Albert Einstein is famously quoted as saying
"How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?" - Albert Einstein
Mathematics is what happens when you observe that the world is regular and works in a regular fashion. Two eggs, and two eggs more always make four eggs, except when you drop one. Addition, subtraction, multiplication, division, fractions, Algebra, Calculus...all these are things we SEE in the world, and were developed (theoretically) in order to correspond to the world we live in. Why is it that all these crazy scientists/mathematicians think that just because we took an idea (algebra -- what's still true if I don't tell you what numbers you're using) and extended it a little (abstract algebra--what happens when I don't tell you which operators/number systems you're using) that it wouldn't still be talking about the elements of the world? Are they surprised to find out that because the things we work (eggs, apples, $) with and the operators we normally care about (+,-,*) exhibit regularity (Commutativity, Associativity), that there are other parts of the world (electromagnetism, Relativity, QM, QCD) that exhibit the same conformance to mathematics that mathematics was originally designed to reproduce? It's not like we can't learn almost everything we needed to know about Groups/Rings/Cohomologies from basically looking at numbers of eggs or apples. Reimann geometry is just regular Geometric theorizing, applied to a sphere (or hyperbola) rather than to rectilinear space. So what's shocking?
What's shocking to me is the number of people who think that deduction is more certain/reliable than induction, or that induction isn't the base of our collective comprehension of the world. I mean, I suppose that there are some folks who gain some status from assuming that their abstract theorizing is somehow higher/better/purer than the observational induction made by a car mechanic. But their status aside, it doesn't make it true.