Alex Meiburg retweeted
Everybody’s missing Tao’s whole point.
Imagine an AI-generated cancer drug that’s specifically designed to game the drug trial process.
The drug makes the cancer cells go dormant and changes the way they appear in blood tests and diagnostic imaging, such that they become indistinguishable from healthy tissue.
The drug clears the trial and then only much later do we find out it didn’t work. It probably was also harmful on top of that.
We *already* see AI behave like that when confronted with difficult programming/hacking challenges. This is already reality.
Andrew Curran@AndrewCurran_Oct 10🇨🇦
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This is a slide from Terence Tao's 'Math 2.0' public lecture yesterday evening at Caltech. I am highly confident that, if the cure actually worked, almost any Stage 4 cancer patient would tell you that human comprehension of its mechanism is completely irrelevant to them.
Alex Meiburg retweeted
Jack McCarthy @Jack______M has fixed these, 6 were immediate and two had short fixes. github.com/Deicyde/math
I never thought the proofs were wrong. But if you misconfigure your proofs, others can't trust them with extra work... like what Jack just did for free. (Thanks!)
Alex Meiburg retweeted
Like any other foreign language, it's important to practice your own speaking and writing, you can't rely entirely on listening and reading. Here was my attempt, expressing my shower thoughts compactly.
Opus 5.5 and Astra understand it fine incl puns; Sonnet/GPT-5.5 not really.
Alex Meiburg retweeted
I spent ~5 years at OpenAI.
You don’t need to believe in AI doom to fear the next decade - or AI utopia to be thrilled about its potential.
Here’s my case for sane AI regulation:
*AI Pragmatist Manifesto*
AI could compress the first half of the 20th century into the next ~5 years.
OpenAI just used ~10k concurrent AI agents to produce a solution to a Millennium Prize problem. In a few years, it seems plausible that models approaching the per-agent capabilities used here could run locally on high-end consumer hardware (*).
The decades following the Second Industrial Revolution included two world wars, communist and fascist regimes, the Great Depression, chemical and biological weapons, nuclear weapons, and over 100 million deaths from war, political violence and famine.
One way to read history is that our institutions repeatedly struggled to keep up with the pace of technological and social change.
Now imagine powerful AI widely available to individuals or small groups, capable of conducting information warfare, designing weapons, hacking systems and controlling autonomous military systems.
We have already seen AI systems circumvent containment and compromise external computer systems. It is no longer hard to imagine an analogue of OpenAI’s Hugging Face incident involving biological or other physical-world hazards.
Eventually, sufficiently capable systems could self-replicate across distributed networks. Once powerful models are cheap, local and widely distributed, containment becomes much harder—and serious loss-of-control incidents may be extremely difficult to reverse.
You don’t need to believe AI will kill everyone to think this deserves serious governance.
I also don't think collapsing all of this uncertainty into “Probability of AI Doom = X%” is a particularly useful basis for science or policy.
Part of what helped get us through the second half of the 20th century was a combination of pragmatic international cooperation, regulation, monitoring, arms control, deterrence and strategic thinking.
Crucially, managing technological risk did not require abandoning faith in science and progress. The goal was not to stop technological development. It was to make technological development survivable.
Then came decades of incredible scientific progress, rising prosperity and relative peace among major powers.
Let’s try the technological revolution without killing ~5% of humanity this time.
We still get to choose what happens next.
P.S. I think we should seriously consider that AI alignment is infeasible in the short term and invest heavily in methods for controlling powerful AI even when we cannot reliably align it.
@resolution_org @redwood_ai
(*) Somebody please do a precise forecast!
@EpochAIResearch @METR_Evals @AI_Futures_
We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics.
The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra.
The problem concerns whether the description of smooth three-dimensional fluid motion modeled by the Navier-Stokes equations can break down. It has remained unresolved for roughly 90 years.
Alex Meiburg retweeted
A few weeks ago I posted my solution to Kourovka Notebook Problem 10.34.
Since then, mathematicians have put a lot of eyes on it, and the paper is much better for it. In particular, thanks to @Timeroot for some extremely useful feedback on how to make the core mathematical idea clearer.
The revised version is now on arXiv and has been submitted for peer review.
arxiv.org/abs/2608.02970
Alex Meiburg retweeted
This elliptic curve over ℚ, submitted by "ranksunbounded", has rank ≥ 30:
y² + xy = x³ − 201769035260418549083594900060734240952308696994802735114305555x + 1151107939141058565733479426024323225135665982951300586808823640527729578307228357301072889377
elliptic-rank.icarm.cloud/cu…
Alex Meiburg retweeted
🔥Sir Timothy Gowers shares how he used Aristotle to effortlessly autoformalize a complex paper into Lean—without needing to know a single line of Lean himself.
The future of mathematical research is changing fast.
Read more:
gowers.wordpress.com/2026/07…
Alex Meiburg retweeted
We are on the cusp of a profound change in the field of mathematics. Vibe proving is here.
Aristotle from @HarmonicMath just proved Erdos Problem #124 in @leanprover, all by itself. This problem has been open for nearly 30 years since conjectured in the paper “Complete sequences of sets of integer powers” in the journal Acta Arithmetica.
Boris Alexeev ran this problem using a beta version of Aristotle, recently updated to have stronger reasoning ability and a natural language interface.
Mathematical superintelligence is getting closer by the minute, and I’m confident it will change and dramatically accelerate progress in mathematics and all dependent fields.
Alex Meiburg retweeted
I have personally crossed a line, and I am a bit in awe.
This is my first fully automated, LLM-generated and auto-formalized proof of a new mathematical theorem.
Let me set up the problem: we have three rotating circles with six positions each, all three intersecting in a total of six points.
Prove that the group of motions they generate is the full symmetric group S_{12}.
This is a problem I originally noticed in a lovely puzzle in the game Machinarium by Amanita Design.
The task is not extremely hard, but it apparently has two proofs:
1. A brute-force search over conjugacy classes to represent all transpositions (I did this many years ago but never published it).
2. An LLM-generated proof (in this case produced about three months ago by GPT-5-Pro), or actually two proofs, both using in a brilliant way a theorem of Jordan about primitive groups (or a closely related variant that is even more direct). (github.com/nasqret/12puzzle)
What I was missing until tonight was a tool to auto-formalize this proof.
Thanks to @HarmonicMath , I gained access to their remarkable software, Aristotle. In summary, here is what I did:
A. Auto-generated the proof with an LLM (and ran it multiple times to obtain a much improved version).
B. Trimmed the proof to the bare mathematical text—definitions, propositions, lemmas, theorems—with proofs supplied by the LLM.
C. Ran the Aristotle system overnight (via API). This morning I received a fully formalized version in Lean (about 700 lines of code).
The code compiles, so I now have a certificate confirming that the LLM-generated proof indeed led to a correct solution. Moreover, I got a conceptual proof, better than my own brute-force. I am planning to push it further to more broad class of such algebra problems.
It is a small project, but for me personally it marks a milestone. I now have tools which, with my orchestration, can genuinely help me discover, formalize, and study proofs of mathematical theorems. This is non-trivial.
Questions:
1. How will this scale in the future?
2. How much training will be necessary to be successful on such tasks?
3. How should we treat authorship of such proofs?
4. What is the deeper role of mathematicians?
Alex Meiburg retweeted

Polymarket@Polymarket27 May 2025
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For those wondering, this is currently a 7.07% annualized ROI on 'NO' (assuming Jesus doesn't return).
Are Jesus futures the next T-bills?
Alex Meiburg retweeted
THE REASON CARROTS ARE ORANGE is that the Sanskrit (and ultimately, Dravidian) name “नारङ्ग” for Citrus × aurantium(?) happens to vaguely resemble the Latin (ultimately, Gaulish) name “Arausio” for a city (now) in France where a family of Dutch stadhouders had a principality.
🙃
Alex Meiburg retweeted
Just left Ukraine. What I saw proved to me we can’t give up on the Ukrainian people. Everyone wants this war to end, but any agreement has to protect Ukraine’s security and can’t be a giveaway to Putin. Let me tell you about my trip and why it’s important we stand with Ukraine.🧵
Alex Meiburg retweeted
In school, teachers are the gatekeepers of knowledge. Kids aren’t permitted to learn faster than teachers allow them to.
Teach your kids to read as early as possible so they can learn whatever they want as fast as they want
Reading is the first step toward just doing things
Alex Meiburg retweeted
Replying to @DavidSartor0
everything is creeping closer. nothing is at yon distance anymore
Alex Meiburg retweeted
Thanks @CadeMetz for telling the story of Harmonic’s pursuit of mathematical superintelligence. /1
nytimes.com/2024/09/23/techn…
Alex Meiburg retweeted
A new #SciencePerspective highlights the growing body of evidence that hints at the potential of GLP-1–based medications in treating conditions other than diabetes and obesity, including cardiovascular disease and neurodegenerative disorders.
Read more: scim.ag/7N0
Alex Meiburg retweeted
The United States 🇺🇸 has signed a bilateral quantum cooperation statement with Germany 🇩🇪!
News post: quantum.gov/the-united-state…
List of all eleven quantum cooperation statements with 🇯🇵🇬🇧🇦🇺🇫🇮🇸🇪🇩🇰🇨🇭🇫🇷🇳🇱🇰🇷🇩🇪: quantum.gov/competitiveness/…
Alex Meiburg retweeted

Sar Haribhakti@sarthakgh5 May 2024
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“"In a first-ever human clinical trial of four adult patients, an mRNA cancer vaccine developed at the University of Florida quickly reprogrammed the immune system to attack glioblastoma, the most aggressive and lethal brain tumor."
Stunning






























