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Thursday, February 21, 2019

A mathematical formula for sharing fair and square | Science - The Irish Times

Photo: Peter Lynch

That’s Maths: Even the naming of the Thue-Morse sequence is about fair play, says Peter Lynch, emeritus professor at UCD School of Mathematics & Statistics – he blogs at thatsmaths.com.

Sequencing is important in sports: penalty shoot-outs in football, service order in tennis tie-breaks and choice of colour in chess matches.
Photo: Clive Rose/Getty Images

It is common practice in science to name important advances after the first discoverer or inventor. However, this process often goes awry. A humorous principle called Stigler’s Law holds that no scientific result is named after its original discoverer.

This law was formulated by Prof Stephen Stigler of the University of Chicago in his publication “Stigler’s law of eponymy”. He pointed out that his “law” had been proposed by others before him so it was, in a sense, self-verifying. 

The Calculus Wars
Occasionally, mathematical inventions are made simultaneously by more than one person. Perhaps the greatest example is the formulation of calculus by Isaac Newton and Gottfried Wilhelm Leibniz. Jason Bardi, The Calculus Wars. The conflict between British and European mathematicians raged for decades before joint credit for independent discovery was accepted.

The Calculus Wars
The ensuing controversy over priority was described in a book by Jason Bardi, The Calculus Wars. The conflict between British and European mathematicians raged for decades before joint credit for independent discovery was accepted.
 
Axel Thue (1863-1922) and Marston Morse (1892-1977)
A remarkable numerical sequence that has been discovered several times by different mathematicians in different circumstances illustrates Stigler’s Law. It was originally called the Morse sequence when, in 1921, it was popularised by the American mathematician Marston Morse, who applied it in differential geometry. Today, it is usually called the Thue-Morse sequence: the Norwegian mathematician Axel Thue discovered the sequence while studying “combinatorics” on words; this was in 1906, well before Morse. But, more recently, the name Prouhet has been prefixed to the title of the sequence, which was first studied by Eugène Prouhet in 1851...

But what use is the Thue-Morse sequence? It arises in a remarkably wide variety of contexts. It is valuable in number theory, combinatorics, computer graphics, fractal geometry and equitable sharing. Let’s look at the last of these.

Source: The Irish Times