I couldn’t resist adding a little anecdote by way of a postscript to yesterday’s item about the the late Tom Lehrer. I didn’t know anything about this story until yesterday when I saw it as a thread on Bluesky (credit to @opalescentopal). The whole thread can be read here, so I’ll just give you a short summary and add a bit of context.
Tom Lehrer’s debut album, Songs by Tom Lehrer, released in 1953, contained a number called Lobachevsky. At concerts he would introduce this song with the words “some of you may have had occasion to run into mathematicians and to wonder therefore how they got that way”. If you don’t know the song then you can listen to it, for example, here. This song contains this verse:
I am never forget the day
I am given first original paper to write
It was on "Analytic and Algebraic Topology
Of Locally Euclidean Metrizations
Of Infinitely Differentiable Riemannian Manifolds"
Bozhe moi!
That’s relevant to what follows.
In 1957, while he was still working as a mathematician, Lehrer co-wrote a paper for the U.S. National Security Agency, with R.E. Fagan, under the title Gambler’s Ruin With Soft-Hearted Adversary, the full text of which can be found here. For those of you unaware, the Gambler’s Ruin is an important problem in the theory of probability. The paper was an internal document but was unclassified. It was later published, in 1958, with some modifications under the title Random Walks with Restraining Barrier as Applied to the Biased Binary Counter.
The 1957 paper was filed away, attracting little attention until 2016 when the person who wrote the Bluesky thread looked at it and noticed something strange. The reference list contains six papers, indexed numerically. References [1], [2] and [4] are cited early on in the paper, and references [5] and [6] somewhat later. But nowhere in the text is there any mention of reference [3]. So what is reference [3]? Here it is:
(It’s a pity about the spelling mistake, but there you go.) Although the song Lobachevsky had been written a few years before the Gambler’s Ruin paper, and had proved very popular, nobody had spotted the prank until 2016. This is episode is testament to Lehrer’s mischievous sense of humour, and to his patience. He made a joke and then kept quiet about it for almost 60 years, waiting for the payoff!
P.S. The Lobachevsky reference was omitted from the modified paper published in 1958.
In the Dark 