ProofAtlas asks GPT, Claude, GLM and DeepSeek to decide which math problems matter most

By Zendoric · October 7, 2026.

ProofAtlas, a project that catalogues mathematical advances, formalizations and manuscripts, has published its October 6, 2026 edition of a 'Top 500': five hundred open mathematical problems spread across 17 areas, from number theory (117 entries, the largest) and theoretical computer science (57) to geometry and topology (73) or quantum information (17), according to the site's own classification. What is striking is not the exercise of listing famous problems — expert panels have been doing that for decades — but who decides the order this time: language models (LLMs, the chatbot-style generative AI systems).

The method, described by ProofAtlas, has several LLMs compare the problems in pairs and judge which carries more weight by its scope, its centrality in the field, its historical fame and its scientific or practical impact. Those comparisons are combined into what the site calls 'a reliability-weighted model': not all AI families vote equally; each is given a fixed weight — OpenAI 1.00, Claude (Anthropic) 1.00, GLM (Zhipu) 0.95 and DeepSeek 0.90. ProofAtlas is explicit that those figures 'are design decisions, not measured probabilities of being right': there is no empirical evaluation behind them of which model better judges mathematical importance, only an editorial choice about how much each one's vote counts. It is a clarification worth taking seriously, because it is easy to read those decimals as an objective measurement when they are, by their very definition, a choice made by the team that built the ranking.

The source adds caveats that do credit to its own rigor. Of the 500 problems, 239 remain simply open, 243 are 'open with solved subcases', 11 are listed as 'open with disputed claim' and 2 remain in 'reviewed hold' with conditional rank, each with its reason on record. But only 144 of the 500 entries carry their own status-review date, which ProofAtlas itself clarifies is not the same as a recent bibliographic review of the whole list. And the uncertainty ranges and comparison counts shown come from an earlier fit over 1,275 candidate problems, not recalculated for the current set of 1,273 — a technical detail, but a telling one, since even the authors themselves distinguish between what they have re-measured and what they have simply carried over from a previous edition.

That methodological transparency is, for us, the most interesting fact in the whole piece, more than the ranking itself. It fits something we keep repeating at Zendoric about AI benchmarks: a score is never a property of the phenomenon it measures, but of the method — which models, with what weight, with what comparison harness — that produced it. The same thing happens here, but in reverse: it is not AI being measured, but mathematics itself being ordered according to the aggregate judgment of several AIs. ProofAtlas even includes a 'family crowding' diagnostic to prevent groups of very similar problems (a conjecture and its variants) from monopolizing the top positions simply by being numerous, which suggests they are aware of how a counting bias can masquerade as consensus.

The underlying question this experiment leaves open is whether a consensus among language models about which mathematical problem 'matters most' bears any resemblance to the real consensus of the mathematical community, or whether it simply reflects which problems appear most cited and best explained in the material those models were trained on — which is not necessarily the same thing. Using AI to prioritize which problems are worth investing attention, compute or formal proof assistants in (the site also links to formalization sections on Mathlib, the community library of the Lean proof assistant) is an idea with legs: if AI is going to help more and more with exploring proofs, someone has to decide where to start, and model-assisted triage is cheaper than convening a panel of Fields medalists. But that triage should not be confused with real mathematical authority; for now it is, as ProofAtlas itself says, a model-based assessment, not an expert consensus.

This connects with the underlying thesis we defend: AI's contribution to hard science — including pure mathematics, the antechamber of much of the progress in physics, cryptography or biomedical modeling — will come first through support tasks like this one (prioritizing, cataloguing, suggesting routes) rather than through genuinely solving the great open problems. It is a small, almost administrative step toward a horizon in which AI accelerates scientific discovery that in the long run can translate into more health and more abundance. But today's step is a modest one, and ProofAtlas does well not to sell it as more than it is.