Last month, I interviewed mathematicians who were seeking a very peculiar set of dice. For no reason other than they found the problem fun, they had hunted for five dice that could be thrown to decide who moves first in a board game. Crucially, each dice must have the same odds of winning and throws must never tie.
Their search took more than a decade, but they finally cracked it. I have also spent a lot of time reporting on the growing power of artificial intelligence to solve mathematical problems, including this week’s shock Fermat’s last theorem formalisation. The two ideas began to commingle in my head after I got off the phone with the dice hunters.
Could AI, I wondered, go one better and find a solution for six players, with six dice that decide who goes first? AI’s solution to 87-year-old riddle takes mathematicians by surprise Brute force wasn’t the answer: there are more possible designs of five dice than there are atoms in the universe. So, I fired up ChatGPT, described the problem, and asked for a solution.
I nudged and clarified twice, and in total it “thought” for around 13 minutes. I promptly fired the solution off to Eric Harshbarger at Auburn University, Alabama, one of the researchers working on the five-dice problem. I accept my solution wasn’t a particularly elegant or aesthetically pleasing one.
Five of my dice had 720 sides; another had 20. Try rolling a 720-sided dice in the real world, or convincing players that a lop-sided set is fair. Nor was my AI-derived solution even the best we know of.
Harshbarger and his colleagues have already been able to adapt their five-dice solution to create a six-dice one, where all dice have 360 sides, they told me. This isn’t good enough for a public announcement and still isn’t very practical, although undeniably much better than mine. However, a layman like myself, with at best dusty mathematics, found a solution to a thorny, if unserious, problem in minutes by doing nothing more than describing it in plain English to an AI model.
Extract — continue reading at the source.
