शोध पथComputationपाठ उपलब्ध
AI-assisted mathematical research
Optional research direction: how AI systems are used in mathematical research — literature search, code and experiments, search for constructions, conjecture generation, proof drafting, autoformalisation and formal proof search — organised around the generate-and-verify loop, with a dated record of results since 2021 that separates what was announced, independently checked, formally verified and published, and the norms of credit, disclosure and checking.
math.comp.ai-assisted-mathematics
इस पर आधारित
Formalising published mathematicsExperimental mathematics: conjectures and counterexamplesResearch ethics and attribution
53 अनिवार्य पूर्वापेक्षाएँ (बिल्कुल नीचे तक)
आप सीखेंगे
- Describe the ways AI systems assist research, from literature search to formal proof search, and the generate-and-verify loop that makes their output trustworthy.
- Distinguish a checkable construction (a lower bound) from an optimality or universal claim, and verify a machine-found certificate exactly, including in Lean.
- Read an announcement of an AI-assisted result critically: who checked it, whether it is formally verified, whether it is new, and what it does not show.
- Use AI tools in your own work responsibly, with verification, disclosure and fair credit.
परिभाषा
- A certificate is an object, such as a colouring, a construction or a formal proof, whose correctness can be checked by a simple, trusted procedure.
- In a generate-and-verify loop an untrusted generator proposes candidates and a trusted verifier accepts or rejects them.
- Autoformalisation is the machine translation of informal mathematics into the language of a proof assistant.
प्रमेय
- Search guided by language models has improved constructions in combinatorics and geometry, such as cap sets (FunSearch, 2023) and kissing configurations (AlphaEvolve, 2025); each improvement is a verified lower bound, not an optimality proof.
- In 2025 AI systems reached gold-medal standard on the problems of the International Mathematical Olympiad; Google DeepMind's result was graded by the IMO's coordinators.
- In May 2026 a proof generated by an OpenAI model disproved Erdős's unit distance conjecture; the proof was checked and written up by independent mathematicians.
आम भ्रांतियाँ
- Treating a fluent AI-generated proof as checked, or the agreement of several AI systems as verification.
- Treating a search's failure to find a construction as evidence that none exists.
- Assuming that an open problem solved by AI was difficult, or that the solution is new, without checking the literature.
वैकल्पिक खोजें
- Extremal and additive combinatorics Cap sets, Schur colourings and Ramsey colourings are typical of the constructions that AI-guided searches have improved.
अधिगम पथ
आगे पढ़ने के लिए
- Alex Davies et al., Advancing mathematics by guiding human intuition with AI (2021) — Nature 600, 70–74
- Bernardino Romera-Paredes et al., Mathematical discoveries from program search with large language models (2023) — Nature 625, 468–475
- Bogdan Georgiev, Javier Gómez-Serrano, Terence Tao and Adam Zsolt Wagner, Mathematical exploration and discovery at scale (2025)
- Mohammed Abouzaid et al., First Proof (2026)