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Don't Explain Maths; it's Easier to Explain how Hard it is to Explain

One of my interests is improving the public understanding of science and maths. There's so much maths that would be really useful to programmers, AI people, cognitive scientists and others — if only somebody would explain it in ways they can understand. So I want to show you an n-Category Café thread, Gerbes in the Guardian. Compare the Guardian science-writer's explanation near the top of the thread with those of John Baez and Urs Schreiber further down. Which is better?

As Todd Trimble says in the same thread:

The idea is supposed to be that math is "cool", in a way — at least we use a bunch of cool-sounding and mysterious words — but please let'ss keep it at arm's length, because you have to be a genius (or weirdo) or something to actually understand it. It's hard to find the idea in mass culture that anyone does math because it's fun.