem, which was proposed back in the 1960s. Tune in to “The Joy of Why” with co-host @jannalevinastro.bsky.social:
Our ICALP 2025 paper is now available here! We present the first example of a locally checkable labeling problem that becomes much easier to solve with distributed algorithms if you have access to shared randomness.
doi.org/10.4230/LIPI...