Reinforcement Learning Tackles Age-Old Kissing Numbers

The Kissing Number Problem has puzzled mathematicians since 1694. Isaac Newton himself was the first to take a stab at it. The challenge? Determining the maximum number of non-overlapping spheres that can surround a central sphere. A classic in discrete geometry, it has stumped even the brightest minds.

A New Player Enters the Game

Enter PackingStar, a reinforcement learning system that's shaking things up. By reframing the problem as a cooperative matrix-completion game, this AI isn’t just crunching numbers. It’s sparking breakthroughs that have eluded mathematicians for decades. PackingStar is like a chess grandmaster, filling in cosine entries while correcting errors on the fly. The result? It’s making explosive geometric complexity look like child's play.

Cracking Old Codes

PackingStar isn’t just playing games for fun. It has improved 15 strong bounds in kissing numbers and their generalizations. Many of these solutions are provably optimal under natural inner products. And that’s not all. The system has unveiled the first explicit spherical-code realization of the Fischer group Fi22. Mathematicians, take note. The AI is extending classical Euclidean representations and inspiring new breakthroughs.

Why Should You Care?

Now, you might ask, why does this matter? Well, the implications reach far beyond just solving a math puzzle. It’s about AI bridging gaps that once seemed insurmountable. Show me the product, you say? Look no further than the fact that a centuries-old problem is now seeing progress fueled by AI.

This work isn’t just a flash in the pan. It’s an early example of AI-driven progress on a problem of Hilbert calibre. So the question is, what other age-old challenges are ripe for an AI overhaul?

The reality is this: AI isn’t just here to assist. It's here to lead. discrete geometry, PackingStar is proving that AI can do more than just scratch the surface. It’s digging deep and unearthing solutions we never thought possible.