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tdvance · #8 (**permalink**) 04-April-2008, 03:54 PM

Mathematics is amazing in that you can take some axioms that appear to hold in practice, do a lot of stuff on paper involving manipulating symbols without actually touching what you are modelling, derive some theorems, go out and measure things, and find out they agree with the theorem to many decimal places. Some author called it "the unreasonable effectiveness of mathematics". An example, take a rectangular patio. measure the two sides, square the lengths and sum them, then take the square root. A mathematical theorem says that this will be the diagonal length. Measure it, and find that it is right. In fact, if it doesn't come out right, it means you screwed up measuring!!!

Yes, if you use a poor-fitting model, it won't give the right results. But the fact is, good-fitting models have been found for so many things--Newton's "incorrect" mechanics is still good enough to put a man on the moon. The mathematical consequences of Einstein's general relativity give precise enough answers that GPS works--and we know this is not a complete model either because it contradicts Quantum Mechanics which also gives very accurate answers in its domain.

Roger Penrose suggested that mathematics is "unreasonably effective" because there is a "platonic world of mathematics" that exists independently of human mathematicians (i.e. if aliens did math, they'd come up with the same stuff, though with different names of course!), and that the universe's fundamental laws, whatever they are, are mathematically consistent.

Oh yeah, Hardy's own number theory research is today used in cryptography, so his ideal (a pun, an ideal being a mathematical object used in number theory) of non-usefulness didn't pan out even for his number theory work!