White Paper: “Mathematics of Intelligences 2024”
The quest to understand intelligence is one of the great scientific endeavors, on par with quests to understand the origins of life or the foundations of the physical world. Several scientific communities have made significant progress on this quest. Relevant fields like animal cognition, cognitive science, collective intelligence, and artificial intelligence (AI)—as well as the social and behavioral sciences—have generated a wild variety of new experimental and observational data. They have also built mathematical and computational models of impressive sophistication and performance. Yet these communities remain largely disconnected; in no small part, this is because they lack a common framework and a shared (mathematical) language.
The IPAM Long Program on the Mathematics of Intelligences (MOI) aimed to bring these communities together with mathematicians to work toward the mathematical foundations necessary for transformational advances in our understanding of natural and artificial intelligences. This white paper was drafted at the culminating retreat of the Long Program and synthesizes the view of the field developed by its core participants. That said, it is not meant to be a comprehensive account of everything that happened at the Long Program. Likewise, the views expressed here do not necessarily reflect the views of IPAM or all the authors.
“Intelligence” is an ambiguous term. It can refer to an “intelligent system,” as when we speak of an “artificial intelligence.” It can also refer more broadly to a general capacity; roughly speaking, something that enables (intelligent) systems to solve problems more easily, whether they be organisms, collectives, or artificial agents. Although the former usage is returning to prominence in the age of Large Language Models (LLMs), we will generally refer to “intelligent systems” rather than “intelligences” to avoid confusion.
We also (attempt to) avoid the anthropocentric bias that makes humans the paradigm of intelligence. MOI explored intelligence as a multifaceted, multiscale phenomenon; it is for this reason that the Long Program was called the Mathematics of Intelligences, with the final embracing this multiplicity and variety.
