Terence Tao warns AI proof-solving threatens open math

A MathOverflow post traces mathematics' history of secrecy: in medieval times, reputation and livelihood depended on hoarding techniques. Scipione del Ferro discovered a method for solving depressed cubic equations around 1510 but kept it hidden for 20 years because the knowledge secured his professional standing, disclosing it to a student only on his deathbed. The habit persisted into the era of Newton and Leibniz, whose priority dispute over calculus centered on Newton's decision to delay publication and keep his framework secret; a Royal Society committee, appointed while Newton was the Society's president, concluded he was calculus' sole author. The post argues that the modern norm of publishing results openly, however imperfect the journal system, is now under strain again because large AI companies are pursuing famous unsolved problems for publicity. The author points to the disputed claimed counterexample to the Navier-Stokes equations as the live example: Capital&Compute estimated its compute cost at about $6.5 million, TensorFeed put the figure at $10 million to $15 million once costs beyond raw tokens are included, and Business Insider estimated a total cost of $10 million to $40 million. The post quotes Terence Tao's warning on Mastodon that identifying a promising problem, not solving it, is now the scarce resource, since even a rumor that someone is working on a problem can trigger a burst of AI-powered effort to solve it before the original researcher can finish, which risks discouraging mathematicians from sharing promising directions at all and reversing centuries of open-science tradition. The author proposes two partial remedies: crediting a result only when a human or group of humans can reasonably be said to be behind it, similar to how US copyright law reserves registration for works created by human beings, and requiring that the full methodology behind a result, including the complete system prompts and agent setup for an AI system, be published alongside it, since firms currently treat that setup as a trade secret.

Key facts

Scipione del Ferro kept his method for solving depressed cubic equations (discovered around 1510) secret for 20 years, disclosing it only on his deathbed.
The Newton-Leibniz calculus dispute turned on Newton delaying publication and keeping his framework secret; a Royal Society committee, with Newton as the Society's president, ruled him sole author.
Estimates for the compute cost behind a disputed claimed Navier-Stokes counterexample range from about $6.5 million (Capital&Compute) to $10-$15 million (TensorFeed) to $10-$40 million (Business Insider).
Terence Tao warned on Mastodon that identifying a promising problem, not solving it, is now the scarce resource, since a mere rumor of research can trigger a rush of AI-powered effort to preempt it.
The post proposes crediting only humans for results and requiring full disclosure of an AI system's methodology, including its system prompts, to curb the incentive toward secrecy.

Why it matters

The post's argument is that AI-powered proof generation is reviving an incentive structure mathematics moved away from centuries ago: keeping partial results secret to protect a claim to credit. If confirmed at scale, that shift would undo the norm of open publication that has governed the field since the era of grant-funded, journal-published research.

Who it affects

Individual mathematicians working on well-known open problems are most exposed, since the post argues that companies with large compute budgets can now race to a formal solution once a problem or a rumor of progress becomes public. Institutions like the Royal Society, which historically arbitrated priority disputes such as Newton and Leibniz's, and prize-granting bodies such as the Millennium Prize organizers, are named as examples of structures set up before this dynamic existed.

How to use it

The post proposes two concrete mechanisms rather than a ban on AI tools: credit a result only when a human or group of humans can reasonably be said to be behind it, drawing an analogy to US copyright law's restriction of registration to human-created works, and require publication of the full methodology behind an AI-derived result, including the complete system prompts and agent setup, since that setup is currently kept as a trade secret.

How solid is it

The historical claims, Del Ferro's two-decade secrecy and the Newton-Leibniz dispute, are well-documented episodes the post uses as established background. The current-day claims rest on three third-party cost estimates for a single disputed claimed Navier-Stokes counterexample, which the post itself flags as uncertain ("regardless of the true cost"), and on Terence Tao's Mastodon warning, which is a personal assessment rather than a measured trend.

Risks and caveats

The post does not name the AI company or companies it says are pursuing famous problems for publicity, nor does it link or attribute the claimed Navier-Stokes counterexample to a specific person or team, and none of the three cost estimates comes with a stated methodology or date. The proposed remedies are the post author's own suggestions, not adopted policy, and the piece itself calls the underlying question open-ended.

“It is now the identification of a promising problem which is the scarce and precious resource.”

— Terence Tao, on Mastodon