Over the past few months, AI models have started resolving major mathematical problems, including ones that have withstood decades of human effort. Claude Fable disproved the Jacobian conjecture in three dimensions, and OpenAI announced a list of 10 problems that its Astra model solved or made significant progress on. Even more recently, an unreleased OpenAI model solved the Navier-Stokes Millennium Prize Problem, one of the most famous open problems in mathematics.
These are tremendous accomplishments, but very little about our day-to-day life will actually change as a result. This is because most well-known open mathematical questions are relatively insulated from practical applications. However, there are a few open mathematical problems that do have serious real-world implications. Chief among these is whether public-key encryption is fundamentally secure: that is, whether two strangers can share a secret message over public channels, such as the internet, without eavesdroppers having an efficient way to decipher it.
