I often hear people say things like “the universe is made of math” or “faster than light travel has been mathematically proven to be impossible”. This sort of thing always annoys me, particularly when it comes from educated people.

Mathematics is a descriptive language, that attempts to model reality so closely that it can be used to calculate physical values accurately without direct measurement. It can also be used to make predictions that can be verified through experimentation.

Kurt Gödel’s work implies that this may be an inherently flawed approach to some enterprises; it’s possible that any language that can approach an accurate representation of reality must necessarily allow paradoxes (like Russell’s Antinomy, for instance). The answer to some questions may well be mu rather than true or false.

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But math never “proves” anything. That’s not what math is for! Logic, reason, experimentation, observation, measurement – these are the sources of proof. Reason and logic can employ mathematics, just as a book can employ the English language – but when experimentation disproves a prediction made by a descriptive system like mathematics, we revise the math; reality does not magically reorganize itself to fit our incorrect description.

Some people believe that the Universe is comprised of a systematic computational architecture, that we perceive as physical reality. See Rechnender Raum, for example. Those people sometimes also believe that once we’ve got math really and truly figured out, our math will be equivalent to or congruent with reality. But nobody sane thinks we’re at that point yet, not even Wolfram, so the idea that something can be “mathematically proven” to be true in the real physical world is a conceit.