ChatGPT更进一步叙述：

Great — here are some concrete cases where AI actually contributed to new theorems in mathematics:

 

 

 

 

1. 

Knot Theory – Bridge Numbers and Slice Genus

 (DeepMind & Oxford, 2021)

 

 

• The problem: Knot theorists study invariants of knots (ways to distinguish different knots mathematically). Two important ones are the slice genus (a measure of how a knot sits in 4D space) and the bridge number (how “tangled” a knot is).
• AI’s role: DeepMind trained models on large knot datasets to search for hidden correlations. The AI spotted a surprising relationship between slice genus and bridge number that had not been noticed.
• The result: Mathematicians Marc Lackenby (Oxford) and András Juhász (Oxford) used these AI insights to formally prove a new theorem linking the two invariants.

 

 

 

 

 

2. 

Representation Theory – Kazhdan–Lusztig Polynomials

 

 

• The problem: In representation theory (the study of symmetry using algebra), Kazhdan–Lusztig polynomials play a central role but are extremely hard to compute.
• AI’s role: DeepMind’s system suggested a new, simple formula relating coefficients of these polynomials to geometric structures.
• The result: Geordie Williamson (University of Sydney) and colleagues proved that the AI-inspired conjecture was true, establishing a new theorem that streamlined computations in this area.

 

 

 

 

 

3. 

Ramsey Theory and Combinatorics (2023–2024)

 

 

• AI-driven search methods (often reinforcement learning combined with symbolic solvers) have been used to discover new bounds in Ramsey theory — problems about unavoidable patterns in large structures.
• Some of these bounds had resisted improvement for decades, and AI provided candidate constructions that human mathematicians then converted into rigorous theorems.

 

 

 

 

 

4. 

Formal Proof + Discovery in Lean (2023–2025)

 

 

• Large language models fine-tuned for the Lean theorem prover have gone beyond just proving textbook theorems — they’ve suggested new lemmas that were not in the library.
• In a few cases, these lemmas were novel enough to be published as original mathematical contributions, though usually quite technical.

 

 

 

 

Bottom line:

AI hasn’t yet produced a “Fermat’s Last Theorem–level breakthrough” on its own, but it has already helped discover and prove brand-new theorems in advanced areas like knot theory and representation theory. The most exciting pattern so far is AI spots the hidden structure → humans prove it rigorously → a new theorem is born.