What does it feel like to invent math?
An exploration of infinite sums, from convergent to divergent, including a brief introduction to the 2-adic metric, all themed on that cycle between discovery and ...
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Take 1+2+4+8 and continue on and on adding the next power of 2 up to infinity. This might seem crazy, but there’s a sense in which this infinite sum equals -1. If you’re like me, this feels strange or obviously false when you first see it but I promise you, by the end of this video you and I will make it make sense. To do this, we need to back up, and you and I will walk through what it might feel like to discover convergent infinite sums, the ones that at least seem to make sense to define what they really mean, then to discover this crazy equation and stumble upon new forms of math where it makes sense. Imagine that you are an early mathematician in the process of discovering that 1/2 + 1/4 + 1/8 + 1/16, on and on up to infinity, whatever that means, equals 1, and imagine you n...
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Take 1+2+4+8 and continue on and on adding the next power of 2 up to infinity. This might seem crazy, but there’s a sense in which this infinite sum equals -1. If you’re like me, this feels strange or obviously false when you first see it but I promise you, by the end of this video you and I will make it make sense. To do this, we need to back up, and you and I will walk through what it might feel like to discover convergent infinite sums, the ones that at least seem to make sense to define what they really mean, then to discover this crazy equation and stumble upon new forms of math where it makes sense. Imagine that you are an early mathematician in the process of discovering that 1/2 + 1/4 + 1/8 + 1/16, on and on up to infinity, whatever that means, equals 1, and imagine you n...
