A new arXiv essay skips the usual AI-does-math benchmark chase and asks a blunter question: how would a machine know a good conjecture when it saw one?
The paper does not train a model or report test scores. It argues today's AI is good at fast, intuitive pattern matching, what the essay calls system 1, but weak at the slower, deliberate reasoning mathematicians actually use, system 2. It reframes the goal of an AI mathematician away from proving theorems that are already stated and toward discovering new, interesting ones. Using ideas from information theory, it proposes judging a set of theorems by compression: a good body of theorems should be short to describe yet close, in proof steps, to many other provable statements.
That reframing matters because most AI-math coverage is really about proving known problems faster on a benchmark. This essay treats discovery, not verification, as the harder and more useful problem, and it swaps vague praise for a concrete yardstick: does a theorem explain a lot while costing little to state.
It is a framework paper, not a demo. No model, no results, just a proposal, which means the real test comes if and when someone builds a system to chase this definition of interesting math, the way prior AI-math efforts eventually chased their own benchmarks.