Terence Tao on Everyday AI in Mathematics: Hypothesis Generation and Verification
Terence Tao, a Fields Medalist, uses AI daily in mathematical research. The cost of generating ideas has dropped to zero, but verification remains a bottleneck. Models solve simple problems from the Erdős list with a 1-2% probability, requiring human oversight for complex issues.
Idea Generation in the Age of Kepler
AI generates thousands of hypotheses with high temperature, akin to Kepler sifting through theories about the Solar System. Most are noise, but in datasets with reliable verification (like Tycho Brahe's observations), useful signals emerge. Tao emphasizes: without data, ideas remain in the garbage category. Kepler's book "Harmonices Mundi" contained the third law of planetary motion amid speculations about celestial notes—a classic example of signal in noise.
In development, this manifests in code generation: LLMs produce variants faster than review. Automated tests check syntax, but semantic correctness and task alignment require human analysis.
Who is Terence Tao and Why His Insights Matter
Tao works in number theory, combinatorics, harmonic analysis, differential equations, and random matrices. First publication at age 15, Fields Medal at 31. As a practitioner without commercial interests, he evaluates AI based on real results. In an interview with Dwarkesh Patel (March 20, 2026), Tao analyzes AI through the lens of the historical scientific method.
- Key areas of Tao's expertise: number theory, combinatorics, harmonic analysis.
- Advantage of his opinion: no financial motivation, focus on practice.
- Comparison with AI leaders: Amodei and Altman promote products, Tao promotes reputation.
The Collapse of Idea Generation Costs
AI has made idea generation as cheap as the internet made communication. Previously, science focused on insights (Archimedes, Newton). Now, thousands of hypotheses per minute overwhelm peer review. Journals are drowning in AI submissions; the old system can't cope.
For developers: AI speeds up coding, but the backlog of pull requests grows. CI/CD catches basic errors but doesn't guarantee solving the right problem. Tao highlights the role of verifiers like Tycho Brahe: 20 years of precise data made Kepler's laws possible.
Results on Erdős Problems: Statistics Without Illusions
AI has solved about 50 of the 1100 Erdős problems, some open for decades. After a surge—a plateau: models find minor observations or known solutions, but no new breakthroughs.
- Success probability per problem: 1-2%.
- Scale compensates for low accuracy.
- Selection bias: Twitter shows victories, ignoring 98% failures.
Tao's metaphor: AI is a robot jumping 2 meters higher than a human. Conquers low peaks but doesn't climb ridges. With model upgrades—a new surge, then plateau.
Tao's Practice: Accelerating Auxiliary Tasks
A 2023 prediction came true: AI is a reliable co-author. Tao's papers have become richer: more code, graphs, experiments. Literature reviews are deeper, LaTeX formatting faster (agent adjusts brackets). Without AI—5x slower.
But the core—solving complex problems—is on paper. Papers are broader and richer, but not deeper.
In development similarly:
- Acceleration: boilerplate, refactoring, tests, documentation.
- Unchanged: architecture, domain decomposition, approach selection.
Cleverness vs Intelligence
Tao distinguishes artificial cleverness (jumping to a goal) from artificial intelligence (iterative progress). Models are clever: solve decade-old problems one-shot. But without session memory, no cumulative learning. Each iteration starts from scratch.
In mathematics, solutions are months of steps building on each other. AI doesn't construct chains. Analogy in engineering: coding vs designing systems with constraints.
A Copernican Shift in Understanding Intelligence
Human intelligence is not the center. AI shows other types of cognition: strong in jumps, weak in chains. Re-evaluating tasks: multiplying numbers is hard for humans, easy for machines; proving theorems—the opposite.
The Threat to Serendipity
Tao noted the loss of randomness: search engines give precise results, without adjacent finds in a library. Zoom removed unplanned conversations. AI optimizes by filtering noise—but serendipity arises from it. Tao intentionally introduced chaos for inspiration.
What's important:
- AI generates hypotheses cheaply, but verification is the bottleneck.
- Success on Erdős problems: 1-2% probability, scale matters.
- 5x acceleration on auxiliary tasks, 0 on core.
- Models are clever, not intelligent: no cumulative progress.
- Risk of losing serendipity in an optimized world.
— Editorial Team
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