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OpenAI Claims to Solve Math, Computer Science, and Physics Challenges, with Nobel Laureates Verifying the Results

AI2 min read

OpenAI says its AI system produced new proofs for three long-standing problems in math, computer science, and physics. Famous scientists, including a Nobel Prize winner, will check the results.

What happened

On the 26th (local time), OpenAI said its own AI model had made new research findings in three fields: harmonic analysis, computational complexity theory, and quantum field theory. The company says the AI solved math guesses that had been open for decades and proved a hypothesis that computer scientists widely accept. Independent experts will check and explain the results, including a Nobel Prize-winning physicist.

Key facts

  • Three fields: math, computer science, and physics
  • Math: the 1991 'local smoothing conjecture' was proved for all dimensions. It had only been proved for 2 dimensions in 2019.
  • Computer science: the 'Exponential Time Hypothesis (ETH)' was tested. The AI made a proof that goes against ETH, and the proof was checked in Lean.
  • Physics: a proof of existence for 4-dimensional quantum field theory was presented. It includes a proof for pure Yang-Mills theory, which is linked to a Millennium Prize problem.
  • OpenAI gave $5 million to the Simons Foundation to support AI research events and programs.

Some background

A conjecture is a math idea that people think is true but have not proved yet. A proof is a step-by-step logical argument that shows an idea is always true. Lean is a tool that checks whether each step in a proof is correct, so computers can confirm it. The Millennium Prize problems are seven very hard math problems. Each one carries a $1 million prize from the Clay Mathematics Institute if solved.

Why it matters

If these results hold up, they could change how scientists think about hard math and computing limits. ETH is used in hundreds of papers to explain why some problems are hard to compute, so a result against it could open the door to faster algorithms. OpenAI also says that real speed gains will need a lot more research. Outside checks are key, because the company says AI-made proofs must be independently verified before they count as true science.

What to watch

  • Whether outside experts agree with OpenAI's proofs
  • The physics results: OpenAI paused release of AI-made material at outside researchers' request, and the team will write up the findings itself
  • Whether faster algorithms come from the ETH result
  • How the $5 million Simons Foundation funding is used

Glossary

OpenAI
An AI company that makes large AI models, such as the one used in this research.
Lean
A computer tool that checks whether each step of a math proof is correct.
ETH
Exponential Time Hypothesis: a guess about how much computing time some hard problems need.
Millennium Prize
A set of seven famous, very hard math problems, each with a one-million-dollar prize.
Simons Foundation
A US group that funds science and math research and education.

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