Mathematicians will need years to check what the proof machine just wrote

The argument arrived as a single PDF: 412 pages, no figures, and a claim that a forty-year-old problem in combinatorics had been settled.

Why checking is harder than writing

A proof is only as useful as the community's confidence in it. Machine-written arguments tend to be long, unidiomatic and full of lemmas no human would have bothered to state.

The formal route

Several groups are now translating the argument into a proof assistant, where every step is checked by software.

theorem bound_holds (n : ℕ) (h : 4 ≤ n) : f n ≤ 2 ^ n := by
  induction n with
  | zero => simp at h
  | succ k ih => omega

We have spent a century learning to read each other's proofs. Now we have to learn to read a stranger's.

Estimates for a full formal check range from eighteen months to "longer than anyone wants to say on the record."