A team at three Chinese institutions just solved part of a math problem that's stumped some of history's sharpest minds — including Isaac Newton himself.
The "kissing number problem" sounds whimsical, but it's genuinely hard. It asks: how many identical spheres can touch a central sphere without overlapping? In our familiar three-dimensional space, the answer is 12. Newton and Scottish mathematician David Gregory debated this in the 1690s; it took until the 1950s to prove they were right.
But jump to four dimensions, and the answer becomes 24. Jump to the 24th dimension, and it's 196,950. Beyond that, the math becomes so geometrically tangled that human intuition simply fails. That's where things have stayed — until now.
We're a new kind of news feed.
Regular news is designed to drain you. We're a non-profit built to restore you. Every story we publish is scored for impact, progress, and hope.
Start Your News DetoxTeaching Machines to See in Higher Dimensions
Researchers at Fudan University, Peking University, and Shanghai's Academy of AI for Science built an AI system called PackingStar that does something unusual: it searches for sphere arrangements in high-dimensional spaces without being told what to look for. Two AI agents work together, testing configurations and refining them through trial and error — learning from scratch, no human guidance baked in.
The system found thousands of new valid sphere packings in the 13th dimension alone. "Leveraging AI for this problem," the team wrote in their preprint paper, "is not just part of the AI hype that surrounds it, but also a necessity for technological advancement."
Here's the honest part: PackingStar doesn't prove these solutions are optimal. It finds patterns that look right, but humans still have to verify the math. The AI is a spotter, not a referee.
Why does any of this matter beyond a dusty math textbook? These sphere-packing configurations have real uses. They help compress information into fewer bits, optimize how communication signals distribute across satellites, and improve quantum coding schemes. The better we understand how to pack spheres in abstract mathematical spaces, the better we can encode and transmit information in the physical world.
The breakthrough represents three centuries of accumulated difficulty finally giving way — not because one person got smarter, but because we built a tool that could see patterns humans couldn't. What comes next is the slower, essential work: mathematicians verifying these solutions and finding the proofs that explain why they work.
