#eulersidentity — Public Fediverse posts

Following my earlier posts on historical aesthetic judgements of Euler's identity, I just found another one, in Constance Reid's popular mathematics book ‘From Zero to Infinity’ [https://en.wikipedia.org/wiki/From_Zero_to_Infinity], where it is called ‘elegant’. This appears on p.165 of the 1964 third edition. Can anyone confirm if it appears in the first or second editions? (1955, 1960)

I am still interested in other aesthetic judgements of Euler's identity before 1988 (I know of few, although one more than I knew of yesterday), and especially before 1940 (I currently know of none).

Incidentally, as printed in the third edition of Reid's book, the equation would evoke a shudder from any typographer (see attached image).

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RE: https://mathstodon.xyz/@ajcain/115831036668298738

Actually, I would be interested in any examples (other than Kasner & Newman 1940 and Le Lionnais 1946, 1948) of aesthetic judgements of Euler's identity \(e^{i\pi} + 1 = 0\) before 1988, when it appeared (if the form \(e^{i\pi} = -1\)) in a questionnaire about beautiful results posed David Wells in the ‘Mathematical Intelligencer’. It was rated highest by respondents to the questionnaire, after which — possibly in part because of which? — it seems to have been much more commonly called beautiful.

In the four decades between Le Lionnais's essays and Wells's questionnaire, the closest approach to aesthetic praise of Euler’s equation that I located is a passing reference in Arthur C. Clarke's (1917–2008) novel ‘The Fountains of Paradise’ (1979), in which a character considers it to be ‘profound yet beautifully simple’.

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Today's post from @paysmaths @Theoremoftheday was on #EulersIdentity or #EulersEquation \(e^{i\pi} + 1 = 0\) (also given in various equivalent forms), which prompts me to talk about a little historical mystery.

Euler's identity is often held up as as exemplar of mathematical beauty, or called the most beautiful or most elegant equation in mathematics.

But when I was researching my book ‘Form & Number: A History of Mathematical Beauty’ [https://archive.org/details/cain_formandnumber_ebook_large], I was unable to find *any* aesthetic judgement of the equation before the 1940 book ‘Mathematics and the Imagination’ by Kasner & Newman [https://archive.org/details/mathematicsimagi0000edwa_l2s0], where it is called ‘elegant’ (p.103). The earliest explicit judgements of it as *beautiful* that I found are in essays by Le Lionnais in the late 1940s.

Does anyone know of any aesthetic judgements of Euler's equations before 1940? (I know of earlier non-aesthetic judgements like ‘mysterious’ or ‘paradoxical’.)

(The history of aesthetic judgements of Euler's equation is on pp.835–9 of ‘Form & Number’, #OpenAccess at the link above.)

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