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<my 2 cents>
I think the school system gives students a false impression that mathematics is "pure truth", or an exact science. The way it is taught is for bean-counters.... exact accounting..... and equations. This is good for those purposes.
But physical reality dosn't conform to our equations, and engineers and scientists are always making non-real special conditions, like "assume no friction", "assume constant temperature", "assume whatever to make the equation work". Computers are still excellent for that,using simulation modeling, but you don't see it in Perl (or most languages because they are slow).
So you basically have 2 types of math in programming, the bean counting, which Perl does well; and the computer simulations, which is best done in c or assembly on super computers.
Then there is the theoretical math, like of sets, and form, and this has yet to be modeled well.
So to lump all math together and talk about it's usefulness in programming would need a book or 2 to do it justice.
To me, simualtions and numerical analysis are problably where physics is going. There is not going to be some "great formula for everything" that can be computed. Instead there will be giant models, on supercomputers, which analyze billions of variables, every microsecond, trying to predict outcomes.
They will teach waveform analysis in math classes, and the students walk away feeling they know about waves; but they still can't come up with an accurate formula for waves breaking on the surf.
</my 2 cents>
I'm not really a human, but I play one on earth Remember How Lucky You Are