Can AI Solve Complex Math Problems? Where It Works and Fails

Can AI solve complex math problems?

Yes, under narrow conditions: specific problem types, enormous compute, and often a formal system checking the work behind the scenes. No, not reliably, if you mean everyday arithmetic, word problems with an irrelevant detail thrown in, or anything that has to be right without a human or a proof checker standing over it. Those two answers sound contradictory. They aren't. They describe two different skills that happen to live in the same model.

What are AI's biggest math wins?

Start with the headline results. They're real and they're big.

In July 2025, OpenAI's experimental reasoning model and Google DeepMind's Gemini Deep Think each independently scored 35 out of 42 points on the 2025 International Mathematical Olympiad, the gold-medal threshold. Both solved 5 of the 6 problems, under the same rules human contestants face: 4.5-hour sessions, no tools, proofs written in natural language and graded by former IMO medalists.

That's a jump from the year before. In 2024, DeepMind's AlphaProof and AlphaGeometry 2 scored 28/42, silver-medal level, but needed problems manually translated into formal language first and ran past the official time limit. The 2025 systems did it live, under contest conditions, in plain English.

Then in 2026, things got stranger. An unreleased OpenAI model found a counterexample disproving Paul Erdős's 1946 "unit distance" conjecture, a problem that had sat open for 80 years. Mathematicians including Timothy Gowers and Jacob Tsimerman said the result would merit publication in a top journal. Around the same time, a DeepMind team's "Aletheia" agent autonomously resolved 9 of 353 open Erdős problems it was pointed at, including two that had been unsolved for more than 56 years, at a compute cost of a few hundred dollars per problem.

These aren't toy results. This is the same territory covered in how AI's math breakthroughs are changing software engineering, where gold-medal reasoning started showing up as a tool for proving code correct, not just plausible.

Why are these wins real but narrower than they look?

Here's the catch most headlines skip. The IMO and Erdős wins came from massive test-time compute, meaning the model gets to think, generate, and check far longer than a normal chat response allows. They also leaned heavily on problem types where AI already does well, like number theory and combinatorics, and less on geometry or anything requiring a genuinely novel construction.

And 26 of the 630 human contestants at IMO 2025 still outscored both AI systems. Both models scored zero on Problem 6, the hardest problem on the exam, which only 6 of 630 human contestants solved perfectly. Gold medal, yes. Best in the room, no.

The gap shows up again on FrontierMath, a benchmark of research-level problems vetted by more than 60 mathematicians. When it launched in late 2024, leading models solved less than 2% of its problems, despite scoring above 90% on simpler benchmarks like GSM8K and MATH. A later MIT competition had OpenAI's o4-mini-medium score 22% on a FrontierMath subset, beating the average human team's 19% but falling short of the 35% that human teams reached when you count any team solving each problem. Epoch AI's own read: AI isn't yet unambiguously superhuman on hard research math, even if it's getting close. It's a reminder that chasing a benchmark score tells you less than it seems about whether a model will actually hold up on your problem.

There's also a quieter failure mode worth knowing: false positives. On Christmas morning 2025, a team posted what they believed was the first fully autonomous LLM resolution of an Erdős problem. Hours later, someone pointed out that Erdős himself had already solved it, in a 1977 paper. The model wasn't wrong, exactly. It just didn't know what it didn't know.

Why does AI still fail basic, verifiable math?

Now flip to the bottom of the skill range, where the same models stumble on problems a sharp ten-year-old would get right.

Apple's GSM-Symbolic study took grade-school math questions and changed only the numbers, not the underlying logic. Accuracy dropped across every state-of-the-art model tested. Worse: adding a single clause to a problem that sounds relevant but doesn't actually affect the answer caused performance drops of up to 65% across the board. The researchers' conclusion was blunt: this looks like pattern matching, not reasoning. The models were doing something that resembled math, built from statistical association with similar-looking problems, rather than tracking the actual logic of the question.

This is the same family of model that just won an Olympiad medal. The contradiction isn't a glitch. It's the point.

Why can one model be a genius and a liar?

OpenAI's own research on hallucination explains the mechanism plainly. Standard training and evaluation setups reward confident guessing over honest uncertainty, because benchmarks grade exact-match correctness and give zero credit for "I'm not sure." A model that always guesses will score better on average than one that sometimes says "I don't know," even though the second model is more trustworthy. OpenAI's example: asked for the title of a researcher's PhD dissertation, a widely used chatbot confidently produced three different answers. None of them correct.

This is the dividing line between the two sides of this article. The Olympiad and Erdős wins happened in settings where answers can be checked, either by expert graders scoring a written proof against a rubric, or by a formal proof assistant like Lean, which verifies a proof mechanically, line by line. Harmonic's Aristotle, the system behind one of the 2025 gold medals, runs on Lean for exactly this reason. Free-text math, the kind with no formal checker standing behind it, has no such backstop. The model is just as confident either way. Only one of those confidences is earned.

The mechanics of why a next-token predictor can also formalize a 13-million-line proof of Fermat's Last Theorem are worth understanding on their own; we cover that in how LLMs actually work.

What does this mean for AI writing your business logic?

This isn't an academic distinction once AI starts writing code, generating reports, or drafting filings for your business.

It's already gone wrong in public, confident, polished, and wrong:

• Deloitte partially refunded a government report after it was found to contain fabricated citations and a fake court quote.
• EY Canada withdrew a report after discovering it included mostly hallucinated citations and made-up data.
• Sullivan & Cromwell, a major law firm, apologized to a New York court after an AI-assisted filing misquoted the U.S. Bankruptcy Code.

None of these outputs looked uncertain. That's the whole problem. A model that aces a hard proof and a model that invents a court citation are running the same underlying process: generate the most statistically plausible continuation and present it with full confidence. One happens to land on something checkable and true. The other doesn't, and nothing in the model's tone tells you which.

Developers have noticed. Even as AI tool usage climbed, with 84% of developers using or planning to use AI tools in 2025, trust in AI coding tools actually fell to 29%, down 11 points from the year before. That's backwards for a maturing technology, and it tracks almost exactly with how hard hallucinated-but-plausible code is to catch by eye.

How can you trust AI-generated logic with verification over vibes?

The lesson from the Olympiad wins isn't "AI can do complex math now, relax." It's "AI can do complex math reliably only when something external checks its work." Apply that same discipline to anything AI builds for your business:

1. Use deterministic tests, not confidence as a signal. Unit tests, integration tests, and property-based tests don't care how sure the model sounded. They care whether the output matches the expected behavior.
2. Add a formal verification layer for anything high-stakes. Type checks, schema validation, and in the most critical cases, formal proof-style verification, do for your code what Lean does for a math proof: catch errors a confident paragraph would hide.
3. Ground outputs in real sources, not model memory. If AI is citing a case, a figure, or a dissertation title, require it to pull from a verified source rather than recall one, the same gap that produced the Deloitte and EY corrections.
4. Treat AI output like a junior engineer's first draft. Reviewed, tested, and signed off by a human, not shipped on the strength of how polished it reads.
5. Match the verification effort to the stakes. A throwaway internal script needs less scrutiny than logic touching customer money, compliance, or legal filings.

The companies getting burned aren't the ones using AI. They're the ones who let a model's confidence substitute for a verification step they'd never have skipped for a human's work. The Olympiad proved AI can do real math. It also proved that real math, done by AI, still needs a referee.