Terence Tao

You have to either go to extremely insane particle accelerations or the early universe or things that are really hard to measure in order to get any deviation from either of these two theories.

to the point where you can actually figure out how to combine them together.

But I have faith that we've been doing this for centuries.

We've made progress before.

What often happens is that when the physicists need some theory of mathematics, there's often some precursor that the mathematicians worked out earlier.

When Einstein started realizing that space was curved, he went to some mathematician and asked, is there some theory of curved space that mathematicians already came up with that could be useful?

He said, oh yeah, I think Riemann came up with something

Wiemann had developed Riemannian geometry, which is precisely a theory of spaces that are curved in various general ways, which turned out to be almost exactly what was needed for Einstein's theory.

This is going back to Wiemann's unreasonable effectiveness on mathematics, I think.

The theories that work well to explain the universe tend to also involve the same mathematical objects that work well to solve mathematical problems.

Ultimately, they're just both ways of organizing data in useful ways.

Yeah, that was a leading candidate for many decades.

I think it's slowly falling out of fashion because it's not matching experiment.

what that reality really is like this is why analogies are so important you know i mean so yeah the round earth is not intuitive because we're stuck on it um but you know but you you know but round objects in general we have pretty good intuition a little bit uh and we have interest about light works and so forth and like it's it's actually a good exercise to actually work out how eclipses and phases of the sun and the moon and so forth can be really easily explained by by by round earth and round moon you know um

models.

And you can just take, you know, a basketball and a golf ball and a light source and actually do these things yourself.

So the intuition is there, but you have to transfer it.

Right, yeah.

So modern science is maybe, again, a victim of its own success is that

in order to be more accurate, it has to move further and further away from your initial intuition.