Iowa State University mathematicians Leslie Hogben and Carolyn Reinhart have received a long-awaited solution to one of their mathematical problems. Adam Wagner, a researcher at Tel Aviv University, solved the problem of scientists, but not with the help of any of the usual mathematical or other computing technologies. Instead, he used artificial intelligence during the game.
Although AI had previously contributed to mathematics, Wagner used it unconventionally — he turned the search for a solution to the Hogben and Reinhart problem into a kind of competition. According to Quantamagazine, the researcher used an approach that other experts have applied with great success to popular strategy games such as chess.
Wagner began using a similar strategy to create counterexamples that contradict the mathematical hypothesis and thereby prove its falsity. He presented the search for counterexamples as a guessing game, and then tested his program on dozens of open math problems.
Reinforcement learning models use a laissez-faire approach, allowing the computer to repeatedly work out a task (for example, a game). The model intervenes only to evaluate the performance of the computer. In response, the computer adjusts its strategy, learning which approaches lead to the best results.
Wagner applied the same basic scheme to dozens of tasks, varying only the score and the types of moves that the computer is allowed to make. All the tasks were from discrete mathematics and concerned objects that are separate and distinct from each other.
However, computers still cannot compare with the human brain in many parameters important for mathematical research. Trying to refute one of the hypotheses of the new paper, the Wagner model ran into an obstacle It had too little computing power to find a counterexample on its own. Despite this, he generated a lot of guesses that allowed Wagner to easily find one of them on his own.