Friday, September 11, 2020

217. William Wordsworth & } a number “n.”

Stumbled across this passage in the little book The Great Mathematicians (Herbert Western Turnbull):
… But the greatest figure of all was William Rowan Hamilton, who made two splendid discoveries, an early one in optics, on the Principle of Least Action, and later the Quaternions in algebra. He was born in 1805, and educated at Trinity College, Dublin, where at the age of twenty-one he became Professor of Astronomy, continuing to hold the office until 1865, the year of his death. He was a poet, and a friend of Wordsworth and Coleridge, and between these three passed a highly interesting correspondence, dealing with philosophy, science, and literature.
Ah-ha! Just months earlier I read the following lines in Wordsworth’s Prelude (1850):

‘Tis told by one whom stormy waters threw,
With fellow-sufferers by the shipwreck spared,
Upon a desert coast, that having brought
To land a single volume by chance,
A treatise on Geometry, he wont,
Although of food and clothing destitute,
And beyond common wretchedness depressed,
To part from company and take this book
(Then first a self-taught pupil in its truths)
To spots remote, and draw his diagrams
With a long staff upon the sand, and thus
Did oft beguile his sorrow…

Alas, according to a footnote in the Norton Critical Prelude, the shipwrecked mathematician is not Hamilton, but John Newton. & John is not either of the Newtons mentioned in The Great Mathematicians, nor was John Newton acquainted with Wordsworth or Coleridge; Dorothy Wordsworth read his book & shared Newton’s geometry anecdote with her brother.

Hamilton’s thesis, Account of a Theory of Systems of Rays has to do with how light travels. According to Turnbull, Hamilton’s thesis has the “hard-won distinction of triumphantly surviving the latter-day revolution caused by the theory of Relativity.”

My expectation was that Turnbull’s The Great Mathematicians would end with Albert Einstein, but no; it ends with Srinivasa Ramanujan, whose “greatest monument is a theorem that he discovered jointly with [Harold Godfrey] Hardy, dealing with the partitions of a number n.” As I understand it, Ramanujan worked his way through the history of mathematics by his own genius. Based on “the contents of his mystifying notebooks” he was invited to England where he became a Fellow of Trinity College and of the Royal Society. “Unhappily,” writes Turnbull, “[Ramanujan’s] residence in England destroyed his health, and the year after his return to India he died.”

[ Image: Ramanujan's geometric construction for approximately "squaring the circle" lifted from the blog post "Who Was Ramanujan?" by Stephen Wolfram. ]

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