OpenAI Releases AI Proofs for Hundreds of Major Math Problems
OpenAI released 372 major mathematical proofs and results, solving longstanding open problems with the help of artificial intelligence. Human mathematicians are now racing to read, check, and understand these complex AI-generated proofs.
In short: OpenAI released 372 major mathematical proofs and results, solving longstanding open problems with the help of artificial intelligence. Human mathematicians are now racing to read, check, and understand these complex AI-generated proofs.
Imagine spending your entire career trying to climb a steep intellectual mountain, only for a machine to suddenly teleport you straight to the snowy peak in the dark.
What happened, in plain words
OpenAI released 372 major mathematical results and proofs after an advisory group of mathematicians recommended them. Among these was a proof for Subhash Khot's Unique Games Conjecture, a problem complexity theorist Dana Moshkovitz worked on for her entire career. The AI model used about three hours of GPT-Pro level compute per problem and successfully solved about 5 percent of the roughly 8,000 longstanding open problems it was tested on. While Lean certificates back up some of the results, human mathematicians note that the AI-generated papers are poorly written, hard to read, and feel like they were written by someone on psychedelics.
Key points
- Hundreds of open problems solved OpenAI released 372 breakthrough math and theoretical computer science results, including a proof for the Unique Games Conjecture and progress on other major problems.
- Human comprehension lag While computer verification like Lean certificates exist for some results, no human has fully understood most of these new proofs yet, launching a race to decipher them.
- Low success rate per try The AI model attempted about 8,000 problems and successfully solved about 5 percent of them, using roughly three hours of GPT-Pro level compute for each solved problem.
- Different release models OpenAI dumped 372 undigested papers onto the world for anyone to sort through, while Anthropic chose to let specific human researchers write and announce digested versions of its findings.
Terms explained
- Complexity theorist — A scientist who studies the fundamental limits and difficulty of solving computational and mathematical problems. Example: A complexity theorist figures out why certain computer puzzles take billions of years to solve while others take mere seconds.
- Unique Games Conjecture — A major proposal in computer science about how hard it is to find approximate solutions to certain optimization problems. Example: Trying to find the absolute cheapest way to deliver packages across a massive country with heavy traffic.
- Lean certificate — A formal computer-checked verification file that proves a mathematical argument is logically sound. Example: A digital math referee that checks every single step of a puzzle solution to make sure there are no cheating or logic mistakes.
- Quantum query complexity — A measure of how many questions a quantum computer must ask to find a specific piece of information. Example: Asking a magical searching box multiple yes-or-no questions to find a single hidden marble.
Why it matters
These AI breakthroughs provide solutions to theoretical math and computer science problems that human experts spent decades working on. They open a new era where artificial intelligence can generate complex proofs, changing how mathematical research is conducted.
What we still don't know
It remains unknown if all the AI-generated proofs are fully correct or sound, as humans are only beginning the difficult task of reading them. The AI only solved about 5 percent of the open problems it attempted, and massive challenges like the Riemann Hypothesis remain unsolved.
Based on reporting from Scott Aaronson (UT Austin). This is an independent explainer, written in our own words with AI assistance; Scott Aaronson (UT Austin) has not reviewed or endorsed it. Read the original for the full details.