We do curiosity-driven theoretical research. We build theories—concise mathematical descriptions of patterns—and identify their testable consequences. We pursue the most intriguing patterns, without concern for their usefulness, which leads to the most transformative breakthroughs.
Understanding the relations between different branches of pure mathematics, and creating overarching theories that bind them together.
Tackling big questions about the fundamental forces, symmetry and information, and the intimate interplay between physics and mathematics.
Developing mathematical foundations for life and artificial life, machine intelligence, and other emergent phenomena that defy reductionism.
Developing mathematical models of markets, innovation and organisations, so that we can predict them and enhance them through interventions.