Terence Tao

So it unifies geometry through dilation and exponential growth, or dynamics, through this act of complexification, rotation by i. So it connects together all these fields of mathematics.

complex and the complex numbers, they're all considered almost, they're all next door neighbors in mathematics because of this identity.

Right.

Well, it's confirmation that you have the right concepts.

So when you first study anything, you have to measure things and give them names.

And initially, sometimes because your model is, again, too far off from reality,

you give the wrong things the best names.

And you only find out later what's really important.

Physicists can do this sometimes.

I mean, but it turns out okay.

So actually, with physics, so E equals mc squared.

So one of the big things was the E. So when Aristotle first came up with his laws of motion and then Galileo and Newton and so forth,

They saw the things they could measure.

They could measure mass and acceleration and force and so forth.

Newtonian mechanics, for example, I think it was MA, was the famous Newton's second law of motion.

Those were the primary objects.

They gave them the central building in the theory.

It was only later, after people started analyzing these equations, that there always seemed to be these quantities that were conserved, in particular momentum and energy.

And it's not obvious that things happen in energy.

It's not something you can directly measure the same way you can measure mass and velocity.