As anyone who fought their way through analysis in their first term will know: very little in maths comes easy. The most fundamental and fundamentally obvious properties of spaces can be hidden in a world of axiomatic obfuscation, leaving you wondering whether such an obvious truth should be a fair assumption to make. More often than not the answer is "No!" "...and go sit in the corner 'til you learn to be a proper mathematician!"- these dubious assumptions need to be proved from first principles, and it is not likely to be easy.

But in this difficulty often lurks a surprising elegance, elucidating truth from dry and unforgiving axioms tells deeper truths about our system, minimising assumptions to make a cohesive whole devoid of redundancies.

That n different points determine (lines with) at least n-1 different slopes, with equality only possible when n is odd, is one such assumption: conjectured in about 1970, it took 12 years to find a proof. Join us as Cosmin Davidescu takes us through the surprisingly beautiful argument that won the day- a must for fans of all things combinatoric or geometrical.

Then pub.

MS.03 7:30-9:00ish