A very simple answer to a complicated question

Was maths invented or discovered?

The fact that 1 plus 1 equals 2, or that there’s an infinite number of primes, are truths about reality that held even before mathematicians knew about them. As such, they’re discoveries – but they were made using techniques invented by mathematicians. For example, according to Pythagoras’ theorem, the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. This is true for all right-angled triangles on a level surface, so it’s a discovery. Showing it is true, however, requires the invention of a proof. And over the centuries, mathematicians have devised hundreds of different techniques capable of proving the theorem. In short, maths is both invented and discovered.

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