The mathematical framework of the three-body problem is absolutely historical. The Birthday Competition1 occurred exactly as described, down to the unsigned manuscripts identified by epigraphs; several of the authors, in fact, have never been identified even to this day. The manuscript concerned in this story has borrowed its title from one of those.
The competition was organised by Gösta Mittag-Leffler (1846–1927)2 under the auspices of King Oscar II of Sweden; Mittag-Leffler’s villa still exists and is now a famous mathematical institute. The announcement of the competition in the mathematical journal Acta Mathematica is accurately reproduced, and the end result of the competition was historically just as described in the book. There was in fact a further development; Poincaré discovered that his prize-winning paper contained an error, which he rectified after all the copies of Acta Mathematica had already been printed; he insisted on paying himself for them all to be reprinted, which cost him all of his prize money. The events concerning the supposed solution of Lejeune-Dirichlet (1805–1859) to the n-body problem and his deathbed confidences to Leopold Kronecker (1823–1891) also occurred as told.
Arthur Cayley (1821-1895) and Grace Chisholm (1868–1944) were really members of the Cambridge Mathematics Department during the period described; Cayley’s defence of teaching Euclid and Chisholm’s departure to Germany in order to write a thesis are factual. Karl Weierstrass (1815–1897) and his famous student Sonya Kovalevskaya (1850–1891) were real people, and Kovalevskaya was, as described, the first woman professor of mathematics in Europe. Henri Poincaré (1854–1912) was of course one of the greatest mathematicians of his time. The n-body problem was a burning subject of research in the 1880s, and Poincaré’s work on it was seminal; it is still a most popular research subject today. As Poincaré showed, there can be no general solution in closed form; however, many astonishing special solutions have been found in recent years.3
The Victorian girls’ magazine The Monthly Packet really existed; it contained many mathematical tales and problems by Lewis Carroll (1832–1898), including the Tangled Tale reproduced in the book. For that matter, Oscar Wilde really did undertake to edit the magazine Woman’s World, and evinced a great interest in women’s clothing, being strongly against corsets and all other fashionable constrictions: ‘It is from the shoulders, and from the shoulders only,’ he wrote, ‘that all garments should be hung’.
A final remark: the answers to the tea-party charades are Vanes-sa (as in ‘weathervanes’ and ‘sa majesté’) Dun-can, Weather-burn, Miss-For-Scythe.
1 The book Poincaré and the Discovery of Chaos by June Barrow-Green contains a great deal of interesting scientific information as well as a historical chapter.
2 A website containing brief biographies of a great number of mathematicians can be found at http://www-gap.dcs.st-and.ac.uk/~history/BiogIndex.html
3 Moving versions of some of these special solutions can be charmingly visualised on the internet at http://www.cse.ucsc.edu/~charlie/3body/