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.

Read the rest of this entry »

Final countdown

October 3, 2009

Frankly panicking about final OU exam, due in a couple of weeks. It all seems so obvious in tutorials or when looking at the unit handbooks, but in timed practice exams all seems to go out of the window.

Tutorials have been first-rate, and any failing are entirely due to my own stupidity. Am humbled by Hardy’s achievements in Mathematician’s Apology – only Underwood’s brilliance prevented him from scoring top marks in the tripos – and his greatest achievement, he says, was to “collaborate with Underwood and Ramanujan on something like equal terms”. (Ramanujan, of course, being the brilliant Indian mathematician who, upon being told on his hospital bed that the number of the taxi cab which had delivered his visitor to him was1729, observed this was a particularly interesting number, being the least number which could be expressed as the sum of two different cubes (1729 = 13 + 123 = 93 + 103).

Read the rest of this entry »

Dirac – quantum genius

March 27, 2009

Delighted to have just received a copy of the new biography of Paul Dirac, The Strangest Man. Apart fromthe ocassionally technical Dirac: The Man and His Work, there doesn’t appear to be much available on the life of this most eccentric of mathematical physicists.

P A M Dirac

P A M Dirac

Dirac has long been one of my maths heroes (along with Richard Feynman and G H Hardy).

I’ve struggled with his lectures on quantum mechanics and general relativity and unfamiliar as I am with the mathematics, found them strangely fascinating, in particular where Dirac in a tour de force derives fundemental physical properties from the form that certain equations take.

Of course, it was an analysis of his wave equation for an electron that led Dirac to posit the existence of the positron, the antimatter particle which was only discovered experimentally four years later in 1932.

UPDATE (June 2): An article in New Scientist magazine claims the elusive monopole, also predicted by Dirac, may have been discovered. It is only the latest in a line of claimed discoveries (such as this in 2003 – registration required), but this time round seems convincing.