Theorems (and their proofs) are the building blocks of all Mathematics – in fact they ARE the whole of Mathematics.
But the concept of proof is barely mentioned in the school curriculum until Further Maths. Maybe it is thought to be too difficult or complex. It does not have to be.
Every GCSE Maths student is expected to learn Pythagoras’ Theorem. ‘In a right angle triangle the square of the hypotenuse (the longest side or side opposite the right angle) is equal to the sum of the squares of the other two sides.’ It is often written in shorthand as a² = b² + c².
But how many students (even at A-level) can prove it? There are many simple and elegant proofs. Have a go.