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AI in Mathematics: From Olympiad Gold Medals to Erdős Problems — How Far Can It Go?
Artificial intelligence keeps expanding into new domains — and mathematics is no exception. Over the past few years, AI has made a series of striking advances in math, from solving school-level word problems to contributing to century-old unsolved conjectures. But how deep does this progress really go?
AI in Mathematics: A String of Recent Wins
The milestones are piling up fast:
- AI can already solve school-level math problems, including word problems
- In 2025, two AI systems — Gemini and OpenAI — reached gold medal level at the International Mathematical Olympiad, solving 5 out of 6 problems
- Since October 2025, AI has helped close more than 100 problems from the Erdős list, including several autonomously — among them Problem #728. OpenAI recently made a breakthrough on Erdős’s 80-year-old difference sets problem
- Startups building “AI mathematicians” are raising tens of millions: Harmonic (co-founded by Robinhood CEO Vlad Tenev) raised $100M in July 2025 and is valued at $1.45B; Axiom Math raised $64M in a seed round
- Terence Tao — the most prominent mathematician of our time — actively uses AI in his work. With AlphaEvolve, he proved 21 new mathematical results by the end of 2025
Terence Tao on AI in Mathematics: Cautious Optimism
Yet even Terence Tao, when asked when AI will solve a Millennium Prize Problem or produce any genuinely significant result, declines to give a direct answer.
He does expect AI to become a real co-author in research. But in his words, even if AI manages to formulate just one meaningful, non-trivial hypothesis over the next 5 to 10 years, that would already be major progress.
The Real Gap: Breadth vs. Depth in Mathematical AI
AI excels at breadth of knowledge — but depth still belongs to humans. The current system of mathematical research is built precisely on depth and specialization. It demands breakthrough ideas, not just exhaustive search.
This is the paradox: AI is getting smarter at mathematics, yet remains far from the truly hard problems and the kind of genius-level insights they require.
Where AI Still Struggles — and Why Mathematics Is Especially Hard
There are domains where AI performs poorly because of the “human factor” — where relationships between people matter more than dry facts. That’s almost everywhere, which is why AI makes a poor CEO or manager today, but a solid assistant for both.
But mathematics presents a different kind of challenge. Over centuries, humans have pushed so deep into this field that even the most powerful AI systems cannot yet approach the frontier of knowledge — or the breakthrough ideas that live there.
For now.