Simon Donaldson develops in 1982-1983, in his doctoral thesis at Oxford, a new class of invariants for 4-dimensional differentiable manifolds, constructed from the study of moduli spaces of solutions to the Yang-Mills equations (gauge theory), borrowed from theoretical physics. The work reveals that there exist manifolds that are topologically identical in dimension 4 but do not, however, admit the same differentiable structure — a phenomenon that does not occur in any other dimension — and opens a deep, lasting connection between differential topology and mathematical physics. Donaldson received the Fields Medal in 1986.