Brady Haran interview with Terence Tao
He's talking about the New New Math: My comment : 9:47 He's analogous to a Category Theorist then? Douglas Hofstadter too, see What is Formal Logic? Subscribe to Numberphile . See Brady Haran Interview with Hugo Duminil-Copin . Andrej Bauer just gave a lecture to his students on Arithmetic of Sets, or Cartesian Closed Categories or something. I'm sure students would be much less put off by logarithms if they learned this first, ... See Logic and Sets by Andrej Bauer and Davorin Lešnik. The name of the game is to explain this oft-commented-upon wrinkle in Arithmetic: In other words, why is 0⁰=1? I mean 0¹=0 so why is a higher exponent less than a lower one? I remember the first time I tried to use higher-order functors in Moscow ML, I wrote a functor which took a pair of functors as an argument and somehow applied the first one to the second. It was something like a successor function and a zero element, but completely abstract. It was based ...