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AlphaProof Nexus’s reported results include 9 solved open Erdős problems and 44 proved OEIS conjectures—but those are two separate groups, not dozens of Erdős problems. The paper, “Advancing Mathematics Research with AI-Driven Formal Proof Search,” was published in Science on October 8, 2026. Its Lean proof artifacts are available for inspection, though a machine-checked proof does not by itself settle whether a problem was formalized as intended or how significant the result is.
What is AlphaProof Nexus?
AlphaProof Nexus is the name used in the 2026 paper for a formal proof-search framework. It uses Lean, a proof assistant, to produce proofs whose encoded steps can be checked by software. The framework is intended for mathematical research, rather than only solving competition problems.
Google DeepMind’s public repository provides successful Lean proof artifacts alongside natural-language proofs. The repository notes that its displayed collection covers successful problems; attempted problems that remain unsolved are recorded separately. Explore the AlphaProof Nexus results repository.
How many problems did it solve?
The paper reports two evaluation sets. Its most capable agent resolved 9 of 353 attempted open Erdős problems. Separately, it proved 44 of 492 OEIS conjectures. The authors describe the Erdős results as costing a few hundred dollars per problem, per problem; that figure refers to the paper’s reported cost for those resolutions, not a general price for using the system.
#1 Best Overall
| Problem set | Reported result | What the count means |
|---|---|---|
| Open Erdős problems | 9 of 353 attempted | The paper reports 9 resolutions in this attempted set. |
| OEIS conjectures | 44 of 492 | A separate set of conjectures, not additional Erdős problems. |
So “dozens” is accurate only when describing the combined headline-level picture across these distinct categories. It would be misleading to say that AlphaProof Nexus solved dozens of open Erdős problems.
Was the paper peer reviewed?
The article record lists the paper in Science, with a publication date of October 8, 2026. That means the work is no longer only a preprint. See the Science article record.
What does a machine-checked Lean proof establish?
Lean checks whether the encoded proof steps establish the statement that has been formalized. That is valuable evidence: readers can inspect the proof artifact and check it with the proof assistant. But proof checking and mathematical interpretation are related, distinct questions.
- Proof correctness: Does the artifact formally prove the encoded statement? Lean checking addresses this.
- Faithful formalization: Does the encoded statement accurately capture the original mathematical problem? A checked proof alone does not answer this.
- Research significance: Is the result new, useful, or consequential? Formal verification does not determine its importance.
- Autonomy: Does the artifact establish that the system generated every mathematical idea and surrounding step without human input? The existence of a successful proof artifact alone does not establish that.
The repository makes artifacts available for inspection, but their availability is not the same as an independent audit of every formalization or a fresh verification of the results.
Rank #3
How is this different from AlphaProof’s Olympiad results?
AlphaProof is an earlier system discussed in a 2025 Nature paper and associated with results at the 2024 International Mathematical Olympiad. Those competition results are separate from AlphaProof Nexus’s research-scale evaluations on Erdős problems and OEIS conjectures. The counts measure different tasks and problem sets, so they should not be combined or used to claim a direct performance ranking. Read the Nature paper on AlphaProof.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.What the result does—and does not—show
The authors say the system is being deployed in combinatorics, optimization, graph theory, algebraic geometry, and quantum optics research. The reported outcomes show formal proof search producing checkable results on selected mathematical problems. They do not show that the system has solved mathematics generally, nor that every attempted problem was solved.
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Rank #4
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