Terence Tao about Math, Physics, AI

15. 6. 2025

https://www.youtube.com/watch?v=HUkBz-cdB-k

Interaction of disciplines ↓

Science in general is interaction between 3 things. The real world, what we observe of the real wolrd (observation) and mental models as to how we think the world works. We can’t directly access reality. All we have are observations, which are incomplete and they have errors. And then we have these simplified models sometimes making unrealistic assumptions (spherical cows in vacuum). 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 we stay within the model and we ask what are the consequences of that model? What observations, predictions would the model make of the future observations or past observations, does it fit observed data. There is symbiosis. Math can go from conclusions to theory and also from theory to all directions.

Really novel ideas? ↓

Real interaction is needed between things. Over time the observations and the theory and the modeling should both get close to reality. They are always far apart to begin with. One needs to push the other…

misc video