Terence Tao

You get as many zeros as ones, as many ones as twos.

There's only a very small fraction of numbers that exhibit bias.

It's a very useful law.

This is why, for example, we can do polling.

Like if you want to poll 300 million Americans and see what they're thinking, you can't poll 300 million Americans, but you can poll 1,000, 2,000.

And the law of large numbers actually tells you that as long as you poll a very representative set of people, the outcome of that poll is actually pretty close 99% of the time to the general population.

That would be about 10 to the 10.

So I guess 10 billion.

Right.

Yeah.

So applied math, it's still not quite directly applied to the real world.

That's what scientists and engineers do.

But it's about the mathematics that is of practical value to those scientists.

So, for example, an atmospheric scientist might care about predicting climate or the weather.

And applied mathematicians might develop the software or the equations to actually model the atmosphere or oceans.

They may not actually work directly with real data.

They may only work with sort of test data or something.

And it still has a lot of theory to it, but it's sort of intermediate between the pure mathematicians and scientists and engineers.

Yeah.

Yeah.