Over the past day, a rumor about Claude’s mathematical abilities spread rapidly on social media.
Yesterday, blogger Andrew Curran posted a "prediction" that Anthropic has solved a Millennium Prize Problem—the existence and smoothness problem related to the Navier-Stokes equations—with the results currently under expert review and potentially set to be disclosed before Anthropic’s IPO.
This post quickly garnered over 2.5 million views and was increasingly shared by more accounts.
To date, no corresponding papers, proof documents, or expert review materials have been publicly available, and the Clay Mathematics Institute still lists the Navier-Stokes existence and smoothness problem as an unsolved Millennium Prize Problem.
However, this rumor is not without basis; one important context comes from a series of posts published two days ago by mathematician Terence Tao.
A hypothetical article about AI
On September 3, Terence Tao discussed the potential impact of AI on mathematical research, using the Navier-Stokes equations as an example.
https://mathstodon.xyz/@tao
The Navier-Stokes equations describe how fluids such as water and air move. The fundamental unresolved question for mathematicians is whether, in the three-dimensional incompressible case, solutions starting from smooth initial conditions remain smooth indefinitely or develop singularities in finite time. This problem has been designated as one of the Millennium Prize Problems by the Clay Mathematics Institute, with a $1 million prize for its solution.
Terence Tao envisioned in his post a future research process: autonomous AI systems, equipped with vast computational resources, could continuously experiment with different mathematical constructions, analyze reasons for failure, adjust approaches, verify results, and ultimately generate an extremely complex candidate proof, which would then be formally verified using systems like Lean.
His focus is on how the mathematical knowledge generated during this process can be preserved.
In traditional mathematical research, a difficult problem often generates a wealth of byproducts over years of exploration: new lemmas, new tools, new research directions, and subsequent problems worth pursuing. Terence Tao worries that if AI completes the entire exploration process in a closed environment and humans ultimately receive only a verified final result, many valuable intermediate pathways may struggle to enter the mathematical community.
The scenario described in the post is highly specific: AI searches for candidate structures, performs numerical verification, generates a massive Lean proof file, and ultimately solves the Navier-Stokes regularity problem.
Thus, the familiar internet storyline emerged.
Some began speculating whether Terence Tao had access to undisclosed information. Social media quickly saw discussions arise asking, “Is Terence Tao hinting that Claude has solved the Navier-Stokes equations?” Soon after, Curran made an even more explicit prediction: “Claude has solved the Navier-Stokes equations.” This claim rapidly spread.
As speculation grew, Terence Tao subsequently issued a specific clarification.
His attitude is cautious: he is currently unaware of any significant new developments regarding the Navier-Stokes problem, and previous discussions belonged to a hypothetical AI research scenario. At the same time, given the current pace of AI technological advancement, such a scenario has become somewhat plausible.
He then discussed the concept of "opportunity cost."
Open problems like the Navier-Stokes equations have, for decades, driven the emergence of new methods, new questions, and new researchers. If AI can rapidly arrive at final answers, the mathematical community must next consider how to re-embed the processes, methods, and dead ends discovered by machines into mathematical knowledge that humans can understand and build upon.
This has gradually become a practical issue in AI mathematical research.
AI is changing the "scarce resource" in mathematics
Why is this rumor so popular?
In recent months, AI has indeed crossed several thresholds in mathematics that were once hard to imagine.
Yesterday, Anthropic announced Claude's formalization of Fermat's Last Theorem.
https://www.anthropic.com/research/formalizing-fermats-last-theorem
Fermat's Last Theorem was proven in the 1990s by mathematicians such as Andrew Wiles. For decades, the mathematical community has hoped to fully translate this extremely complex proof into formal languages like Lean, enabling computers to verify each step incrementally.
Anthropic stated that Claude autonomously completed an end-to-end Lean formalization over 11 days, resulting in a final codebase of approximately 13 million lines, during which it generated about 30,300 machine-verifiable theorems, with around 29,500 incorporated into the final proof. Mathematician Kevin Buzzard, who is involved in the long-term formalization project of Fermat’s Last Theorem, also provided positive feedback on these results.
One month earlier.
On August 10, Anthropic announced that an unreleased Claude research model made progress on a related problem while attempting the Riemann Hypothesis: raising the lower bound of the proportion of known zeta function zeros satisfying the Riemann Hypothesis from 41.6% to 67.2%. The Riemann Hypothesis is closely tied to the distribution of prime numbers and is one of the Millennium Prize Problems.
https://www.anthropic.com/research/riemann-zeta
In May of this year, OpenAI also announced a result in discrete geometry: a general reasoning model constructed a new set of unit-distance points, refuting a long-standing conjecture related to the Erdős unit distance problem in the plane. The proof was subsequently verified by external mathematicians. This result resolves an important conjecture within the problem, but further progress on the full unit distance problem remains possible.
https://openai.com/en-us/index/model-disproves-discrete-geometry-conjecture/
By August, OpenAI further announced ten results in mathematics and theoretical computer science, including solutions or significant progress on several long-standing open problems.
https://openai.com/en/index/ten-advances-in-mathematics/
A few years ago, the most notable achievements of large models in mathematics were solving Olympiad problems. Now, research has progressed to 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 role mathematicians will primarily fulfill in the future.
One change is that the importance of verification is increasing.
Language models can rapidly generate vast quantities of mathematical derivations, but may also produce highly subtle errors. Proof assistants like Lean can break proofs down into forms that machines can verify step by step. As AI-generated proofs become faster, formal verification is emerging as an increasingly critical infrastructure. Terence Tao has previously emphasized that, in future mathematical research, bottlenecks may gradually shift toward 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 occurred in the division of labor among mathematicians.
If routine derivation, literature searches, computational experiments, and even some proofs can be delegated to AI, human researchers may shift their focus toward selecting research topics, formulating appropriate hypotheses, designing research pathways, and distilling machine-generated results into new, interpretable theories.
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 collaborating, and then machines verify and reassemble the results.
https://spectrum.ieee.org/ai-in-mathematics
As answers become increasingly "cheap," what constitutes the truly scarce part of mathematical research?
In the past, a major open problem could sustain an entire research direction for decades. The detours mathematicians took in addressing it often gave rise to new theories. If AI significantly compresses this process, the final answers will arrive faster, but the mathematical community will also need to redesign methods for preserving research processes, allocating credit, and nurturing the next generation of researchers.
Terence Tao used the Navier-Stokes equations as an example to discuss this very change.
Whether Claude has truly solved this millennium problem remains at the stage of social media rumors.
But this somewhat confusing discussion has made one thing clear: a few years ago, the idea of "AI solving the Millennium Problems" was closer to science fiction; by 2026, people are already seriously considering what the mathematics community should do if it actually happens.
Reference link:
https://x.com/AndrewCurran_/status/2096062392442724805
This article is from the WeChat public account "Machine Heart" (ID: almosthuman2014), authored by someone interested in mathematics.