Technology, algorithms and AI · Methods and tools
If an AI system produces a correct proof, does anyone know the result?
AI systems have begun to solve competition problems and to suggest new constructions in research mathematics. This question asks where the knowledge sits when a machine finds a proof: in the machine, in the people who check it, or nowhere until someone understands it.
Claims
- If the proof is checked, for example by a proof assistant, the result is known, whoever or whatever found it; discovery and justification are different things.
- AI can widen what mathematicians can explore, just as computers did for calculation.
Counterclaims
- Knowledge may require understanding; a verified result no human understands is closer to a reliable rumour than to mathematical knowledge.
- AI systems can produce convincing but wrong arguments, so trusting them without independent checks is risky.
Real-life situations from mathematics
AI at the International Mathematical Olympiad
In July 2024 Google DeepMind reported that its AlphaProof and AlphaGeometry 2 systems together solved four of the six problems from that year's olympiad, a score at silver-medal level. AlphaProof's solutions were checked in the Lean proof assistant.
FunSearch and the cap set problem
In December 2023 researchers reported that FunSearch, a method combining a language model with an automatic evaluator, found larger examples of 'cap sets' in some dimensions than mathematicians had found before. The constructions could be checked directly.
Check dates and figures in a reliable source before you use them, and cite that source.
Use this in your TOK work
Essay. Fits titles about technology, the knower, or what counts as understanding. Keep your facts dated: this area changes quickly.
Exhibition. A printout of an AI chatbot's (flawed or correct) attempt at a proof is a timely object; label it as AI output and comment on it.
Link it to the prescribed title or the exhibition prompt you are working on, in your own words. See using maths examples in your essay and choosing exhibition objects.
Themes and study heading
Knowledge and technology Knowledge and the knower Methods and tools
How mathematical knowledge is produced and justified.