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Millennium Prize Problems

Seven mathematics problems named by the Clay Mathematics Institute in 2000, each carrying a $1 million prize for a generally accepted solution.

Known aliases

  • Clay prize
  • Millennium Prize Problem

Current stories

investConfirmed3 publishers

Lean proof checks cover about 300 of the 722 math manuscripts OpenAI's unreleased model produced

OpenAI published 722 math manuscripts across 372 result families, all produced by an internal model it has not released. About 300 come with Lean formalizations a machine can check, Crypto Briefing reported, so the rest wait on human reviewers whom one mathematicians' group is urging to stop working with OpenAI.

Perspective Coverage

3 publishers
Builder
Builder 30%
Operator
Operator 47%
Investor
Investor 23%

Reality

Evidence55
Adoption20
Hype gap+35
Incentives65
Confidence55
buildConfirmed6 publishers

OpenAI hands mathematicians 372 AI-generated proofs to check on GitHub

OpenAI posted 372 results from an internal model to GitHub, at about three hours of ChatGPT Pro compute each on average. Finding proofs is now cheap enough that the slow step is mathematicians checking and judging them.

Perspective Coverage

6 publishers
Builder
Builder 44%
Operator
Operator 31%
Investor
Investor 25%

Reality

Evidence58
Adoption10
Hype gap+35
Incentives72
Confidence60
productOne report1 publisher

OpenAI hands its new math advisory panel a backlog of results from an unreleased model

OpenAI's new mathematicians' panel must first help release scores more results the company says an unreleased model produced. Researchers call the panel a good first step, though many are unsure how much say it will have over how OpenAI announces what its models find.

Publishers:theverge.com

Reality

Evidence45
Adoption
Not scored
Hype gap+25
Incentives65
Confidence40
scienceOne report1 publisher

Epoch AI enlists mathematicians to pick 50 open problems a computer can check

Epoch AI, which benchmarks AI systems, had mathematicians nominate 50 high-stakes open problems chosen so a computer can check any proposed solution. The rule lets research mathematics be graded as a test of AI, but only problems whose answers a machine can confirm get in.

Reality

Evidence45
Adoption
Not scored
Hype gap+25
Incentives60
Confidence40
scienceOne report1 publisher

Terence Tao names AI's arrival in math research a crisis in the field's values

Scientific American's account from the mathematicians' congress in Philadelphia has a Fields medalist quitting for OpenAI and a Millennium Prize problem falling to an opaque mix of models, with no verification trail reported for either.

Reality

Evidence30
Adoption35
Hype gap+45
Incentives65
Confidence35
scienceOne report1 publisher

A prompt to an unreleased Claude lifted the elliptic curve rank record from 29 to 31

Levent Alpoge and Ava Howell used a simple prompt to an internal Claude and got elliptic curves of rank at least 30 and at least 31 in days, in a field where the last single-rank step took more than 18 years.

Reality

Evidence27
Adoption14
Hype gap+40
Incentives68
Confidence45
buildConfirmed3 publishers

Twenty-five Fields medalists call the AI industry's goals severely misaligned with mathematics

Their joint statement argues that famous open problems were only ever a proxy for understanding, and that benchmarks miss the years of talks and simplifications that follow a proof.

Publishers:dev.to seangoedecke.com the-decoder.com

Perspective Coverage

3 publishers
Builder
Builder 40%
Operator
Operator 43%
Investor
Investor 17%

Reality

Evidence72
Adoption58
Hype gap+18
Incentives68
Confidence70
productOne report1 publisher

OpenAI gave two different answers about Buckmaster's Codex prompts in one week

Tristan Buckmaster told the ABC that the game is up for mathematicians. In the same week, OpenAI described what his Codex prompts did to its models in two incompatible ways, and a customer has no way to pick between them.

Publishers:gizmodo.com

Reality

Evidence34
Adoption22
Hype gap+45
Incentives76
Confidence42
productOne report1 publisher

Mathematicians set the verification bar for AI proofs by shipping the Lean file

OpenAI says roughly 10,000 agents produced a Navier-Stokes singularity proof in about 88 hours, but the only proofs an outsider can run belong to two mathematicians who posted Lean formalisations with their preprints.

Publishers:thenextweb.com

Reality

Evidence42
Adoption22
Hype gap+45
Incentives78
Confidence52