Terence Tao says AI drives idea generation cost to near zero but shifts the bottleneck to verification

Mathematician Terence Tao compares the influence of AI and formalization on mathematical practice with the impact of the automobile on urban development. The analogy could apply just as well to other fields, including coding.

Cars were faster than any previous mode of transportation, but they clogged roads built for people, horses, and carriages. New roads and highways made fast travel possible but led to urban sprawl, traffic congestion, and environmental problems. Only thoughtful urban planning and traffic regulations could have united both worlds in a sensible way, Tao writes.

The existing infrastructure of mathematics—journals, conferences, mentoring, citations—is like old, narrow roads: built for humans. Human proofs may be slow, but they generate valuable side effects: researchers develop expertise, map mathematical terrain, discover new research directions, and document instructive dead ends and detours.

AI-assisted proofs, Tao argues, can lead efficiently from hypothesis to result but lose exactly these side effects along the way. They're often unsuitable for traditional journals because the expected narrative about the path to proof is almost entirely missing. Tao compares attempts to upgrade AI models so they produce publishable papers with trying to retrofit cars for streets designed for humans.

Mathematics needs new infrastructure built for machines

Rather than forcing AI into existing structures, Tao thinks the better approach is to create new machine-friendly mathematical infrastructure that complements rather than replaces human paths. As examples, he points to large mathematical challenges where solutions are verified by formal proof assistants or automatically generated libraries of rough proofs that humans then refine into higher-quality versions. Tao also suggests a new discipline of "AI planning," modeled on urban planning, to preserve the "walkable" nature of mathematics.

In a conversation with Dwarkesh Patel, Tao expands on this view: AI does make his work "richer and broader," through more graphics, code, and deeper literature research, for example. But he still does the core of his mathematical work with pen and paper. Without the additional elements that AI makes possible in the first place, a paper wouldn't come together much faster today than it did in the past, Tao says. AI hasn't sped up the actual work so much as opened up new possibilities.

"I think AI has driven the cost of idea generation down to almost zero, in a very similar way to how the internet drove the cost of communication down to almost zero. It's an amazing thing, but it doesn't create abundance by itself. Now the bottleneck is different. We're now in a situation where suddenly people can generate thousands of theories for a given scientific problem. Now we have to verify them, evaluate them," explains Tao.