> AlphaEvolve’s procedure found an algorithm to multiply 4x4 complex-valued matrices using 48 scalar multiplications, improving upon Strassen’s 1969 algorithm that was previously known as the best in this setting. This finding demonstrates a significant advance over our previous work, AlphaTensor, which specialized in matrix multiplication algorithms, and for 4x4 matrices, only found improvements for binary arithmetic.
> To investigate AlphaEvolve’s breadth, we applied the system to over 50 open problems in mathematical analysis, geometry, combinatorics and number theory. The system’s flexibility enabled us to set up most experiments in a matter of hours. In roughly 75% of cases, it rediscovered state-of-the-art solutions, to the best of our knowledge.
> And in 20% of cases, AlphaEvolve improved the previously best known solutions, making progress on the corresponding open problems. For example, it advanced the kissing number problem. This geometric challenge has fascinated mathematicians for over 300 years and concerns the maximum number of non-overlapping spheres that touch a common unit sphere. AlphaEvolve discovered a configuration of 593 outer spheres and established a new lower bound in 11 dimensions.
Well to me personally it at least proves something that's long been touted as impossible, that the current architecture can in fact do better than all humans at novel tasks, even if it needs a crutch at the moment.
An LLM-based system now holds the SOTA approach on several math problems, how crazy is that? I wasn't convinced before, but now I guess it won't be many decades before we view making new scientific advancements as viable as winning against stockfish.
Yeah, but those rely on setting up the evolve function. And they aren't well guaranteed to be better than humans. They might find you an improvement, but aren't guaranteed to do as shown here[1] (green means better, red means worse, gray means same).
> To investigate AlphaEvolve’s breadth, we applied the system to over 50 open problems in mathematical analysis, geometry, combinatorics and number theory. The system’s flexibility enabled us to set up most experiments in a matter of hours. In roughly 75% of cases, it rediscovered state-of-the-art solutions, to the best of our knowledge.
> And in 20% of cases, AlphaEvolve improved the previously best known solutions, making progress on the corresponding open problems. For example, it advanced the kissing number problem. This geometric challenge has fascinated mathematicians for over 300 years and concerns the maximum number of non-overlapping spheres that touch a common unit sphere. AlphaEvolve discovered a configuration of 593 outer spheres and established a new lower bound in 11 dimensions.
https://storage.googleapis.com/deepmind-media/DeepMind.com/B...
(this is an LLM driven pipeline)