An AI named Aristotle just finished a mathematical proof that had stumped humans for decades and then verified its own work in a formal coding language.
Number theorists have long struggled to understand the specific gaps between numbers in Sidon sets where every pair has a unique product. A new AI system independently discovered the proof for a long-standing conjecture about these sets. Not only did the machine find the logic, but it also wrote the proof in Lean, a language used to formally verify that mathematical arguments are 100 percent correct. This marks a shift from machines helping humans to machines conducting the entire cycle of discovery and verification. It suggests a future where the hardest problems in math are solved by silicon brains while we simply check the results.