Littlewood defines a Miscellany as “a collection without a natural ordering relation” (p. 23). This book does not have a natural order, but it does have a distribution: roughly 1/3 biographical and autobiographical writings about Littlewood, 1/3 mathematical expository papers, and 1/3 anecdotes, jokes, and bons mots. It is nominally a popular math book, although while reading you are liable to turn a corner and run headlong into an integral sign or a gamma function. The book was originally published in 1953 as A Mathematician’s Miscellany, but Littlewood kept collecting stories to add to it, and after Littlewood’s death Béla Bollobás revised and expanded the book to produce this 1986 edition.
John Edensor Littlewood (1885–1977) and G. H. Hardy (1877–1947) were the two towering figures of British mathematics in the first half of the Twentieth Century, and were responsible for founding the British school of mathematical analysis. They began a collaboration around 1914 that lasted for 35 years (until Hardy’s death in 1947) and produced a hundred joint papers and one book (Inequalities, with George Pólya).
This is a very happy, cheering, and intellectually exuberant book. It is a very different book from Hardy’s memoir A Mathematician’s Apology, which I have always found very gloomy (except for the C. P. Snow Foreword). Littlewood’s is a good book for browsing; it’s full of funny and interesting things.
The autobiographical material is a memoir of Littlewood’s education and a memoir of his working methods. The Foreword to the present book is a 20-page biographical sketch by Bollobás.
The expository papers deal primarily with problems in applied mathematics. There is a very interesting essay titled “Large Numbers” in which Littlewood estimates the sizes of various very large things, such as the number of possible chess games, and looks into how unlikely so-called “amazing coincidences” really are. There’s also a long chapter on “Mathematics with Minimum ‘Raw Material’”, that discusses briefly a large number of essentially-mathematical problems that can be understood with no mathematical background, and often sketches their solutions. My favorite from the purely mathematical part of the book is a Proof Without Words (p. 54) of the theorem, useful in number theory, that f(x) = o(1) as x → ∞ and f '' = O(1) imply f ' = o(1).
The anecdotes deal mostly with Cambridge and Trinity College characters in the early 1900s, especially Hardy and Bertrand Russell. This is a now-vanished world that had its own language and customs, and many of the stories are difficult to interpret today, but most are very witty. Some of my favorites:
I once challenged Hardy to find a misprint on a certain page of a joint paper: he failed. It was in his own name: ‘G, H. Hardy’. (p. 56)
All Bertrand Russell said about their meeting (apart from how wonderful Einstein looked, and his wonderful eyes) was that Einstein told him a dirty story. I said that Einstein was well known for consummate tact in adapting himself to his company. (p. 130)
R. A. Leigh once asked in Hall what Hardy was like. My neighbour and I merely laughed. I should have said: ‘All individuals are unique, but some are uniquer than others.’ (p. 136)
Schoolmaster: ‘Suppose x is the number of sheep in the problem.’ Pupil: ‘But, Sir, suppose x is not the number of sheep.’ (I asked Prof. Wittgenstein was this not a profound philosophical joke, and he said it was.) (p. 59)
Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at MathNerds.org, a math help site that fosters inquiry learning.
Frontispiece; Preface; Foreword; 1. Introduction to A Mathematician's Miscellany; 2. Mathematics with minimum 'Raw Material'; 3. From the mathematical tripos; 4. Cross-purposes, unconscious assumptions, howlers, misprints, etc; 5. The zoo; 6. Ballistics; 7. The dilemma of probability theory; 8. From Fermat's last theorem to the abolition of capital punishment; 9. A mathematical education; 10. Review of Ramanujan's collected papers; 11. Large numbers; 12. Lion and man; 13. People; 14. Academic life; 15. Odds and ends; 16. Newton and the attraction of a sphere; 17. The discovery of Neptune; 18. The Adams-Airy affair; 19. The mathematician's art of work.