Google DeepMind used a large language model to solve an unsolvable math problem
www.technologyreview.com
They had to throw away most of what it produced but there was gold among the garbage.

The researchers started by sketching out the problem they wanted to solve in Python, a popular programming language. But they left out the lines in the program that would specify how to solve it. That is where FunSearch comes in. It gets Codey to fill in the blanks—in effect, to suggest code that will solve the problem.

A second algorithm then checks and scores what Codey comes up with. The best suggestions—even if not yet correct—are saved and given back to Codey, which tries to complete the program again. “Many will be nonsensical, some will be sensible, and a few will be truly inspired,” says Kohli. “You take those truly inspired ones and you say, ‘Okay, take these ones and repeat.’”

After a couple of million suggestions and a few dozen repetitions of the overall process—which took a few days—FunSearch was able to come up with code that produced a correct and previously unknown solution to the cap set problem, which involves finding the largest size of a certain type of set. Imagine plotting dots on graph paper. The cap set problem is like trying to figure out how many dots you can put down without three of them ever forming a straight line.

    • Victor@lemmy.worldEnglish
      71·
      11 months ago

      Kind of abusing the word there a bit though eh. Maybe call them something like “really feggin hard problems” instead.

    • thesmokingmanEnglish
      3·
      11 months ago

      This is mostly incorrect. There are provably unsolvable problems and unsolved problems. Many times someone will mislabel the latter as the former; that doesn’t make it actually provably unsolvable. Often we suspect unsolved problems might be unsolvable but do not go to the extreme of claiming it until it’s proved impossible to solve.