Mathematicians challenge AI with 50 of mathematics' hardest open problems
From Isaac Newton to Srinivasa Ramanujan, the history of mathematics has been crowded with minds fascinated by questions which would not yield. In July, that old appetite acquired a new catalogue: Epoch AI’s FrontierMath: Open Problems expanded to 50 high-stakes research problems - questions chosen by mathematicians and selected so proposed answers could be checked by computer.
The list asks not merely whether machines can solve mathematics. A larger question looms whether the new discoveries could become evident with it.advertisement❮❯ Read Full StoryA ROOM FULL OF UNFINISHED QUESTIONSThe 50-problem list followed workshops held in June in six cities across Europe and America - London, Toronto, Los Angeles, New York, Berkeley and Boston – where mathematicians proposed problems spanning number theory, topology, combinatorics and other fields.
One participant was Yang-Hui He of the London Institute for Mathematical Sciences, who brought his school-age son to the London gathering. He and other mathematicians submitted problems ranging from knot theory to algebra and number theory. The purpose was plain: collect questions whose solutions would matter to mathematicians, not puzzles manufactured merely to defeat an AI.
Epoch AI says the problems have resisted serious human attempts and that a solution should represent meaningful progress in mathematical knowledge. Its unusual safeguard is the verifier: a computer program capable of checking a proposed answer.
Thus the contest is less dependent upon an AI system - or an editor - simply declaring that a proof “looks right.”
Among the stubborn questions is the Sum of Three Cubes. Mathematicians seek integers x, y and z satisfying x + y + z = n. The case n=42 was settled in 2019 by Andrew Booker and Andrew Sutherland after roughly 1.3 million computing hours.
Yet 114 remains open. A successful search may demand enormous computation, showing why such questions are as much about ingenuity as arithmetic.APRY'S SHADOW
Another problem asks for an Apry-style irrationality proof. Roger Apry proved in 1978 that (3) is irrational, a celebrated result in number theory; the proof was later formally verified.
The new challenge concerns whether similar reasoning can establish irrationality for another odd zeta value, such as (5).
Here the mystery is not simply the answer, but the path by which a mathematician might discover it.THE LONELY RUNNER
Then there is the Lonely Runner Conjecture, born in 1967. Imagine several runners circling a track at different constant speeds.
The conjecture says each runner will, at some moment, find sufficient distance from all the others. Simple to picture; notoriously difficult to prove in full generality.WHERE MACHINES ENTER
By July 31, Epoch said three of the 50 problems had already been solved by AI, while the benchmark continued to distinguish human, AI and human-AI results.
In September, researchers also reported a general solution to the “core” problem in approval-based committee elections, with a proof obtained with GPT-6 Astra and checked in Lean.
The blackboard, therefore, has not vanished. It has acquired another collaborator. For mathematicians, the wager is no longer merely whether a machine can calculate faster, but whether it can produce the rare thing that has always animated the subject: a new idea.- Ends
