Microsoft AI Helps Crack 31-Year-Old Math Problem

A 31-year-old math problem that stumped experts has finally been solved, and AI played a key role. The problem, called the KLS conjecture, asks a simple question: when you cut a high-dimensional shape, does the best flat cut work almost as well as the best cut of any shape? For decades, mathematicians suspected the answer was yes, but they couldn't prove it. Now, researchers at Microsoft and their collaborator have shown it's true, no matter how many dimensions the shape has.

Why should you care? This isn't just abstract math. The KLS conjecture is central to how computers sample from complex data—a process used in everything from training AI models to predicting stock markets to designing new drugs. If the conjecture is true, it means many algorithms that rely on random sampling are fundamentally efficient. That could lead to faster, more reliable software that saves time and money across industries.

The proof itself is a story of human-AI collaboration. The researchers used AI agents to explore over 100 possible approaches, many involving heavy calculations. The AI helped with derivations and proof-checking, but humans set the direction and made the key leaps. The final breakthrough came from a clever recursive trick: they repeatedly refined their estimate until the error became negligible. This eliminated the dependence on the number of dimensions, completing the proof.

While the result is a major theoretical advance, it may take years before practical applications emerge. But it's a clear sign that AI is becoming a powerful tool for scientific discovery, not just a gadget for writing emails. It also shows that even in the most abstract fields, human-AI teamwork can crack problems that have resisted solution for decades.