In the past day, a rumor about Claude's mathematical achievements spread rapidly on social media.
Yesterday, blogger Andrew Curran posted a "prediction" that Anthropic has solved a Millennium Prize Problem, namely the existence and smoothness issue related to the Navier-Stokes equations, and the results are currently under expert review and may be publicly announced before Anthropic's IPO.
This post quickly gained over 2.5 million views and was shared by an increasing number of accounts.
As of now, no corresponding paper, proof text, or expert review materials are visible in public channels, and the Clay Mathematics Institute still lists the Navier-Stokes existence and smoothness problem among the unsolved Millennium Prize Problems.
However, this rumor is not without basis. An important background comes from a series of posts by mathematician Terence Tao two days ago.
A Hypothetical Article about AI
On September 3, Tao used the Navier-Stokes equations as an example to discuss the potential impact on mathematical research if AI solves major open mathematical problems.
https://mathstodon.xyz/@tao
The Navier-Stokes equations describe how fluids such as water and air move. The truly unsolved problem for mathematicians is whether, in the three-dimensional incompressible case, starting from smooth initial conditions, the solution remains smooth forever or develops singularities in finite time. This problem has been listed by the Clay Mathematics Institute as a Millennium Prize Problem with a $1 million prize.
In his post, Tao envisioned a possible future research process: an autonomous AI system with abundant computational resources continuously attempts different mathematical constructions, analyzes failure reasons, adjusts strategies, verifies results, and ultimately forms an extremely complex candidate proof, which is then machine-verified using formal proof systems like Lean.
His focus was on how the mathematical knowledge generated in this process could be preserved.
In traditional mathematical research, a difficult problem often produces a wealth of byproducts over years of exploration: new lemmas, new tools, new research directions, and questions worth pursuing further. Tao worries that if AI completes the entire exploration in a closed environment, humans might end up with a verified result, but many valuable intermediate paths may struggle to enter the mathematical community.
The scenario in the post was quite specific: AI searches for candidate structures, performs numerical tests, forms a massive Lean proof file, and finally solves the Navier-Stokes regularity problem.
Thus, the familiar plot on the internet emerged.
Some began to speculate whether Tao had access to information not yet public. Discussions soon appeared on social platforms asking, "Is Tao hinting that Claude has already solved Navier-Stokes?" Subsequently, Curran gave an even more explicit prediction: "Claude has solved Navier-Stokes." This claim spread rapidly.
As speculation grew, Tao subsequently issued a clarification.
His attitude was cautious: he currently has no knowledge of any major new progress on the Navier-Stokes problem, and his earlier discussion was a hypothetical AI research scenario. At the same time, given the current pace of AI development, such a scenario already has a certain degree of practical possibility.
He then discussed "opportunity cost."
Open problems like Navier-Stokes have driven the generation of new methods, new questions, and new researchers for decades. If AI can quickly arrive at the final answer, the mathematical community will also need to consider how to distill the processes, methods, and failed paths from machine exploration into mathematical knowledge that humans can understand and inherit.
This is gradually becoming a realistic issue in AI mathematical research.
AI is Changing the "Scarce Resources" in Mathematics
Why has this rumor become so viral?
In recent months, AI has indeed crossed several thresholds in mathematics that were previously hard to imagine.
Yesterday, Anthropic announced Claude's formalization work on Fermat's Last Theorem.
https://www.anthropic.com/research/formalizing-fermats-last-theorem
Fermat's Last Theorem was already proved by mathematicians such as Andrew Wiles in the 1990s. For decades, the mathematical community has hoped to fully translate this extremely complex proof into formal languages like Lean, allowing computers to verify each step incrementally.
Anthropic stated that Claude essentially autonomously completed the end-to-end Lean formalization in 11 days, with the final codebase reaching approximately 13 million lines. During the process, it generated about 30,300 machine-verifiable theorems, of which approximately 29,500 entered the final proof. Mathematician Kevin Buzzard, who participates in the long-term Fermat's Last Theorem formalization project, also gave positive feedback on this result.
Going back one month earlier.
On August 10, Anthropic announced that an unreleased Claude research model, while attempting the Riemann Hypothesis, made progress on a related problem: improving the lower bound on the proportion of zeros of the ζ function known to satisfy the Riemann Hypothesis condition from 41.6% to 67.2%. The Riemann Hypothesis is closely related to the distribution of primes and is one of the Millennium Prize Problems.
https://www.anthropic.com/research/riemann-zeta
In May of this year, OpenAI also published a result in discrete geometry. A general reasoning model constructed new unit-distance point sets, disproving a long-standing conjecture surrounding Erdős's plane unit-distance problem. The related proof was subsequently checked by external mathematicians. This result resolves an important conjecture within the problem, and the entire unit-distance problem still has further room for exploration.
https://openai.com/zh-Hans-CN/index/model-disproves-discrete-geometry-conjecture/
By August, OpenAI had also published a concentrated set of ten results in mathematics and theoretical computer science, including solutions or substantial progress on several long-standing open problems.
https://openai.com/zh-Hans-CN/index/ten-advances-in-mathematics/
A few years ago, the most prominent achievements of large models in mathematics were still olympiad problems. Now, the research targets have begun to move into open problems, paper-level results, and large-scale formal proofs.
The impact of AI on the mathematical community is also shifting from how many problems it can solve to what mathematicians will primarily be responsible for in the future.
One change is the rising importance of verification.
Language models can quickly generate a vast number of mathematical derivations, but they may also produce very subtle errors. Proof assistants like Lean can break down proofs into a form that machines can check step by step. As the speed of AI-generated proofs increases, formal verification is becoming an increasingly important infrastructure. Terence Tao has repeatedly emphasized that in the future, the bottleneck in mathematical research may gradually shift to checking, organizing, and understanding.
https://academy.openai.com/public/blogs/terence-tao-ai-is-ready-for-primetime-in-math-and-theoretical-physics-2026-03-06
The second change occurs in the division of labor among mathematicians.
If routine derivations, literature searches, computational experiments, and even some proofs can be delegated to AI, human researchers may invest more effort in selecting problems, proposing appropriate conjectures, designing research routes, and distilling machine-generated results into new theories that can be explained.
Terence Tao refers to this future as a "big mathematics" model: complex problems are broken down into many modules, with humans, AI, and formal proof systems participating together, and then the results are reassembled through machine verification.
https://spectrum.ieee.org/ai-in-mathematics
When answers become increasingly "cheap," what truly counts as the scarce part of mathematical research?
In the past, an important open problem could sustain a research direction for decades. The detours mathematicians took around it might themselves give birth to new theories. If AI drastically compresses this process, final answers will come faster, but it also requires the mathematical community to redesign methods for preserving research processes, allocating contributions, and training the next generation of researchers.
Terence Tao's use of the Navier-Stokes example this time discusses precisely this change.
As for whether Claude has truly conquered this Millennium Prize Problem, it currently remains at the stage of social media rumors.
But this somewhat absurd discussion has already illustrated one thing: a few years ago, "AI solving the Millennium Prize Problems" was probably closer to a science fiction setting; by 2026, people have begun to seriously consider what the mathematics community should do if it really happens.
Reference links:
https://x.com/AndrewCurran_/status/2096062392442724805
This article is from the WeChat public account "Machine Intelligence" (ID: almosthuman2014), author: Focused on Mathematics
