Last night we watched The Great Math Mystery, a NOVA episode on PBS television. It was excellent and I recommend it. It can be watched on-line here at least temporarily. There is a full transcript, too. The mystery is: Is math invented by humans, or is it the language of the universe? Reasons are given for both -- some math is invented and some is discovered. I believe the best answer came near the end. Math concepts such as numbers are abstracted by humans, but then they and their relationships are found to apply beyond their origin and lead to further discoveries.
The topics include the Fibonacci sequence, the number pi, Galileo's mathematics of falling bodies, Maxwell's equations, Marconi's discovery of radio telegraphy, the quantitative intelligence of lemurs, and the difference between pure math and applied math. Regarding the last, pure math is exact and imaginative but becomes much more useful via approximating with short-cuts such as done by engineers.
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