A game of chess requires its players to think several moves ahead, a skill that computer programs have mastered over the years. Back in 1996, an IBM supercomputer famously beat the then world chess champion Garry Kasparov. Later, in 2017, an artificial intelligence (AI) program developed by Google DeepMind, called AlphaZero, triumphed over the best computerized chess engines of the time after training itself to play the game in a matter of hours.

More recently, some mathematicians have begun to actively pursue the question of whether AI programs can also help in cracking some of the world’s toughest math problems. But, whereas an average game of chess lasts about 30 to 40 moves, these research-level math problems require solutions that take a million or more steps, or moves.

In a paper appearing on the arXiv preprint server, a team led by Caltech’s Sergei Gukov, the John D. MacArthur Professor of Theoretical Physics and Mathematics, describes developing a new type of machine-learning algorithm that can solve math problems requiring extremely long sequences of steps. The team used their new algorithm to solve families of problems related to an overarching decades-old math problem called the Andrews–Curtis conjecture. In essence, the algorithm can think farther ahead than even advanced programs like AlphaZero.