Affiliation when awarded Breakthrough Prize: Institut des Hautes Études Scientifiques
Citation: For work making a deep impact in a vast variety of mathematical disciplines, including algebraic geometry, deformation theory, symplectic topology, homological algebra and dynamical systems.
Acceptance Remarks: It is very hard, or maybe impossible to say what is the ultimate goal of mathematics. Are we creating new spaces? Finding precise words for old and new structures? Observing mesmerizing coincidences? For me, one of the most fascinating features of mathematics is the duality between space (geometry) and time (algebra). It is a constantly developing liaison, starting in the past with Cartesian coordinates, complex numbers, spectra in algebraic geometry, automorphic forms, and continuing now with homotopy, a new way of thinking, and with numerous infinite-dimensional challenges coming from theoretical physics.