AlphaEvolve - The Future of Math?

[fresh_42]

TL;DR

Discussion of a paper: We showcase AlphaEvolve as a tool for autonomously discovering novel mathematical constructions and advancing our understanding of long-standing open problems.

LLMs and AIs have a bad reputation at PF, and I share this opinion. I have seen too much nonsense they produced, and too many "independent researchers" who weren't so independent after all, since they used them. And then there is a simple question: If we had to check their results anyway, why would we use them in the first place? In fact, their use is forbidden by the rules. I tend to interpret the reason for this rule because nobody wants to talk to a machine via PF. Those who want to can do that directly, not through human third-party filters. And training AIs should be a paid job, as it costs time and effort. Training them for free cannot be in our interest.

On the other hand, they are a fact and a new reality. Bans cannot be the ultimate answer. I subscribed to Tao's blog, and he mentioned an article that he and others wrote about a certain AI technique. Their approach tries to find a more objective answer, freed from possible prejudices and personal opinions. This is, to me, the first time I saw scientific statements in contrast to examples and rumours. Tao said in his blog that their sample size was 67, with different mathematical problems (both solved and unsolved) in analysis, combinatorics, and geometry.

In many cases, AlphaEvolve achieves similar results to what an expert user of a traditional optimization software tool might accomplish, for instance in finding more efficient schemes for packing geometric shapes, or locating better candidate functions for some calculus of variations problem, than what was previously known in the literature.

Source: https://terrytao.wordpress.com/2025/11/05/mathematical-exploration-and-discovery-at-scale/

I decided to create a separate thread for a discussion of this paper. It is 80 pages long, and I cannot expect that it will be read by everybody participating in this discussion, but I ask everyone to please stay on topic: the paper (entire or extractions) and AlphaEvolve. We already have enough other threads in which general opinions on LLMs can be expressed.

Example:

Moreover, in the hands of a user who is a subject expert in the particular problem that is being attempted, AlphaEvolve has always performed much better than in the hands of another user who is not a subject expert: we have found that the advice one gives to AlphaEvolve in the prompt has a significant impact on the quality of the final construction.
...
We stress that we think that, in general, it was the combination of human expertise and the computational capabilities of AlphaEvolve that led to the best results overall.

Mathematical exploration and discovery at scale​

Bogdan Georgiev, Javier Gómez-Serrano, Terence Tao, Adam Zsolt Wagner

AlphaEvolve is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines algorithmic solutions to challenging scientific and practical problems. In this paper we showcase AlphaEvolve as a tool for autonomously discovering novel mathematical constructions and advancing our understanding of long-standing open problems.
To demonstrate its breadth, we considered a list of 67 problems spanning mathematical analysis, combinatorics, geometry, and number theory. The system rediscovered the best known solutions in most of the cases and discovered improved solutions in several. In some instances, AlphaEvolve is also able to generalize results for a finite number of input values into a formula valid for all input values. Furthermore, we are able to combine this methodology with Deep Think and AlphaProof in a broader framework where the additional proof-assistants and reasoning systems provide automated proof generation and further mathematical insights.
These results demonstrate that large language model-guided evolutionary search can autonomously discover mathematical constructions that complement human intuition, at times matching or even improving the best known results, highlighting the potential for significant new ways of interaction between mathematicians and AI systems. We present AlphaEvolve as a powerful new tool for mathematical discovery, capable of exploring vast search spaces to solve complex optimization problems at scale, often with significantly reduced requirements on preparation and computation time.

Source: https://arxiv.org/pdf/2511.02864

 

[jedishrfu]

This is great, @fresh_42.

AlphaEvolve looks pretty interesting and depressing as it could scoop work of researchers doing research today.

 

[BWV]

Here is a link to a podcast from last summer with more background info

 

[Hornbein]

Here is a link to a podcast from last summer with more background info

That's quite a face has Sarah Guo. She invests in AI firms.

 

[Hornbein]

This is great, @fresh_42.

AlphaEvolve looks pretty interesting and depressing as it could scoop work of researchers doing research today.

Well, is the goal to discover better math or is it to provide employment for researchers?