DeepMind's AlphaProof Nexus Solves Nine Erdős Problems, Two of Them After 56 Years

Google DeepMind has published a study in Science on AlphaProof Nexus, a system that solved dozens of open math problems. Nine of them are Erdős problems, and two of those nine had resisted human mathematicians for 56 years. The key difference from most AI announcements in mathematics: reviewers checked the results before they were made public.

What was solved

The Erdős problems are a large collection of questions left behind by the Hungarian mathematician Paul Erdős. Some can be stated in a single line, yet have defied professionals for decades. That makes them a convenient benchmark for math AI: the status of each problem (open or closed) can be checked publicly.

The most significant detail in the announcement is the time span. Two of the problems stayed unsolved for 56 years. Generations of researchers could have worked on them in that time, and no one succeeded. The solutions are now published in a peer-reviewed journal.

The original announcement gives no details about Nexus's architecture, and it would be wrong to guess. All we know is that it continues the AlphaProof line. An earlier version reached silver-medal level at the International Mathematical Olympiad in 2024 and worked with the formal language Lean. How much of that approach Nexus inherited will have to be determined from the text of the Science paper.

Peer review as a stance

The publication arrives at a tense moment. According to The Decoder, OpenAI is currently facing a boycott for posting AI-generated proofs on GitHub without expert review. The complaint is easy to understand: a raw stream of model-generated proofs lands on mathematicians, who then have to work out which parts are rigorous derivations and which are plausible mistakes.

DeepMind chose the opposite order: verification first, publication second. In mathematics this is basic hygiene, but it is uncommon in the world of AI releases. Earlier high-profile claims of "solved" open problems had to be walked back more than once: the answer often turned out to exist already in the literature.

Key facts about the publication:

• Venue: Science, a peer-reviewed journal.
• System: AlphaProof Nexus (Google DeepMind).
• Scope: dozens of solved open problems.
• Erdős problems: nine.
• Time unsolved for two of them: 56 years.
• Process: peer review before publication.

How to read claims like this

After news like this, it is worth checking a few things. First: is there a full list of the solved problems, and can their status be verified in open databases? Second: were the proofs checked independently, and not only by the authors? Third: how formalized is the derivation? If a proof is written in a language like Lean, a machine can check it, and confidence in the result is higher.

For researchers, the practical takeaway is simple: a paper in Science provides material that can be examined, challenged and built on. A repository with a pile of outputs and no expert evaluation provides no such material.

The signal is also clear for companies building products on "reasoning" models. An AI's ability to close open problems can now be judged by externally verifiable results rather than press releases. What exactly Nexus can do, and how reproducible the approach is outside DeepMind's lab, will become clear once the mathematical community has discussed the paper.