AlphaEvolve Tackles Kissing Problem & More

There’s a mathematical concept called the ‘kissing number.’ Somewhat disappointingly, it’s got nothing to do with actual kissing; It enumerates how many spheres can touch (or ‘kiss’) a single sphere of equal size without crossing it. In one dimension, the kissing number is two. In two dimensions it’s 6 (think the New York Times’spelling bee puzzle configuration). As the number of dimensions grows, the answer becomes less obvious: For most dimensionalities over 4, only upper and lower bounds on the kissing number are known. Now, an AI agent developed by Google DeepMind called AlphaEvolve has made its contribution to the problem, increasing the lower bound on the kissing number in 11 dimensions from 592 to 593.

This may seem like an incremental improvement on the problem, especially given that the upper bound on the kissing number in 11 dimensions is 868, so the unknown range is still quite large. But it represents a novel mathematical discovery by an AI agent, and challenges the idea that large language models are not capable of original scientific contributions.

And this is just one example of what AlphaEvolve has accomplished. “We applied AlphaEvolve across a range of open problems in research mathematics, and we deliberately picked problems from different parts of math: analysis, combinatorics, geometry,” says Matej Balog, a research scientist at DeepMind that worked on the project. They found that for 75 percent of the problems, the AI model replicated the already known optimal solution. In 20 percent of cases, it found a new optimum that surpassed any known solution. “Every single such case is a new discovery,” Balog says. (In the other 5 percent of cases, the AI converged on a solution that was worse than the known optimal one.)