WHAT IS SCIENTIFIC BEAUTY, ANYWAY?

WHAT IS SCIENTIFIC BEAUTY, ANYWAY? Philip Ball asks how scientists define beauty (“We have to ask: what is this beauty they keep talking about?”). He posits that simplicity and symmetry go into a scientist’s idea of beauty. Ball describes two theorems that are considered to be beautiful but have ugly proofs. The first is Fermat’s Last Theorem, written in the margins of a book by Fermat in 1637. This wikipedia entry says: “Fermat’s Last Theorem… states that no three positive integers a, b, and c can satisfy the equation a to the nth power + b to the nth power = c to the nth power for any integer value of n greater than two [I can’t figure out how to write exponents so you will have to go to wikipedia to get the equation] . It is also known as “Fermat’s conjecture” because for 300 years nobody could prove that it was true. It was finally proved by Andrew Wiles in 1993. Ball calls the theorem “wonderfully simple and elegant”, but points out that the proof is 100 pages long. The second is the Four Color Theorem (wikipedia entry here). the theorem is simply stated, but Ball says that: “The current proof is ugly as heck – it relies on a brute-force exhaustive computer search….”