Yes — AI has already been used to prove new mathematical theorems, though usually in collaboration with human mathematicians. A few examples:
1. DeepMind and Knot Theory (2019–2021)
Researchers at DeepMind worked with mathematicians to apply machine learning to knot theory and representation theory. The AI system spotted patterns in large datasets that led to new conjectures. Mathematicians then proved these conjectures rigorously, producing new theorems in pure mathematics.
2. Formal Proof Assistants
Systems like Lean, Isabelle, and Coq have been used to formally verify long and difficult proofs — for example, parts of the Feit–Thompson theorem and the Kepler conjecture. These don’t usually discover the theorem, but they ensure that proofs are correct beyond doubt. Increasingly, AI is being integrated into these systems to help automate proof steps.
3. Automated Theorem Provers (ATP)
Programs like E, Vampire, and Prover9 can prove many theorems automatically from given axioms. They’re especially strong in algebra, logic, and combinatorics. These are not “AI” in the modern deep-learning sense, but they are automated reasoning engines that sometimes find proofs too complex for humans to stumble upon easily.
4. Recent Advances (2023–2025)
- Lean + GPT-style AI: Researchers have been training large language models to generate formal proofs inside Lean. These AIs can prove a growing portion of theorems from math libraries without human guidance.
- Discovery: In some cases, AI has gone beyond checking proofs — it has generated new lemmas or proof strategies that human mathematicians hadn’t considered, nudging math toward machine-discovery.
- High-profile result: In 2023, an AI-assisted effort produced a new result in geometry of polynomials, where the machine’s pattern recognition directly guided the conjecture and proof.
So the short answer:
AI has already helped prove existing theorems rigorously and, in a few cases, contributed to the discovery of entirely new theorems. The field is moving quickly, with hybrid human–AI collaboration producing the most exciting results.
Do you want me to give you concrete names of the new theorems AI helped discover, like the ones from DeepMind’s work on knot theory?
