Mathematicians Solve Impossible 1995 Puzzle—And ChatGPT Had Nothing To Do With It
A legendary math riddle that even its own creator thought was completely unsolvable has finally been cracked. It turns out that order hides within multi-dimensional chaos, proving that human brains still have a few tricks up their sleeves.
Michel Talagrand proposed his famous convexity conjecture back in 1995, basically asking if one could predictably force a shape into being "convex" (like a perfect circle or sphere with no weird dents) in any number of dimensions using a fixed number of geometric additions. He was so convinced his theory was an impossible shot in the dark that he personally offered a cool $2,000 bounty to anyone who could prove him wrong.
Geometry gets incredibly messy when you add extra dimensions—a nightmare mathematicians call the "curse of dimensionality," which makes shapes balloon in complexity faster than a corporate meeting's agenda. For decades, the best minds in science looked at this geometric monster and decided that taking Talagrand's money wasn't worth the existential dread.
Now, a trio of researchers from Caltech and Princeton University has finally cracked the code by translating the entire geometric nightmare into the language of probability. By shifting the perspective to random vectors, they proved that any high-dimensional random vector can be neatly broken down into a sum of exactly three standard Gaussian random vectors.
Before this breakthrough, two of the researchers actually tried to get ChatGPT to help them map out the solution, hoping the AI might possess some secret, non-Euclidean wisdom. While the chatbot offered some mild inspiration, the actual final proof was delivered by Stefan Tudose, who joined the team and wrote a clean, conceptual proof that didn't use a single line of AI-generated code.
It is highly amusing that in the middle of a massive global AI hype cycle, one of the most stubborn intellectual bottlenecks in modern mathematics was solved not by a trillion-parameter cluster, but by three guys with pencils and a shared whiteboard. The machines are still waiting for their invitation to the Abel Prize ceremony.
Source: arXiv
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