Grant Sanderson (@3blue1brown) – AI disproved a famous math conjecture. Now what?

Searching axiom spaces can occasionally discover deep mathematical structures because exhaustive or heuristic generation sometimes reveals 'islands' where many theorems follow, though most generated systems will be barren noise until a motivating application is found.

Tasks that lack grindability, such as many web interactions, fall behind because non-determinism, bot detectors, and changing environments prevent massive parallel rollouts and make credit assignment and sample reuse impractical.

A correct but sprawling proof does not equal understanding because humans and applications need compressed, elegant formulations that reveal why something works and how it connects to other ideas.

Training a verifier together with a meta-verifier lets systems learn to judge informal natural-language proofs at scale because the meta-verifier supervises the verifier to distinguish correct from incorrect reasoning, creating a reliable practice-driven feedback loop without full formalization.

Human mathematicians remain valuable because they supply taste, curation, trust, and social motivation that guide which problems are pursued and which results get adopted, roles that raw automated proofs do not replace.

Creating diverse agent priors increases the chance of creative heuristics because some agents will explore negations or orthogonal strategies and thus uncover low-probability, high-value ideas missed by homogeneous search.

Shaping training environments and data is more likely to produce connector abilities than tinkering with architecture because deliberately composed, grindable tasks create the incentives and examples models need to learn cross-domain linking.

Autoregressive training biases models toward predictable, context-constrained continuations, which makes generating rare but insightful cross-domain leaps unlikely unless training or objectives explicitly reward those jumps.