One day a mathematician doesn’t know a thing. The next day they do. In between they made no observations with their senses of the world.
It’s possible to make progress through theoretical reasoning. It’s not my preferred approach to the problem (I work on a heavily empirical team at a heavily empirical lab) but it’s not an invalid approach.
One day a mathematician doesn’t know a thing. The next day they do. In between they made no observations with their senses of the world.
It’s possible to make progress through theoretical reasoning. It’s not my preferred approach to the problem (I work on a heavily empirical team at a heavily empirical lab) but it’s not an invalid approach.
I agree, and I was thinking explicitly of that when I wrote “empirical” evidence and predictions in my original comment.