Terence Tao

but nothing that big.

And so I personally find once you finalize an infinite statement, it does become much more intuitive and it's no longer so weird.

Yeah.

The downside is that the finalized proofs are just much, much messier.

So the infinite ones are found first, usually, like decades earlier.

And then later on, people finalize them.

Right.

So I think science in general is interaction between three things.

There's the real world.

There's what we observe of the real world, our observations.

and then our mental models as to how we think the world works.

So we can't directly access reality.

All we have are the observations, which are incomplete, and they have errors.

And there are many, many cases where we want to know, for example, what is the weather like tomorrow, and we don't yet have the observation that we'd like to predict.

And then we have these simplified models, sometimes making unrealistic assumptions, you know, spherical cow type things.

Those are the mathematical models.

Mathematics is concerned with the models.

Science collects the observations and it proposes the models that might explain these observations.

What mathematics does is we stay within the model and we ask, what are the consequences of that model?

What observations, what predictions would the model make of future observations?