Re: Does the universe care if mathematics even exists?

Interesting way to put it! I think that every physicist and mathematician would agree with you that the universe doesn't care one way or the other whether we know mathematics or use it. The universe runs on its own - our theories aren't to help it on its merry way, but simply to describe which way it is headed!

It is certainly true that we do not have the capability to model everything in the universe with mathematics - either the computational power or even the theories to effectively describe the processes. And it is also true that we never will be able to perfectly describe the motion of every particle (at least if our current understanding is true), because that would require us to turn the entire universe into a computer that describes itself. That would seem sort of pointless, wouldn't it?

However, to me - and to most physicists, I think - that is beside the point. The point of physics is to describe parts of the universe mathematically, to some reasonable approximation. That is, perhaps we can't predict where every atom in a mixture of gases will move in the next hour, but we can predict statistically how they will mix. We can't predict exactly which oxygen molecules will combust first as they enter a car engine, but we understand combustion well enough to build the engine. We can't predict the exact position of the planets over ten billion year timescales, but we can predict where they will be in ten years to very good accuracy, which is enough to send the Cassini probe to Saturn! Mathematics may be "labor-intensive" as you say, but it is also elegant and extremely effective at describing the universe around us, which has led to innumerable advances in human understanding! It is this power that answers your question as to why we persist - no other system of knowledge has ever been even close to this effective at describing the universe! So as an astrophysicist, I certainly trust math and continue to use it!

[I'll also point out a second use of mathematics, which is not "labor intensive," but still quite useful. Often it is useful to make "back of the envelope" estimates. These are simple estimates designed to illustrate the physical issues in a problem. In many back of the envelope calculations, one can use only algebra to obtain the answer. Even though the underlying physical theory may be quite complicated (e.g., general relativity or statistical mechanics), initial computations can be done quite simply to determine the extent of the problem, or even if there is a problem. Fellow Moderator]