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What do you think is the most mind-blowing concept in mathematics?

Asked by cockswain (15276points) April 11th, 2011

I was just watching a series of calculus videos on KhanAcademy.org, and over about 1hr he shows how the infinite series representation of sin x and cos x are closely related to the infinite series representation of e^x. e is a pretty wild number for many reasons, not the least being the fact that it’s derivative is e^x. Anyways, when one compares the infinite sums, a pattern emerges, and eventually Khan shows that e^(ix) = cos x + i sin x, where i is the imaginary number. Finally, e^(i pi) = -1. This is a pretty wild fact about the universe, that these numbers from several disciplines of mathematics can be drawn together for such a simple, elegant conclusion.

This is a seven part series. Here is part 6, where things start getting pretty interesting.

So that currently gets my vote for most fascinating mathematical concept. What do you think is the coolest thing?

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