# AI in Mathematics: 50 Solutions from the Erdős Catalog and Fundamental Model Limitations
Terence Tao, Fields Medal winner, assessed AI progress in mathematics based on the Erdős problem catalog. Models have solved about 50 problems, but 600 remain open. Autonomous solutions have stopped; now success comes from collective efforts involving multiple models and humans.
AI Autonomy Has Run Out
Tao describes three systematic runs of frontier models across the entire Erdős catalog. AI finds known solutions from the literature or generates observations, but there are no new fully autonomous breakthroughs. The early period when models solved problems independently has ended.
Now the approach is collective:
- One specialist asks a model for a strategy.
- Another uses a second model for critique.
- A third conducts a literature review with AI.
On a full catalog run, success rate is 1–2%. Scale allows finding rare wins, which are then publicized on social media.
Mountain Ridge Metaphor
Tao offers an analogy: mathematics as a mountain ridge in the dark with ledges of varying heights—from knee-high to sheer cliffs. Mathematicians light candles, draw maps, and feel out paths.
AI is like jumping machines with a two-meter jump, higher than human. They hopped over low ledges but don't secure themselves at intermediate heights:
- They reach the top—full solution.
- They fall back—no progress.
Key limitation: lack of partial progress. Models don't accumulate understanding halfway.
AI as Co-Author: Fulfilled Prediction
Tao's 2023 prediction came true: by 2026, AI has become a reliable co-author. Tao's papers now include more graphs, code, and literature reviews. Without AI, such breadth would take five times longer.
However, the core of research hasn't changed:
- The complex part of the problem is solved with pen and paper.
- AI expands but doesn't deepen the work.
Tao emphasizes: without AI, he wouldn't write so comprehensively. Models are changing the format of publications, but not the essence of discoveries.
Difference Between Resourcefulness and Intelligence
Working with a human colleague involves gradual buildup of understanding: adapting strategy, securing intermediate results. AI can't do this:
- In a new session, it forgets previous context.
- Doesn't adapt on the fly.
Tao sees the future in symbiosis:
- Humans provide depth.
- AI provides breadth of coverage.
Science must restructure methodology: from human depth to machine scale.
Key Takeaways
- AI solved 50 Erdős problems, but 600 are open; autonomous solutions are over.
- Success rate on systematic runs is 1–2%, requiring collective efforts.
- Limitation: inability to make intermediate progress, like jumping machines without securing holds.
- AI speeds up papers 5x, but the core of mathematics remains human.
- Future: human-AI symbiosis with restructuring of scientific approaches.
— Editorial Team
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