Why the world has no place for ugly truths

November 29, 2013

If G. H. Hardy is much thought about these days (and beyond fellow mathematicians, he probably isn’t), it is as much for his dazzling aphorisms as his dizzying flights in the upper reaches of number theory.

“There is no permament place in the world,” he declared, “for ugly mathematics”. This has led to Hardy being characterised as an aesthete in the Wildean mould, compounded by C. P. Snow‘s dark references to his sexuality (in the foreward to Hardy’s autobiographical A Mathematician’s Apology, Snow alludes to “intense affections” for young men, “absorbing … exalted” but – to Snow’s no doubt immense relief – “non-physical”).

But the equivocation is doubly misplaced.

Whatever relationship there may have been between Hardy the gay man and Hardy the mathematician, it was not as a green-carnation sporting, fin de siecle aesthete that he penned the line about the beauty of enduring mathematics.

It was instead an appreciation of the fact that in mathematics, elegant simplicity often goes hand-in-hand with profundity. One of the most beautiful of all formulations is Euler’s equation, both elegant and eloquent:

The Euler equation, linking fundamental mathematical constants

The physicist Richard Feynman, coming across this at the age of 14, copied it into his notebook under the heading, “The most remarkable formula in math”.

The intimate connection between beauty and truth is a point which Ian Stewart makes in his engaging history of the subject of symmetry, Why Beauty is Truth.

“Beauty,” he observes echoing Hardy, “is more important than mere truth.” There can be multiple ways of describing the world, all of which may be true – but only some offer insight.

The founding role that symmetry plays in current research in maths and physics tells us that the universe is essentially beautiful.

No mere superifical decoration, no retreat into hyper-aestheticism; beauty trumps truth. How beautiful, Mr Hardy!

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