Terence Tao

It should also be a pleasure to read, motivated, be adaptable to generalize to other things.

It's the same in many other disciplines, like coding.

There's a lot of analogies between math and coding.

I like analogies, if you haven't noticed.

But, you know, like, you can code something spaghettical that works for a certain task, and it's quick and dirty and it works, but there's lots of good principles for writing code well so that other people can use it, build upon it, and so on, and has fewer bugs and whatever.

And there's similar things with mathematics.

sort of the programs or in this case the proofs but also the different languages maybe that's a different notation or whatever to use to accomplish a different task yeah you learn a lot I mean it may seem like a frivolous exercise but it can generate all these insights which if you didn't have this artificial objective to pursue you might not see

Yeah.

Well, as I said, I mean, what I find most appealing is connections between different things.

So if the pi i equals minus one.

So yeah, people are like, oh, this is all the fundamental constants.

Okay, that's, I mean, that's cute.

But to me, the exponential function was to measure exponential growth.

Compound interest or decay, anything which is continuously growing, continuously decreasing, growth and decay or dilation or contraction is modeled by the exponential function.

Whereas pi comes around from circles and rotation.

If you want to rotate a needle, for example, 180 degrees, you need to rotate by pi radians.

And I, complex numbers, represents the swapping between rule and imaginary axes of a 90 degree rotation, so a change in direction.

So the exponential function represents growth and decay in the direction that you already are.

When you stick an i in the exponential, instead of motion in the same direction as your current position, it's motion at right angles to your current position, so rotation.

And then so, e to the pi i equals minus one tells you that if you rotate for time pi, you end up at the other direction.