“Dividends and Divisors Ever Diminishing”

Next Saturday is Bloomsday, the anniversary of the date on which the action of Ulysses took place. Mathematical themes occur occasionally throughout Ulysses, most notably in the penultimate episode, Ithaca, where the exchanges between Leopold Bloom and Stephen Dedalus frequently touch on weighty scientific matters. [Last week’s ThatsMaths post]


Joyce in Zurich: did he meet Zermelo?

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Leopold Bloom’s Arithmetical Adventures

As Bloomsday approaches, we reflect on James Joyce and mathematics. Joyce entered UCD in September 1898. His examination marks are recorded in the archives of the National University of Ireland, and summarized in a table in Richard Ellmann’s biography of Joyce (reproduced below)  [TM140 or search for “thatsmaths” at irishtimes.com].


Joyce’s examination marks [archives of the National University of Ireland].

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Motifs: Molecules of Music

Motif: A short musical unit, usually just few notes, used again and again.  

A recurrent short phrase that is developed in the course of a composition.

A motif in music is a small group of notes encapsulating an idea or theme. It often contains the essence of the composition. For example, the opening four notes of Beethoven’s Fifth Symphony express a musical idea that is repeated throughout the symphony. 


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A Glowing Geometric Proof that Root-2 is Irrational

Tennenbaum-00It was a great shock to the Pythagoreans to discover that the diagonal of a unit square could not be expressed as a ratio of whole numbers. This discovery represented a fundamental fracture between the mathematical domains of Arithmetic and Geometry: since the Greeks recognized only whole numbers and ratios of whole numbers, the result meant that there was no number to describe the diagonal of a unit square.

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Mathematics at the Science Museum

The new Winton Gallery at London’s Science Museum in South Kensington holds a permanent display on the history of mathematics over the past 400 years. The exhibition shows how mathematics has underpinned astronomy, navigation and surveying in the past, and how it continues to pervade the modern world [see TM139, or search for “thatsmaths” at irishtimes.com].


Central Display at the Science Museum

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Marden’s Marvel

Although polynomial equations have been studied for centuries, even millennia, surprising new results continue to emerge. Marden’s Theorem, published in 1945, is one such — delightful — result.


Cubic with roots at x=1, x=2 and x=3.

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Stan Ulam, a mathematician who figured how to initiate fusion

Stanislaw Ulam, born in Poland in 1909, was a key member of the remarkable Lvov School of Mathematics, which flourished in that city between the two world wars. Ulam studied mathematics at the Lvov Polytechnic Institute, getting his PhD in 1933. His original research was in abstract mathematics, but he later became interested in a wide range of applications. He once joked that he was “a pure mathematician who had sunk so low that his latest paper actually contained numbers with decimal points” [TM138 or search for “thatsmaths” at irishtimes.com].


Operation Castle, Bikini Atoll, 1954

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