Kenneth A. Ribet

Works in arithmetical algebraic (or arithmetic), a field of number theory that uses tools from algebraic geometry to study diophantine problems. Such problems arise when one seeks to identify all solutions to an equation (or family of equations) that are whole numbers, fractions, or other quantities in number theory. For example, whole number solutions to the diophantine equation X2 + Z2 -2Y2 correspond to triples of perfect squares, like (1,25,49), in which the middle entry is the average of the first and third entries. Although the field of arithmetic uses many technical tools of recent vintage, its study is motivated by some of the oldest problems in mathematics. In the last decade, the most notable success of arithmetic was the proof of Fermat''s Last Theorem, a simple statement about perfect powers whose demonstration had eluded mathematicians for over 350 years.