Jeffrey Lin

Just as mathematicians are now learning how many insights lie in the "convex hull" of existing ideas, the rest of science is about to learn this lesson at even more dramatic scale. Few realize the ridiculous inefficiency of the pipeline from theoretical innovation to practical use. Early versions of GPT made it easier to find existing knowledge. But finding a theorem is not the same as recognizing that it offers a radically different way to conceptualize a problem. Doing the latter requires expertise across fields that almost nobody possesses. Most of the people doing applied work are completely unaware of the conceptual tools that are being developed in more theoretical fields, and the people doing high-level theory do not understand the practical problems applied researchers are trying to solve. Almost no one doing practical work of any importance has an operational understanding of the web of ideas underlying the langlands conjecture or condensed mathematics, and virtually no one doing biology, chemistry or economics is knows anything about 90% of the math used in theoretical physics. And for good reason! Most of these ideas would be completely useless. But the scope for possible innovation from drawing the rare useful connections is immense. Think of Paul Samuelson borrowing ideas from thermodynamics to model equilibrium in economics, or Ed Witten using quantum field theory to revolutionize geometry. A few startling successes, not feasible to most: trying to venture into a more theoretical or more practical discipline to find insights of use is like searching for a needle in a haystack. What I suspect we will see in the next few years is a scientific revolution brought on by models that combine deep theoretical insight with deep practical knowledge and judgment. Existing publicly available models are lacking in all three departments, but getting better. When searching for useful connections between distant fields becomes cheap, even a low hit rate could produce an explosion of innovation. Even without new ideas (which will also be forthcoming...), the convex hull of existing science would push far beyond the status quo.