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Not reliably across new research problems. Current AI systems have produced genuine mathematical advances and can sometimes solve or substantially advance difficult open questions. However, controlled evaluations on curated, research-level tasks still show low, uneven success rates. A successful demonstration proves that a system can contribute; it does not establish that the system will solve the next unfamiliar research problem dependably.
The most accurate answer is therefore two-part: AI has real research-level mathematical capability, but reliable, general-purpose autonomous problem solving has not been demonstrated.
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What “research-level mathematics” means
Research-level mathematics asks for more than applying known methods to a difficult exercise. A problem may require a genuinely new theorem, counterexample, construction, classification, or proof strategy. The necessary background can span several specialized fields, and even an apparently plausible argument may conceal a gap that takes an expert weeks to find.
Why competition performance is not enough
Olympiad and other competition benchmarks usually have a known answer, a short intended solution, and a tightly bounded range of techniques. Research problems can be open-ended, poorly specified until the work begins, and dependent on discovering useful definitions or intermediate conjectures. A model that performs well on competition mathematics has demonstrated valuable reasoning ability, but that score does not establish dependable performance on novel research.
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Riemann-Bench was designed around this distinction. Its authors describe a private research-level set and report that every evaluated frontier model scored below 10%. That result is not a universal measure of mathematical ability, but it is evidence that high performance on easier or more familiar tasks does not transfer automatically.
What the strongest evaluations report
There is no single “AI math accuracy” number. The benchmarks below use different problems, access rules, budgets, scoring procedures, and verification standards. Their results should be read as separate measurements.
| Evaluation | Task and protocol | Reported result | What it shows |
|---|---|---|---|
| FrontierMath initial evaluation (Epoch AI, 2024) | Hundreds of expert-crafted problems across modern mathematics; intended to require specialists hours or days. Six leading language models were evaluated. | No model solved more than 2%. | Early frontier systems struggled on a broad, difficult research-oriented set. This is not a current score for every model. |
| FrontierMath v2 (Epoch AI, released June 12, 2026) | Updated benchmark organized into tiers; Tier 4 is identified as research-level. | Errors were addressed in 42% of problems. | Benchmark quality and verifier maintenance materially affect reported results. |
| FrontierMath Erdős (Adamczewski and Bloom, preprint submitted September 6, 2026) | 68 open Erdős problems; five systems; each problem evaluated with a shared $300 budget; a Lean proof or disproof was required. | GPT-6 Astra: 3%. Each of the other four systems: 0%. | Even with a substantial fixed budget, autonomous success remained rare on this fixed open-problem collection. |
| Soohak (version revised May 19, 2026) | Mathematician-curated research-level benchmark with separate Challenge and refusal subsets. | Challenge subset: Gemini-3-Pro 30.4%, GPT-5 26.4%, Claude-Opus-4.5 10.4%. No model exceeded 50% on the refusal subset. | Scores vary sharply with task design; a model’s willingness to decline an unsolved or unsuitable task is itself measured. |
| Riemann-Bench (version revised June 23, 2026) | Private “moonshot mathematics” research-level set evaluated on frontier models. | Every evaluated model scored below 10%. | Results remain weak on another independent, high-difficulty set. |
FrontierMath’s early result
Epoch AI’s original FrontierMath account described expert-created problems spanning modern mathematics, with many expected to take a specialist hours or days. In the initial evaluation, none of six leading models solved more than 2% of the problems. Because this was an early evaluation, the figure should not be presented as a current all-model rate. It is best understood as a baseline showing how far systems had to go on carefully selected difficult tasks.
Why the Erdős result matters
The FrontierMath Erdős study narrows the question to 68 open problems associated with Paul Erdős and applies the same $300-per-problem budget to five systems. GPT-6 Astra solved 3%; the other four systems solved 0%. The authors required a Lean proof or disproof, which makes the success criterion more checkable than an unverified natural-language answer. A fixed budget and fixed collection do not represent every research setting, but they make the comparison meaningful within that study.
How to read Soohak’s higher percentages
Soohak reports substantially higher numbers on its Challenge subset: 30.4% for Gemini-3-Pro, 26.4% for GPT-5, and 10.4% for Claude-Opus-4.5. Those percentages cannot be averaged with FrontierMath or Riemann-Bench. Soohak uses its own mathematician-curated tasks and also reports a separate refusal subset, on which no model exceeded 50%. The difference illustrates how selection, expected answer format, tool access, and scoring can change a headline result.
Evidence that AI can make real mathematical contributions
Low benchmark scores do not mean that every reported advance is illusory. They mean that isolated successes should not be converted into a reliability claim.
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OpenAI’s October 2026 disclosure
In a disclosure dated October 6, 2026, OpenAI described a broad set of new mathematical results produced with an internal frontier model. It said that many proofs are being released in Lean formalizations and that details of the process are available. The disclosed average effort used compute equivalent to roughly three hours of ChatGPT Pro thinking. That figure characterizes the effort behind the reported results; it is not an average accuracy rate or a promise that a user will obtain a proof in three hours.
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Random freezes, missing sound and display glitches usually trace back to one bad driver. Find and replace yours safely.Free scan · under a minuteFormalized proofs provide a strong check that the stated derivation compiles in the chosen formal system. They do not, by themselves, establish that a result is important, novel, optimally formulated, or correctly attributed. Those judgments still require mathematical review.
Human-plus-AI work in the Open Problems tracker
Epoch AI’s Open Problems tracker separates autonomous solutions from “human-plus-AI” cases. Its September 2026 changelog says that this category is used when “AI was instrumental in solving a problem, but did not solve it autonomously.” That distinction matters: a model may discover a key lemma, search a large case space, or suggest a construction while a mathematician chooses the direction, repairs gaps, and establishes novelty.
The tracker also records provisional classifications and changes when verification or notability standards are not met. For example, it treats a reported Hadamard matrix solution as provisional and did not classify the M23 inverse Galois result as solved by AI because the core AI contribution was not unambiguous. These cases show why “AI solved it” is often too coarse a description.
Capability and reliability are different claims
Capability asks whether a system can produce a correct, useful contribution under at least some conditions. The OpenAI results and the human-plus-AI entries tracked by Epoch are evidence that the answer is yes.
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Reliability asks whether the system succeeds at a predictable rate on a broad stream of new problems, while recognizing when it is wrong and avoiding unsupported conclusions. The reviewed evaluations do not establish that. Success rates range from zero or low single digits to higher percentages on particular subsets, and the task definitions are not interchangeable.
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There is also a difference between an answer that sounds convincing and a result that survives verification. A fluent proof can contain a subtle invalid inference; conversely, a system may find a useful idea without presenting a complete proof. Reliability therefore includes problem selection, intermediate checking, error detection, and appropriate refusal—not just the final percentage of accepted answers.
How to compare an AI-math claim responsibly
Before treating a result as evidence of general research ability, record the following details:
- Task set and difficulty: Is it a public exercise collection, an unpublished private set, or genuinely open research? Are the problems known to the model or newly held out?
- Model and version: Name the exact system, release, context window, and any specialized mathematical mode.
- Tools: State whether the model could use a computer algebra system, web search, code execution, theorem prover, retrieval system, or other external aid.
- Budget: Report token, time, inference, or dollar limits. The $300-per-problem limit in FrontierMath Erdős is not equivalent to an unrestricted laboratory run.
- Autonomy: Say whether a human selected subproblems, supplied hints, corrected errors, or decided when to stop.
- Verification: Identify whether answers were checked by Lean, a bespoke programmatic verifier, independent referees, or only a language-model judge.
- Benchmark revision and date: Note the release version and when the evaluation occurred. Epoch reported that 42% of FrontierMath problems had errors addressed in its June 12, 2026 v2 release, demonstrating why revisions can change what a score means.
Without these details, two percentages may look comparable while measuring different abilities.
What AI is useful for in a research workflow
The evidence supports using AI as an assistant whose output is aggressively checked, not as an autonomous replacement for mathematical judgment. A practical workflow keeps the human responsible for correctness and significance.
1. Define the exact question
State the objects, assumptions, field, and desired conclusion precisely. Ask the system to list ambiguities and edge cases before attempting a proof. This reduces the risk that it silently solves a nearby but different problem.
2. Use it for exploration
Request candidate lemmas, examples, counterexamples, equivalent formulations, and small computational experiments. Treat every proposal as a conjecture. An attractive pattern can fail outside the tested range.
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3. Separate discovery from proof
Once a promising route appears, ask for a dependency graph of lemmas and for explicit statements of every assumption. Check the simplest cases independently. Do not accept a polished narrative as evidence that all implications hold.
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Where feasible, encode the argument in Lean or another suitable proof assistant, or build a programmatic verifier for finite and computational claims. Formalization can expose missing hypotheses and illegal transformations, while still leaving novelty and mathematical importance for human assessment.
5. Reproduce and challenge the result
Run the argument from a clean session, vary examples, and ask another person or system to search specifically for counterexamples. Keep unsuccessful attempts; they reveal where the method is fragile.
6. Make attribution explicit
Record which ideas came from the model, which were supplied by researchers, and who closed proof gaps. A contribution can be substantial without being an autonomous solution.
Why benchmark maintenance and refusal matter
A benchmark is not a permanent measuring stick. Problems can contain errors, have ambiguous verifiers, become widely known, or turn out not to meet the intended standard of difficulty or notability. Epoch’s revisions and removals show that maintaining a trustworthy test can be as important as running the models.
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The practical verdict
AI can solve some research-level mathematics problems and can materially accelerate others. The strongest evidence includes independently checkable formalizations and documented human-plus-AI advances. But the controlled results remain inconsistent: below 10% for every model tested on Riemann-Bench, at most 3% for the best system in the fixed-budget FrontierMath Erdős evaluation, and no more than 2% for any of six systems in FrontierMath’s initial evaluation. Higher Soohak Challenge scores demonstrate that task design matters, not that a general reliability rate has been established.
For a new problem, the defensible expectation is assistance with exploration, computation, proof search, and formalization—not dependable autonomous resolution. Until evaluations cover broader and changing problem pools with transparent budgets, robust verification, and clear authorship categories, the answer to “reliably?” remains no.
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