(For spectacular contributions to number theory and related fields, major advances on undamental conjectures, and for settling FermatĀ“s last theorem.)
(For his contribution to elementary particle theory, including recognition of the role played by spontaneous symmetry-breaking in analogy with superconductivity theory, and the discovery of the color symmetry of the strong interactions.)
(For designing and developing novel chemical reactions which have opened new avenues to the synthesis of the synthesis of complex molecules, particularly polysaccharides and many other biologically and medicinally important compounds.)