The study of Diophantine Equations, that is, equations to which we want to find integer solutions, is one of the oldest and most fruitful areas of number theory. Many famous problems, such as Fermat's Last Theorem or Catalan's Conjecture ("the only two consecutive powers are 8 and 9") are examples of Diophantine equations which have sparked great interest and, in some cases, entire areas of mathematics which have been developed in order to solve them (ring theory and elliptic curves being two notable examples).

The name is derived from Diophantus of Alexandria, a greek mathematician and philosopher who wrote "Arithmetica", a book about solutions to such equations (notably to the Pythagorean equation: ). It's in the margin of this book that Pierre de Fermat wrote his famous conjecture some 1300 years later, which itself was only solved about 350 years after that, giving an idea of the number of centuries the study of such problems spans.

Join us at 7:30 PM in MS.03 this Monday as Alex Oakes takes us through an introduction to this fascinating subject, followed by a short break at the Grad before we head on to "Topological Banana".