How is it that math, a product of the human mind, manages to describe the world so well? Perhaps because, when asking that question, we pick and choose just what aspects of the world we have in mind. Derek Abbot, an Australian engineer argues that math really isn't all the effective. As reported Phys.org:
So if mathematicians, engineers, and physicists can all manage to perform their work despite differences in opinion on this philosophical subject, why does the true nature of mathematics in its relation to the physical world really matter?
The reason, Abbott says, is that because when you recognize that math is just a mental construct—just an approximation of reality that has its frailties and limitations and that will break down at some point because perfect mathematical forms do not exist in the physical universe—then you can see how ineffective math is.
And that is Abbott's main point (and most controversial one): that mathematics is not exceptionally good at describing reality, and definitely not the "miracle" that some scientists have marveled at.
And some of us spend a lot of time dealing with phenomena that aren't handled very effectively by mathematics.
"Analytical mathematical expressions are a way making compact descriptions of our observations," he told Phys.org. "As humans, we search for this 'compression' that math gives us because we have limited brain power. Maths is effective when it delivers simple, compact expressions that we can apply with regularity to many situations. It is ineffective when it fails to deliver that elegant compactness. It is that compactness that makes it useful/practical ... if we can get that compression without sacrificing too much precision.