Google DeepMind’s AlphaProof Nexus has reportedly solved nine open Erdős problems, alongside dozens of other mathematical questions, in work described in a study published in Science. The result is a substantial research claim, and the reported use of Lean offers a checkable route for validating the proofs.
Google DeepMind Watch analysis
What happened
The Decoder reports that AlphaProof Nexus solved nine of 353 open Erdős problems, including two that had remained unsolved for 56 years. The report also credits it with proving 44 conjectures from the OEIS integer-sequence database, solving an open question in algebraic geometry and improving a known bound in min-max optimisation.
According to The Decoder, the system uses Gemini 3.1 Pro to draft and revise proofs in Lean, a formal language in which proofs can be checked. For harder sub-problems, it can also call on DeepMind’s AlphaProof tool. The report says the work was published in Science and subjected to peer review.
Why it matters
Mathematical proof is a particularly demanding test for AI: a plausible-looking answer is not enough. Lean’s formal checking gives researchers a way to verify whether a proof follows the rules, rather than relying on the system’s confidence or a persuasive explanation.
The reported results are more specific than a single headline-grabbing puzzle. They span several areas of mathematics, while the Erdős count also provides a useful measure of what remains unsolved. The Decoder says the system solved nine of 353 problems, not that it has cracked the wider catalogue.
Our read
If these reported results hold up, this is a serious example of AI contributing to mathematical research, not merely dressing up a solution in impressive notation. The combination of model-generated reasoning and formal proof checking is the part to watch: one proposes, the other checks. A machine claiming it has done the maths is one thing; a verifiable proof is rather less hand-wavy.
What to watch
- The paper’s methods and the proofs made available for independent inspection.
- Whether mathematicians confirm the results and what further work builds on them.
- How much the system’s progress depends on AlphaProof for harder sub-problems.
Discussion spark: Should AI mathematics be judged mainly by the number of problems solved, or by whether its methods and proofs can be independently checked?
Sources and evidence
- Google Deepmind's AlphaProof Nexus solved dozens of open math problems and actually got peer reviewed (12 October 2026, 09:35 UTC)
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