AI Just Solved a 350-Year-Old Math Problem By Writing the Longest Proof Ever
OpenAI agents solved the Navier-Stokes math problem after a computation that ran for only 88 hours. Mathematicians state that the artificial intelligence solution remains nearly incomprehensible and currently offers little insight to humans. The equations at the center of the claim are two centuries old, while the prize question has been open since 2000. Meanwhile, artificial intelligence has also apparently answered a separate 79-year-old mystery regarding whether a six-dimensional sphere can be described using complex numbers.
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- ✓ OpenAI agents solved the Navier-Stokes problem after a computation that ran for only 88 hours.
- ✓ Mathematicians state that the artificial intelligence solution is nearly incomprehensible.
- ✓ The equations at the center of the Navier-Stokes claim are two centuries old.
- ✓ The Navier-Stokes prize question has been open since 2000.
What changed
OpenAI agents successfully executed an 88-hour computation to solve the Navier-Stokes problem, leaving mathematicians to unpack an almost incomprehensible proof.
Live updates
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OpenAI Solves Navier-Stokes Math Problem Using AI Agents
OpenAI agents solved the Navier-Stokes math problem after a computation that ran for only 88 hours. Mathematicians state that the artificial intelligence solution remains nearly incomprehensible and currently offers little insight to humans. The equations at the center of the claim are two centuries old, while the prize question has been open since 2000. Meanwhile, artificial intelligence has also apparently answered a separate 79-year-old mystery regarding whether a six-dimensional sphere can be described using complex numbers.
Why it matters
The Navier-Stokes problem centers on partial differential equations describing fluid motion, featuring an unsolved question of smooth solutions in three-dimensional Euclidean space that dates to the early 20th century. While computational solutions have practical engineering applications, a complete analytical understanding of fluid turbulence remains elusive. These breakthroughs arrive as researchers examine the implications of machine-generated proofs.
What is confirmed
- OpenAI agents solved the Navier-Stokes problem after a computation that ran for only 88 hours.
- Mathematicians state that the artificial intelligence solution is nearly incomprehensible.
- The equations at the center of the Navier-Stokes claim are two centuries old.
- The Navier-Stokes prize question has been open since 2000.
Still unconfirmed
- An artificial intelligence has apparently answered whether a six-dimensional sphere can be described using complex numbers.
What to watch next
- Independent reviewers completing their examination of the Navier-Stokes proof
- Mathematicians publishing detailed peer reviews on the comprehension of the machine-generated proof
confidence 95%Sources used for this update (8)
- www.ksmu.org — AI solved one of math's hardest problems. Humanity learned nothing (so far)
- futurism.com — Mathematicians Can’t Make Sense of How OpenAI’s Agents Solved One of the Toughest Math Problems Because the AI’s “Proof” Is Borderline Incomprehensible
- www.tuftsdaily.com — Mathematicians still checking the Navier-Stokes proof that ...
- www.scientificamerican.com — AI solves 79-year-old math mystery of six-dimensional spheres
- www.iolaregister.com — Area man says he solved math mystery - The Iola Register
- en.wikipedia.org — Collatz conjecture - Wikipedia
- en.wikipedia.org — Navier–Stokes existence and smoothness - Wikipedia
- www.yahoo.com — AI solves 79-year-old math mystery of six-dimensional spheres
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AI Models Accelerate Breakthroughs in Complex Mathematical Problems
Artificial intelligence systems are rapidly advancing across complex mathematical fields, matching recent disputed claims involving the Navier-Stokes problem with new developments. Anthropic's Claude defeated human records by discovering the most complex elliptic curves within days of searching. Meanwhile, OpenAI broke a barrier regarding high-dimensional sphere packing used in text applications and reported substantial progress on a second undisclosed Millennium Prize math problem. These achievements arrive as scholars debate the implications of machine-generated proofs and independent reviewers examine ongoing claims.
Why it matters
These machine-driven achievements follow a warning by UCLA professor Terence Tao at the International Congress of Mathematicians that rapid AI advancement is causing a crisis in mathematical values and practices. OpenAI recently presented a possible solution to the Navier-Stokes problem, sparking widespread speculation among mathematicians. Scholars continue to debate the implications of machine-generated proofs while independent reviewers examine the validity of the work.
What is confirmed
- Anthropic's Claude beat the record for finding the most complex elliptic curves in days.
- OpenAI broke a 48-year-old barrier regarding high-dimensional sphere packing.
- OpenAI stated it made substantial progress on a second Millennium Prize math problem without revealing which one.
Still unconfirmed
- OpenAI models presented a possible solution to the Navier-Stokes problem.
What to watch next
- Independent review of OpenAI's Navier-Stokes claim validity
- OpenAI disclosure of the second Millennium Prize math problem
confidence 100%Sources used for this update (3)
- www.scientificamerican.com — AI steals mathematicians’ record for most complicated curve
- www.scientificamerican.com — The hidden math that keeps your texts from turning to gibberish
- decrypt.co — OpenAI Says It's Made Progress on a Second $1 Million Math Problem
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Mathematicians Speculate After AI Solves Navier-Stokes
OpenAI models recently presented a possible solution to the Navier-Stokes problem, sparking widespread speculation among mathematicians regarding which major unsolved question artificial intelligence could resolve next. This development follows a warning issued in late July by UCLA professor Terence Tao at the International Congress of Mathematicians, where he told a packed lecture hall that artificial intelligence is advancing so rapidly it is causing a crisis in mathematical values and practices. Scholars continue to debate the implications of machine-generated proofs while independent reviewers examine the validity of the work.
Why it matters
The introduction of machine-generated proofs for centuries-old challenges forces the academic community to confront shifting standards of verification and comprehension. As artificial intelligence models tackle millennium-level problems faster than human researchers can adapt, foundational concepts of peer review and human understanding face unprecedented strain. Scholars are grappling with whether proofs spanning thousands of pages of agent-generated logic can truly be mastered by human intellect.
What is confirmed
- In late July, UCLA professor Terence Tao warned an International Congress of Mathematicians audience that artificial intelligence is causing a crisis in mathematical values and practices.
- An OpenAI model presented a possible solution to the Navier-Stokes problem.
What to watch next
- Independent mathematicians completing their review of the Navier-Stokes proof
- Identification of the next million-dollar math problem targeted by artificial intelligence models
confidence 100%Sources used for this update (2)
- www.scientificamerican.com — Which million-dollar math problem could AI solve next?
- www.theatlantic.com — An Existential Crisis in Math
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OpenAI faces credit disputes after solving Navier-Stokes equations
OpenAI claims to have solved the Navier-Stokes equations, a Millennium Problem, using thousands of agents over 88 hours. The achievement is marred by allegations from mathematician Tristan Buckmaster, who asserts OpenAI used its resources to overtake progress made by him and Anthropic researcher Levent Alpöge. While independent mathematicians review the proof, the breakthrough has sparked fears among scholars like Steven Strogatz that mathematics is moving beyond human understanding. Fields Medalist Terence Tao previously warned that AI is solving these challenges faster than human researchers can replace them.
Why it matters
The Navier-Stokes equations are one of seven Millennium Problems. Solving such a problem typically carries a million-dollar prize and represents a major leap in mathematical physics.
What is confirmed
- OpenAI claims to have solved the Navier-Stokes equations using thousands of agents over 88 hours.
- Independent mathematicians are reviewing the paper to verify the proof.
Still unconfirmed
- OpenAI is involved in a controversy regarding the twin prime conjecture.
What to watch next
- The results of the independent mathematical review of the proof
- Confirmation or denial of the twin prime conjecture claims
confidence 90%Sources used for this update (4)
- sports.yahoo.com — MLB Latest Updates - Yahoo Sports
- www.sciencenews.org — A human set a new mathematical record. Then AI came for it
- www.wbur.org — OpenAI claims to have solved a million-dollar math problem. Was credit given where it was due?
- www.wired.com — ‘I’m Really Terrified’: A Mathematician Grapples With AI’s Recent Breakthroughs
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OpenAI Claims AI Solved Navier-Stokes Problem Amid Controversy
OpenAI announced Tuesday that an artificial intelligence model solved the Navier-Stokes equations, one of the seven Millennium Problems in mathematics, after deploying thousands of agents for 88 hours. The milestone is shadowed by an academic dispute. A rival professor accuses OpenAI of improperly using his research team's work, attempting to strongarm him into helping, and threatening him. OpenAI denies these allegations. Independent mathematicians will now review the paper to verify the proof. Meanwhile, Fields Medalist Terence Tao warns that artificial intelligence is solving mathematical challenges faster than researchers can replace them, pointing to a competitive race between OpenAI and Anthropic.
Why it matters
The Navier-Stokes equations model fluid flow and represent a legendary mathematical puzzle that has stumped experts for decades. OpenAI's achievement follows a separate milestone by Anthropic, where Claude spent 11 days formalizing Fermat's Last Theorem into 13 million lines of machine-checkable code. These parallel developments signal an accelerated shift toward automated mathematical discovery.
What is confirmed
- OpenAI stated on Tuesday that its artificial intelligence technology solved one of the Millennium Problems.
- The solved problem involves the Navier-Stokes equations, which describe fluid flow.
- OpenAI claims the task was completed by deploying 10,000 AI agents in 88 hours.
- Independent mathematicians outside the company will review the paper.
- OpenAI denies allegations that it improperly used work from another research team or sought to deny credit.
Still unconfirmed
- An NYU academic claims OpenAI cribbed his work on the decades-old math problem and then threatened him after attempting to strongarm him into helping.
What to watch next
- Independent mathematicians completing their review of OpenAI's Navier-Stokes proof paper.
- Further developments or evidence regarding the credit dispute between OpenAI and the NYU professor.
confidence 90%Sources used for this update (7)
- us.cnn.com — OpenAI says it has solved one of math’s “Millennium Problems”
- www.nbcnews.com — OpenAI says it solved one of math’s hardest problems, but controversy taints the milestone
- nypost.com — OpenAI says it cracked decades-old math problem — but professor claims they cribbed his work and then threatened him
- www.sciencenews.org — AI may have solved one of math’s biggest puzzles, raising controversy
- decrypt.co — AI Is Solving Math's Best Problems Faster Than They Can Be Replaced, Terence Tao Warns
- www.techspot.com — OpenAI claims 10,000 of its AI agents solved one of mathematics' hardest problems in 88 hours
- theconversation.com — OpenAI claims another huge mathematical result amid fights over credit, ethics and privacy
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OpenAI Claims AI Solution to Millennium Prize Problem Amid Credit Dispute
OpenAI announced Tuesday that an unreleased AI model solved a Millennium Prize Problem involving the Navier-Stokes equations. The model demonstrated that these fluid flow equations can sometimes blow up. This follows a separate achievement by Anthropic's Claude, which spent 11 days formalizing Fermat's Last Theorem into a machine-checkable proof of 13 million lines of code. While some compare the Navier-Stokes result to Deep Blue's 1997 victory over Garry Kasparov, the claim is contested by a rival mathematician who asserts he reached the solution first.
Why it matters
Millennium Prize Problems carry a 1 million dollar reward for their solution. Formalizing a proof means translating mathematical logic into code that a computer can verify for absolute accuracy.
What is confirmed
- OpenAI claims an unreleased AI model solved a mathematical puzzle that has eluded mathematicians for generations.
- The OpenAI result shows that Navier-Stokes equations describing fluid flow can sometimes blow up.
- Anthropic's Claude formalized Fermat's Last Theorem in 11 days by making the existing proof machine-checkable.
Still unconfirmed
- NYU's Tristan Buckmaster claims he solved the Navier-Stokes proof first and accuses OpenAI's Sebastien Bubeck of racing to claim credit.
What to watch next
- Verification of the Navier-Stokes proof by independent mathematicians
- Official determination of the 1 million dollar prize award
- Public release of the unreleased OpenAI model used for the proof
confidence 90%Sources used for this update (5)
- www.scientificamerican.com — AI may have just solved a million-dollar math problem. The field will never be the same
- decrypt.co — OpenAI Says It Solved a $1M Math Problem. A Rival Mathematician Says He Did It First
- www.quantamagazine.org — AI Has Solved One of Math’s $1 Million Millennium Prize Problems
- www.zmescience.com — An AI Formalized and Verified Fermat’s Last Theorem in 11 Days, a Task Expected to Take Years
- www.yahoo.com — OpenAI says AI solved one of math's hardest problems in days
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AI Agents Formalize Fermat's Last Theorem
Artificial intelligence agents have solved a 350-year-old mathematical problem by formalizing Fermat's Last Theorem. The process took 11 days to complete, a task that would normally take human mathematicians years. Anthropic utilized its Claude system to accomplish the feat, generating a proof that totals over 13 million lines of code. This achievement represents the longest proof ever written.
Why it matters
Fermat's Last Theorem is a famous mathematical problem dating back centuries. Formalizing such a massive proof through AI demonstrates a massive leap in computational mathematics. The resulting code volume highlights the unprecedented scale of machine-generated proofs.
What is confirmed
- Anthropic used Claude to formalize Fermat's Last Theorem.
- The AI agents completed the task in 11 days.
- The resulting proof totals over 13 million lines of code.
What to watch next
- Further peer review or analysis of the 13-million-line proof by human mathematicians.
- Additional announcements from Anthropic regarding the application of Claude to other complex mathematical problems.
confidence 100%Sources used for this update (5)
- Decrypt — AI Just Solved a 350-Year-Old Math Problem By Writing the Longest Proof Ever
- Anthropic — Formalizing Fermat's Last Theorem
- New Scientist — Fermat’s last theorem formalised by AI agents in just 11 days
- siliconangle.com — Anthropic uses Claude to formalize proof of Fermat’s Last Theorem
- Inshorts — Claude formalises Fermat's Last Theorem in 11 days, task that would take humans yrs | The proof totals over 13 million lines of code | Inshorts
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