Group, ring, field... These words are omnipresent in modern mathematics and one would be hard pressed to find an area of mathematics which does not make at least some use of them. Such has been the impact of abstract algebra in mathematics ever since it has been formalised a few centuries ago. As a result, it has possibly been one of the most studied areas of mathematics and this has given rise to a great deal of fascinating results.

Among the most beautiful of these is Wedderburn's theorem. As you may know, a ring is a set with two binary operations, usually denoted and , which are roughly similar to the usual multiplication in the integers for example. In particular, the addition is always commutative (it does not matter in which order we add things) but the multiplication need not be. What Wedderburn's theorem states is that, if we assume that the ring is finite and that every element except has a multiplicative inverse (another element such that their product is ), the ring must be commutative. This provides an unexpected and fascinating link between two seemingly unrelated concepts relating to the ring: it's multiplication and the number of elements in the ring itself. As such, it has become one of the most celebrated theorems in algebra and has been proved in many different ways (Maclagan Wedderburn himself, who, in 1905, was the first to prove it, provided no less than 3 different proofs of it).

So, if you are intrigued by this and want to know more, come to MS.04 tonight (Thursday) at 7:30 PM as we guide you through what is possibly the most elegant proof of this famous theorem, assuming no background in algebra whatsoever, after which we head on to the pub.