G.H. Hardy

"The beauty is the first test; there is no permanent place for ugly mathematics"  -- G.H. Hardy  

Above is a quote from Hardy's "Mathematician's Apology."  In it he speaks highly of two theorems that possess serious beauty of highest order that people, who possess no special mathematical equipment, with average intelligence can understand and follow (with some diligence, of course).  I concur with G.H. Hardy that people with inquisitive and curious mind from any field can enjoy and appreciate the proofs of following well-known theorems.  Enjoy!!!  

I have taken liberty to share two proofs taken from "A Mathematician's Apology" by G.H. Hardy.

• Euclid's proof of existence of an infinity of prime numbers.
• Pythagoras' proof of the irrationality of square root of two.