I've seen several relevant quotes posted today, so I used GPT-Sol 6.1 to gather expert reactions to the results released on October 6 and checked each quote against its original source.
On “invent a new concept that does real work,” the nearest candidate here is the new code Moshkovitz describes. Ahle describes a different route to a bound, built on Strassen’s existing asymptotic-spectrum framework. These are early reactions to OpenAI’s October 6 mathematics release; the last two discuss the same plane-colouring proof.
Dana Moshkovitz: UT Austin professor specializing in probabilistically checkable proofs and pseudorandomness.
“Upon further inspection, the proof constructs a completely new tree-based code that somehow has a noise test with properties similar to that of the short code.”
Her addendum, posted by her husband Scott Aaronson in comment #2, October 7. In her own comment #5, she emphasizes the existing frameworks and results the AI built on, while calling the results “paradigm shifts.” She also criticizes the exposition and citations.
Thomas Dybdahl Ahle: theoretical computer scientist whose research includes algorithms and tensor sketching; Head of Machine Learning at Normal Computing.
“the new FMM paper is surprisingly elegant. It uses a very different approach than previous results. Instead of powering the CW tensor and trimming it, [they] define a potential function on tensors, and show the whole result by contradiction by studying the simple convolution tensor.”
Original X post, October 7. “CW” means Coppersmith–Winograd; “[they]” corrects a typo. The paper describes a profile, separation construction and growth argument; “potential function” is Ahle’s description.
Simon Pepin Lehalleur: University of Duisburg-Essen; algebraic and arithmetic geometry, particularly motives and motivic homotopy theory.
Of the OpenAI proofs he had skimmed, he singled out:
“The most original … is the algebraicity of the Kuga-Satake correspondence for K3 surfaces, using techniques from mirror symmetry.”
Later that day, on a very superficial reading, he judged the Bloch-conjecture proof “not based on deep new insights into codimension 2 cycles in general,” though “very substantial progress on cycles on (powers of) surfaces.”
Joshua Zelinsky: published number theorist with a mathematics PhD from Boston University.
“I've only had time to start looking at the chromatic plane proof, and it doesn't look like the method is a direction that the prior lit used to my knowledge. This is far beyond merely building on existing methods or seeing connections between different problems.”
Bluesky reply, October 6. The paper credits earlier invariant randomization and calls its averaging standard; the proof combines a transfer to weak measurable colourings with a geometric obstruction to five colours.
Dmitry Rybin: cofounder and chief scientist of a Shenzhen startup working on AI for mathematics; trained in pure mathematics at HSE; CUHK machine-learning PhD, 2026.
“Somehow the model found that any K-coloring <=> "weakly measurable" K-coloring, which seems out of nowhere”
Original X post, October 7. His follow-up says it used “ridiculous human-developed machinery”: amenable groups, Pontryagin duality and Furstenberg–Zimmer towers.
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Many people expect the AI paradigm to approximately AGI complete, and expect it to smoothly scale to AI that can do innovative science. i.e. the kind of science you'd need to do to develop a plague from scratch that actually kills all humans, with very limited opportunity to experiment. Or, the kind of science you'd need to solve alignment, so you could build a more powerful successor AI that shares your values.
A periodic thread of disagreement has been @TsviBT, @Steven Byrnes and some others arguing that, yes, the AIs are getting better at verifiable tasks, but they still seem to be missing some basic sauce that lets them actually form new concepts on the fly and apply them.
The AIs are getting better at "brute force creativity", where you try every single idea ever devised by Man in parallel and maybe one of them works. But there's still a kind of creativity that a) would have way higher efficiency and b) is maybe necessary for doing some kinds of breakthrough work.
On one hand, my subjective experience has been seeing AIs be able to demonstrate increasingly interesting judgement and taste in increasingly many domains (even open-ended ones). But, I do indeed still run into AIs that get confused and "just don't get it", in a way that is pretty suggestive that there is still something significant missing.
OpenAI has lately been shipping some major results in mathematics, for problems that people had previously agreed were important and hard. But, I'd heard for previous results that the proofs turned out sort of "not actually interesting", compared to how sometimes makes you go "Holy shit that's beautiful/elegant/surprising" and conveys someone is a level above you."
Recently they shipped a lot of new proofs on important problems.
I'm not a math guy. But, seems fairly important for some people with enough context to wade through them and figure out "What sort of cognition was involved here?". Do any of the proofs have the vibe of AlphaGo's Move 37? Does it invent a new concept that does real work?
I'm guessing answering this is a nontrivial task that'll involve some... archaeology? Might be cool for a competent math theorist who doesn't have a higher priority project to organize the labor. (I'm guessing the broader math community will do this on their own, but not necessarily organize the information in a way that's optimized for figuring out "is this the kind of mind that could solve its own alignment or quickly develop radically more powerful weapons than we have available?").
I'm shamelessly copying in @DaemonicSigil's quick take about this, to give some hooks for people to start thinking through.