Lloyd Trefethen was born in 1955. He earned his bachelor’s degree from Harvard in 1977 and his doctorate from Stanford in 1982. After two postdoctoral years at the Courant Institute he was at MIT from 1984 to 1991, Cornell from 1991 to 1997, and has been at the University of Oxford since then, where he is Professor of Numerical Analysis and head of the Oxford Numerical Analysis Group. He is the author or coauthor of several books, including Numerical Linear Algebra and Spectra and Pseudospectra. MathSciNet has 137 items listed containing his name. He was made a Fellow of the Royal Society in 2005 and elected to the National Academy of Engineering in 2007. He is, at this very moment, the President of the Society for Industrial and Applied Mathematics. He is a person of eminence. It behooves us to pay attention to what people of eminence have to say; it is more likely to be edifying than the utterances of lesser mortals.
Since 1970 Trefethen has been writing thoughts on index cards, 3ʺ by 5ʺ at first and then 4ʺ by 6ʺ, which he has kept. Trefethen’s Index Cards is a collection of them. They are arranged by subject — among the Ms are Music, Memory, Misperceptions, and Mathematics — and chronologically within subjects. The book consists of 368 index-card sized pages, 4.5ʺ by 6.75ʺ. As an example, here is the entry on page 183 (the one exactly halfway through the book, on page 184, is too long to quote):
Putting caps on pens
I’m careful about putting caps on pens. My father is careless, so his pens dry out.
Maybe I’m too careful. Yesterday I went into the secretary’s office when no one was there and noticed a box of a dozen felt-tip pens on the disk (sic). The cover of the box had an illustration of one of the pens uncapped and ready to write. This bothered me. The sight of an uncapped, unattended pen was not a pretty one.
The only writings that I know of that resemble those in the book are the series of Trivia by Logan Pearsall Smith (1902, 1921, 1931), another American émigré to England (and the brother-in-law of Bertrand Russell), which, because of their breathtaking style, had an edition published as recently as 1984. Professor Trefethen’s style, though polished, is not as brilliant as Smith’s but his subjects have weightier content.
A few of the entries went over my head, as (p. 260) “If no parameters in the world were very large or very small, science would reduce to an exhaustive list of everything” but most were interesting, insightful, entertaining, charming, or several of the above. Readers will find many items that will induce the reaction “Yes, that’s so — I never thought of it that way.” Such items are good to have, and I’m glad that Professor Trefethen, unlike the rest of us, did not let them go unrecorded. He is a smart man, and smart people have things to tell us that we do well to listen to.
Reviewers have the prerogative of trying to show that authors aren’t all that much better than they are. On page 288, Professor Trefethen writes “Are there examples of great errors in mathematics, of big ‘theorems’ that were believed for years until an error in the proof was found? I can’t think of any.” I can — the Four Color Theorem, “proved” in 1879 and not demoted to a conjecture until 1890.
Woody Dudley, who retired from teaching in 2004, will never attain eminence. However, the profession of mathematics, like others, could not get along without its spear-carriers.