Asked by: Leah Victoria Smith, Hereford
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.
- What’s the simplest unsolved maths problem?
- Is there any point to finding ever-bigger prime numbers?