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If you want a mathematically treatment, The Pleasures of Counting is an excellent book about this and sundry other marvelous topics.


Even the index of The Pleasures of Counting has its gems. (A footnote remarks that a discarded alternative for the title had been The Joy of x.)

On having broken 4-rotor Naval enigma decisively (p.389): "A more demonstrative age might have celebrated such a victory with a massive piece of statuary, perhaps showing a handsome but well-draped female representing Science with the armoured God of War prostate under her foot, or perhaps the giant figures of Blackett and Turing gazing forever over the Western Approaches."

see also https://news.ycombinator.com/item?id=23597523




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