system
Given the following post, respond as if you're commenting on Reddit:
human
Why can math predict physics and new scientific discoveries, and what are the philosophical consequences of this?

Some laws of physics were discovered years before their empirical observation by mathematical calculus. How can it be that by a mere syntatic operation on some formulas we can deduce fundamental proprieties of the world?
gpt
> Some laws of physics were discovered years before their empirical observation by mathematical calculus.

I would argue that this is simply a false historical statement. 

Now, to be sure, there have been many cases in which *predictions* were made on the basis of very high-level mathematical manipulations of formulas, fields, etc. But these manipulations were based in physical principles; they weren't *sui generis*. 

Now, how can mathematics do *that*? Because (when practiced correctly), mathematical manipulations are truth-preserving: you take in a true physical statement and build as much mathematics as you want on it and you'll still have a true physical statement. So, someone like Einstein can develop a radical mathematical framework out of the *physical* symmetries establish by the light and equivalence principles, and if those principles are true, than all of the consequences he can deduce from them using pure mathematics ought to be as well. 

Whether that's a particularly accurate presentation of Einstein's methodology is worth questioning, but it is certainly more accurate than the idea that he created SR or GR out of pure mathematics: the existence of those symmetries is a synthetic claim about the physical world, and you need those symmetries (or something that entails them) to get GR off the ground.