Giuseppe Persiano 🇮🇹 🇪🇺

Some thoughts on AI and Theory. 1. To a first approximation, theoretical computer science has been organized around a few major open questions. Much of our work has been motivated by developing approaches to answer these questions. 2. Such “problem-motivated” work has often led to theory-building focused on identifying a general principle that unifies a class of theorems. But much of that theory-building also involved proving new, difficult theorems. 3. Thus, while it’s true that problem-solving was strongly correlated with building understanding, drawing connections, and eventually developing general theories, it would be disingenuous not to admit that our community, perhaps disproportionately in retrospect, focused on and celebrated problem-solving. This was not arbitrary, and was quite defensible. Being able to make progress on central technical questions usually correlated with taste, creativity, persistence, and depth of understanding. Much of our reward structure therefore implicitly relied on the fact that producing an important proof was good evidence that someone possessed these harder-to-observe qualities. 4. It seems likely that we will soon have AI tools available to us that can prove many such theorems in a short time. The cost of obtaining proofs for well-posed mathematical questions will likely fall dramatically. The “scarce” intellectual work will likely shift both upstream: to questions, models and theories, definitions, and conjectures, and downstream: to interpretation, synthesis, explanation, and theory-building. 5. But as long as we believe in humans being meaningfully in charge of our collective decisions and fate, building human understanding of our science (and of science more generally) will remain an essential goal. I plan to expand on this important aspect soon. 6. Historically, finding a solution to an important problem and understanding its significance, implications, and connections were entangled. Finding a proof usually required researchers to discover the right concepts along the way. A dramatic reduction in the time and effort required to prove theorems could break that coupling. We could end up with many more true statements and proofs without a commensurate increase in understanding. Converting an abundance of proofs into human understanding may become one of the central challenges of our field. 7. As a result, I expect the high-level goals of theoretical computer scientists to change. In fact, the advent of powerful theorem provers might help us construct new theories and explore new models far more easily and rapidly, and significantly expand the domains where our models and theories apply. In that sense, the space for theoretical work may significantly expand rather than contract. 8. There’s a high human cost to the disruption that we are likely heading into. Many in our field, and in mathematical communities more broadly, are coming to terms with it. The range of opinions and reactions among mathematicians and theoretical computer scientists is a natural part of this evolution in our thinking as we collectively work through it. Some concrete efforts (including one at @SimonsInstitute) are already underway to think through the immediate scientific and institutional questions arising during this transition.