Olympiad-level formal mathematical reasoning with reinforcement learning \ stacker news ~AI

pull down to refresh

Olympiad-level formal mathematical reasoning with reinforcement learning www.nature.com/articles/s41586-025-09833-y

175 sats \ 2 comments \ @0xbitcoiner 19h AI

Abstract

A long-standing goal of artificial intelligence is to build systems capable of complex reasoning in vast domains, a task epitomized by mathematics with its boundless concepts and demand for rigorous proof. Recent AI systems, often reliant on human data, typically lack the formal verification necessary to guarantee correctness. By contrast, formal languages such as Lean1 offer an interactive environment that grounds reasoning, and reinforcement learning (RL) provides a mechanism for learning in such environments. We present AlphaProof, an AlphaZero-inspired2 agent that learns to find formal proofs through RL by training on millions of auto-formalized problems. For the most difficult problems, it uses Test-Time RL, a method of generating and learning from millions of related problem variants at inference time to enable deep, problem-specific adaptation. AlphaProof substantially improves state-of-the-art results on historical mathematics competition problems. At the 2024 IMO competition, our AI system, with AlphaProof as its core reasoning engine, solved three out of the five non-geometry problems, including the competition’s most difficult problem. Combined with AlphaGeometry 23, this performance, achieved with multi-day computation, resulted in reaching a score equivalent to that of a silver medallist, marking the first time an AI system achieved any medal-level performance. Our work demonstrates that learning at scale from grounded experience produces agents with complex mathematical reasoning strategies, paving the way for a reliable AI tool in complex mathematical problem-solving.

paper: https://www.nature.com/articles/s41586-025-09833-y_reference.pdf

view all related items

21 sats \ 0 replies \ @nkmg1c_ventures 16h

This may also be of interest

https://deepmind.google/blog/alphageometry-an-olympiad-level-ai-system-for-geometry/

0 sats \ 0 replies \ @0xbitcoiner OP 17h

DeepMind’s latest: An AI for handling mathematical proofs

AlphaProof can handle math challenges but needs a bit of help right now.

Computers are extremely good with numbers, but they haven’t gotten many human mathematicians fired. Until recently, they could barely hold their own in high school-level math competitions.

But now Google’s DeepMind team has built AlphaProof, an AI system that matched silver medalists’ performance at the 2024 International Mathematical Olympiad, scoring just one point short of gold at the most prestigious undergrad math competition in the world. And that’s kind of a big deal.

True understanding

The reason computers fared poorly in math competitions is that, while they far surpass humanity’s ability to perform calculations, they are not really that good at the logic and reasoning that is needed for advanced math. Put differently, they are good at performing calculations really quickly, but they usually suck at understanding why they’re doing them. While something like addition seems simple, humans can do semi-formal proofs based on definitions of addition or go for fully formal Peano arithmetic that defines the properties of natural numbers and operations like addition through axioms.

To perform a proof, humans have to understand the very structure of mathematics. The way mathematicians build proofs, how many steps they need to arrive at the conclusion, and how cleverly they design those steps are a testament to their brilliance, ingenuity, and mathematical elegance. “You know, Bertrand Russel published a 500-page book to prove that one plus one equals two,” says Thomas Hubert, a DeepMind researcher and lead author of the AlphaProof study.

DeepMind’s team wanted to develop an AI that understood math at this level. The work started with solving the usual AI problem: the lack of training data.

...read more at arstechnica.com