On the SAIR: Episode 2 — Turning AI‘s Firehose Into Usable Science with Terence Tao & Riley Tao
In the latest episode of the SAIR podcast, we were treated to a unique dynamic: a conversation between Riley Tao and Riley’s father, the renowned mathematician and Fields Medalist, Terence Tao.
While the world speculates on when AI might replace human researchers, Professor Tao offers a more grounded and optimistic perspective. For him, AI is a powerful engine that requires a specific chassis to be safe.
Here are the key takeaways from their conversation regarding the evolving partnership between mathematicians and AI.
The Jet Engine Analogy
When asked how he currently utilizes AI, Tao likens current AI technology to a jet engine: extremely powerful and capable of high speeds, but dangerous if you simply strap it to your back.
"We don't strap jet engines on people and fly around in jetpacks (for commercial transportation)," Tao explains. "But we do have very safe, reliable planes that use jet engines to cross the Atlantic."
We are currently in a transition period. The raw engine (the Large Language Model) is powerful but unreliable. The goal of current research is to build the "plane" around it — the verification tools and workflows that allow us to harness that power safely.
The Firehose and the Filter
One of the most compelling moments of the interview was Tao’s description of the reliability problem. In science and math, we crave the "clean water" of truth and rigorous results.
Tao describes the traditional scientific process as a tap that produces high-quality drinkable water, but at a very slow trickle. AI, conversely, is a "firehose of high volume, high velocity sewage water."
It produces massive amounts of data, code, and text, but it is filled with "crud" and hallucinations. The challenge and the opportunity lies in building a filter.
"In math, I think we really have a chance to make this happen because we understand verification very, very well," Tao says. Unlike other sciences that rely on clinical trials or physical experiments, mathematics has formal proof assistants (like Lean). These act as compilers that can grade the output of an AI with 100% confidence.
If we can successfully attach the "sewage firehose" of AI to the "filter" of formal verification, we can achieve something unprecedented: high-volume, drinkable research.
Ricardo’s Law and Comparative Advantage
So, what does the workflow look like when the water is filtered? Tao references Ricardo’s Law of Comparative Advantage from economics. Even if an AI eventually becomes better than a human at everything (which it isn't yet), it is most efficient to assign tasks based on relative strength.
- The AI's Strength: Synthesizing massive amounts of literature and brute-force exploration. AI can scan millions of papers or generate thousands of object configurations to find hidden patterns.
- The Human's Strength: Generalization from sparse data. A human mathematician can look at five or six examples and intuitively grasp the underlying pattern or "why" something works.
Tao highlighted a recent collaboration with Google DeepMind regarding "Nikodym sets." The AI was able to construct clever, specific examples that optimized a certain score. Tao couldn't scan the millions of possibilities the AI did, but once the AI handed him the examples, he was able to read the code, understand the logic, and write a human-generated proof that generalized the concept for all sizes.
Moving Beyond Benchmarks
Finally, Riley and Terence discussed the state of AI evaluation. While benchmarks (like the International Math Olympiad) were useful early targets, Tao believes we are reaching a saturation point where models might be "teaching to the test."
The next frontier isn't a higher test score, but usability.
Drawing a comparison to Steve Jobs, Tao noted that the next great leap in AI for science won't necessarily be raw power, but the "last mile" of software development — making these tools intuitive and practical for the working scientist.
The Verdict
The future of mathematics isn't about AI solving everything while humans watch. It is about a symbiotic relationship where AI acts as the explorer and synthesizer, and humans act as the verifiers and creative architects.
As Tao concludes, "We need all the help we can get. I think it's a great future for math and science."
Listen to the full conversation on the SAIR Podcast.