Scientific American puts Birch and Swinnerton-Dyer first in line to fall to AI
With Navier-Stokes claimed and five Millennium problems left, the ordering of what falls next turns on which conjectures a single counterexample would settle. Five million dollars of Clay prize money is still unclaimed.
The Scientist · Science desk
What happened
- OpenAI said on September 8, 2026 that an artificial intelligence model may have solved the Navier-Stokes problem, one of the seven Millennium Prize Problems the Clay Institute of Mathematics selected in 2000.
- That takes the tally of solved Millennium problems to two, the other being Grigori Perelman's 2003 proof of the Poincare conjecture.
- OpenAI told the New York Times it has already made significant progress on another of the problems, without saying which one.
- Scientific American introduced the five remaining problems in order of how likely each is to be resolved by the technology, an ordering it attributes to most experts.
- A year ago the reference point for these models was the Mathematics Olympiad, which they were only barely managing, and many researchers doubted the models were useful in research at all.
Why it matters
- What doesn't add up contradiction The public ranking of what falls next is being assembled from outside the labs while OpenAI already says it holds significant progress on one of the five and has not said which, so the speculation may be forecasting a result someone has in hand.
- What's now possible capability Because the prize admits a counterexample as a solution, a lab can win $1 million by handing over one object that other mathematicians can test, without producing a theory.
- What it limits constraint If the opening is the under-searched refutation side of conjectures people believe, then compute goes first at problems that can be killed by an example, and the ones needing structural proof stay where they were.
- What it sets up precedent A claimed solution announced by a company, with no verifier named in the account, sets the terms on which the next five will arrive.
Next story · Invest · Oct 8
Lean proof checks cover about 300 of the 722 math manuscripts OpenAI's unreleased model producedConfirmed3 publishers
Birch and Swinnerton-Dyer's conjecture dates to the early 1960s and concerns elliptic curves, the family of equations y^2 = x^3 + ax + b [14][15]. Those curves are central to cryptography and were the key to solving Fermat's last theorem [18]. The hard quantity is the rank: the number of independent rational starting points on a curve, from which further rational points follow by simple arithmetic [16]. In a computer-aided search, Birch and Swinnerton-Dyer found evidence of a criterion that answers the rank question quickly, and whether it gives the right rank for every curve has stayed open since [17]. One route to the million dollars is a single curve that fails the criterion [7][4].
Scientific American's stated reason for expecting a model to find such a curve has to do with where human effort has gone: "people often invest more resources in proving a hypothesis they believe to be true than in a possible refutation," the magazine wrote [8]. Language models have been good at producing examples of this kind, the article says [9].
The article does not say who has checked the Navier-Stokes argument or whether it has been refereed; it reports that the mathematics community is still in shock [6][5]. The wording of the claim also moves inside the same piece. OpenAI announced that a model may have solved the problem [1], and the article then counts Navier-Stokes among the two Millennium problems solved to date, next to Grigori Perelman [22].
Perelman proved the Poincare conjecture in 2003, twenty-three years before the September announcement [22][1][21]. Each of the five remaining problems carries a $1-million prize, which leaves $5 million of Clay Institute money outstanding [4][23][20].
Second in the ordering is the Hodge conjecture, which William Vallance Douglas Hodge put forward in 1950 and which the article calls arguably the most abstract of the seven [13].
Checking the two kinds of claim is not the same work. A candidate counterexample to Birch and Swinnerton-Dyer can be tested, one curve against one criterion [17][7]. A claimed proof of Navier-Stokes has to be read by people who know the field, and for now the candidates for what falls next are being argued over on social media and at conferences and workshops [19].
What to watch
- Whether OpenAI names the second Millennium problem it says it has already made significant progress on.
- Whether anyone publishes a verification of the claimed Navier-Stokes solution, and who does the reading.
- Whether a candidate counterexample to the Birch and Swinnerton-Dyer criterion is submitted and survives checking.
Clarity's read
What the record supports and how the coverage leans. The claims behind it follow.
Reality
- Evidence55
- Adoption35
- Hype gap+35
- Incentives70
- Confidence50
Perspective Coverage
3 publishers- Builder
- Builder 37%
- Operator
- Operator 40%
- Investor
- Investor 23%
Claim ledger
Ranked by verification strength, evidence, and original report placement.
- [1]
On September 8, 2026, OpenAI announced that an artificial intelligence model may have solved the Navier-Stokes problem.
- [2]
The Navier-Stokes problem is one of the seven Millennium Prize Problems, selected in 2000 by the Clay Institute of Mathematics as challenges that would shape the coming century of mathematics.
- [3]
Just a year ago, AI programs were only barely capable of solving some problems in the Mathematics Olympiad; many researchers laughed at the programs' sometimes embarrassing errors and doubted the models' utility.
- [4]
Solving any of the Millennium Prize Problems, by for instance finding a counterexample that refutes a core conjecture, comes with a $1-million prize.
- [5]
The mathematics community is still in shock, according to Scientific American.
- [6]
The Scientific American article does not report who has checked the claimed Navier-Stokes solution or whether it has been refereed.
- [7]
One way to resolve the Birch and Swinnerton-Dyer puzzle would be for an AI model to construct a counterexample: an elliptic curve that does not meet the criterion.
- [8]
"people often invest more resources in proving a hypothesis they believe to be true than in a possible refutation"
- [9]
Past experience has shown that language models are particularly good at finding such examples, according to Scientific American.
- [10]
OpenAI told the New York Times that it has already made significant progress on another one of the Millennium problems but did not specify which one.
- [11]
Scientific American introduced all five remaining problems in order of how likely it is that each will be resolved by the technology, according to most experts.
- [12]
The Birch and Swinnerton-Dyer conjecture is placed first in Scientific American's ordering of the five remaining problems.
- [13]
The Hodge conjecture is described as a second strong candidate for an AI solution and as arguably the most abstract of the seven Millennium puzzles; William Vallance Douglas Hodge put it forward in 1950.
- [14]
In the early 1960s, mathematicians Bryan John Birch and Peter Swinnerton-Dyer developed a conjecture involving algebraic equations called elliptic curves.
- [15]
Elliptic curves are generated by equations of the type y2 = x3 + ax + b, where a and b can take any value.
- [16]
The complexity or rank of an elliptic curve is the number of independent rational starting points; from one known rational point, other rational points on the curve can be calculated using simple arithmetic, though that method may not find all the points.
- [17]
Through a computer-aided search, Birch and Swinnerton-Dyer found evidence of a criterion that could quickly answer the question of rank, but it remains unclear whether that criterion can truly determine the correct rank for all elliptic curves.
- [18]
Elliptic curves play a central role in cryptography and were the key to solving Fermat's last theorem.
- [19]
In forums, at conferences and workshops and on social media, people are speculating about which of the remaining problems AI will tackle next.
- [20]
With five problems remaining and $1 million attached to each, $5 million of Clay Institute prize money is unclaimed.
- [21]
Twenty-three years separate Perelman's 2003 Poincare proof from OpenAI's September 2026 Navier-Stokes announcement.
- [22]
Two Millennium Prize Problems have been solved to date: the recent Navier-Stokes solution, and mathematician Grigori Perelman's 2003 proof of the Poincare conjecture.
- [23]
Only five Millennium Prize Problems now remain, and major AI companies are racing to solve them.
Sources
3 independent publishers whose own reporting we read for this story.
- livescience.com'Predatory behavior': Elite mathematicians clash over OpenAI's 'solution' to million-dollar math problem
1 article · September 17, 2026
- nature.comAI companies must work with the research community to protect attribution
3 articles · September 17, 2026
- scientificamerican.comWhich million-dollar math problem could AI solve next?
3 articles · September 21, 2026
Topics and entities
Entities
- OpenAI
- Poincaré conjecture
- Grigori Perelman
- Live Science
- Hodge conjecture
- Tristan Buckmaster
- Birch and Swinnerton-Dyer conjecture
- Clay Mathematics Institute
- Lean
- Levent Alpöge
- Navier-Stokes existence and smoothness
- Nature
- Scientific American