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Formal proof verification

The practice of writing mathematics in a machine-readable logic so software can confirm every step, using proof assistants such as Lean, Coq or Isabelle.

Current stories

investConfirmed3 publishers

Shing-Tung Yau launches math-AI alliance of eight institutions aiming to network more than 1,000 researchers

Fields medallist Shing-Tung Yau launched an alliance of eight research institutions to link about 1,000 researchers on AI for mathematics. Output would show whether it works: a specialised model, or conjectures and formalised proofs others can check.

Perspective Coverage

3 publishers
Builder
Builder 42%
Operator
Operator 20%
Investor
Investor 38%

Reality

Evidence35
Adoption
Not scored
Hype gap+30
Incentives55
Confidence58
leadershipConfirmed3 publishers

OpenAI's 372 math results outrun the people who must check them

OpenAI published 372 families of math results from an unreleased model on Oct. 6, more than mathematicians have yet been able to check or understand. Each claim now waits on human readers, who must work without the prompts OpenAI chose not to publish.

Perspective Coverage

3 publishers
Builder
Builder 32%
Operator
Operator 38%
Investor
Investor 30%

Reality

Evidence50
Adoption
Not scored
Hype gap+45
Incentives65
Confidence60
scienceConfirmed5 publishers

Mathematicians face months of reading to judge whether OpenAI's hundreds of proofs contain new ideas

OpenAI released hundreds of results on open problems in math and theoretical computer science, many already verified in the Lean programming language. Those are all but certain to be correct, so the months of reading ahead are about whether they hold new ideas.

Publishers:nature.com newscientist.com phys.org retractionwatch.com scientificamerican.com

Perspective Coverage

5 publishers
Builder
Builder 33%
Operator
Operator 55%
Investor
Investor 12%

Reality

Evidence62
Adoption
Not scored
Hype gap+35
Incentives70
Confidence60
buildConfirmed2 publishers

One sign error pulled three of OpenAI's AI-generated math papers within a day of release

OpenAI withdrew three AI-generated math papers on October 7, one day after releasing 722 manuscripts, because of a sign error in an argument they shared. Only 300 of the 719 remaining results have Lean proofs a computer can check, so most of the collection still depends on human review.

Reality

Evidence62
Adoption
Not scored
Hype gap+35
Incentives65
Confidence60
productConfirmed10 publishers

Lean files let mathematicians machine-check part of OpenAI's 722 AI-written math manuscripts

OpenAI posted 722 model-written math manuscripts in 372 families on GitHub, many with Lean proofs a computer can check. A mathematician citing one has to learn first whether it is a checked proof or a paper still waiting for review.

Perspective Coverage

10 publishers
Builder
Builder 40%
Operator
Operator 27%
Investor
Investor 33%

Reality

Evidence55
Adoption
Not scored
Hype gap+45
Incentives70
Confidence60
buildConfirmed8 publishers

OpenAI ships a Lean build that checks its Navier-Stokes proof against its own definitions

OpenAI's 165-page proof ships with a Lean 4 formalization anyone can download and build, which settles whether the argument follows from its own definitions and leaves whether those definitions state the Clay problem to human readers.

Perspective Coverage

8 publishers
Builder
Builder 41%
Operator
Operator 30%
Investor
Investor 29%

Reality

Evidence50
Adoption
Not scored
Hype gap+40
Incentives70
Confidence60
scienceOne report1 publisher

OpenAI's claimed proof of a famous math problem starts a fight over authorship and standards

OpenAI said on September 8 that its models had solved one of mathematics' most famous problems, setting off a dispute over authorship and proof standards. The fight now turns on whether proofs that mathematicians can barely read can be checked and credited at all.

Reality

Evidence35
Adoption
Not scored
Hype gap
Not scored
Incentives55
Confidence30
productOne report1 publisher

OpenAI takes back $1m of Mathathon credits on the day 771 mathematicians publish their letter

A Caltech open letter says research mathematicians end up verifying and correcting what AI companies announce, without pay or credit. OpenAI's sponsorship was $1m in credits, and it took them back.

Publishers:thenextweb.com

Reality

Evidence62
Adoption58
Hype gap+14
Incentives74
Confidence60
investOne report1 publisher

OpenAI spent more than $1m of compute on a prize it says it will not claim

The Navier-Stokes result cost more in compute than the Clay Institute's award, and the interesting line in OpenAI's blog post is the one conceding it cannot rule out that customers' de-identified prompts helped.

Reality

Evidence32
Adoption14
Hype gap+34
Incentives74
Confidence44
productOne report1 publisher

OpenAI puts a machine-checkable Lean proof of finite-time blowup in a public repo

OpenAI says the result resolves statement C of the official Millennium formulation, then says it will not claim the $1M prize. The smooth force applied to its fluid throughout is why that second sentence carries the weight.

Publishers:thenextweb.com

Reality

Evidence58
Adoption20
Hype gap+35
Incentives72
Confidence52
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