I met Marcus du Sautoy at the Royal Society in London once: I hasten to add that I was a guest of Fellow Ian Mills (he of the 'New SI') to hear Marcus' talk. Marcus explained to Ian that he was succeeding Richard Dawkins as the Simonyi Professor for the Public Understanding of Science. I was half way through saying "Well, at least there's only one mathematics" when I realised this was not true. The Continuum Hypothesis stands beyond the reach of 'the axioms', it can either be a new axiom or not. That gives you two flavours of mathematics. Marcus said that real mathematics had been done down both tracks. I haven't seen any maths done down the 'assuming a third infinity' track. [ Can we prove that if Infinity1 =/= Infinity2, then 2^Infinity1 =/= 2^Infinity2 ? ] g