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).

There shall be a discussion group at the usual time and place this Monday (7:30 in MS.03) but we are not yet sure what the subject of the talk will be. Stay tuned for more details.

UPDATE: This talk has been rescheduled to the following Thursday, the 8th of May.

On August 8th 1900, in what was possibly the most famous lecture in the history of mathematics, the great David Hilbert set a list of 23 open problems that he deemed important enough to set the direction for mathematical research in the 20th century. These problems have all gained a special status in mathematical lore and have gained a great deal of attention during the past 100 years, leading to the resolution of many (though not all) of them.

Discussion Groups are back for term 3, starting with one of our trademark "Free-for-alls" this Monday at 7:30 in MS03: anyone is welcome to bring a piece of maths they find interesting/fun and hold a mini-discussion group about it (even as short as 10-15 minutes). Maths banter aplenty guaranteed, "then pub."