Join us for a talk of astonishing discoveries by John Cosgrave on one of Gauss’s most memorable and beautiful discoveries (with an extremely difficult proof) – his so-called ‘binomial coefficient congruence’. In Cosgrave’s words – “His original mod p theorem seemed a dead end until Karl Dilcher and I discovered the most general extended version of it (i.e., mod p^alpha, again for prime p = 1 mod 4, and all alpha = 2, 3, 4, … ). What I would like to attempt is not just to state what this general extension, but rather show how this extension first occured to us, before we eventually made a proof of it. Not even the mod p^2 extension had ever been guessed. All of this can be described in quite simple language.”