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Verified examples · Last reviewed 31 Oct 2026

What AI has actually achieved in theoretical computer science

This is a short, checked timeline of examples that changed what AI can contribute to a mathematical research workflow. It is not a live news feed and it is not a complete history of the field.

How to read this page: Start with “what it shows”, then read “what it does not show”. A result can be real and still be much narrower than its headline.

Evidence timeline

Three verified examples, three different jobs.

Each entry links to the source we checked. Evidence labels use the same four categories as the rest of the site.

2022 Algorithm discovery Peer-reviewed

AI found new ways to multiply matrices.

AlphaTensor used reinforcement learning to search for matrix multiplication algorithms. The results were checked as valid constructions within the settings studied by the authors.

What it shows

A computer search system can help discover valid algorithms for a narrowly defined mathematical task.

What it does not show

This does not mean AI can solve every algorithm problem, prove general lower bounds, or replace mathematical judgement.

Why it matters: It is a concrete example of AI helping with mathematical construction rather than only predicting text.

Read the primary source · Nature, 2022
2025 Formal proofs Peer-reviewed

AI searched for formal proofs in Lean.

AlphaProof learned inside the Lean proof assistant and found formal proofs for some olympiad-level problems. The paper reports substantial compute use and narrow task limits.

What it shows

AI can participate in a workflow where a proof assistant checks whether a formal proof is valid.

What it does not show

A checked proof for a competition problem is not a general theory of research-level mathematics. The search also requires substantial compute.

Why it matters: It shows why proof checking matters: the checker validates the proof, not the AI's confidence.

Read the primary source · Nature, 2025
2025 Complexity research Demonstrated

AI supplied finite structures inside a human proof framework.

AlphaEvolve found finite combinatorial structures. After computer checking, researchers plugged those structures into established proof frameworks to improve complexity-theory bounds.

What it shows

AI can help with one concrete part of a proof pipeline: finding a finite object that can be checked.

What it does not show

The broader proof still depends on human-designed mathematical frameworks. This is not a blanket claim that AI resolved complexity theory.

Why it matters: It separates a useful component from the wider theorem: finding a finite object is not the same as proving a universal statement.

Read the primary source · Google Research, 2025

What to inspect next

A strong example still has edges.

Read the field guideUnderstand the four areas and the words used in the headlines. Check the career questionsSee why task changes do not automatically settle the jobs question. Check a viral claimUse the five-question checklist before accepting a dramatic headline.