Written: June 11, 2023
I found out about Nick Trefethen's charming book (or rather pamphlet, not counting the index, it is 70 pages), quite by accident. Leafing through the latest issue of SIAM Review (June 2023), I came across Robert Corless's short but very insightful review, and decided that I must read it.
The title was really appealing to me, since I love to hate the famous (or rather infamous) Hardy's Apology with his snotty pure-math-elitism and bragging how useless his work is. I also knew that Nick Trefethen is the "applied analog" of G.H. Hardy, and a great expositor and story-teller (and I recommended his essays to my Spring 2014 grad class).
Hence I was curious to read about Nick's point of view, and at the same time find out about his life. I immediately ordered a copy from amazon, and indeed loved it. I found out that several people who were important to me were also important to Nick. For example, my good friend Dave Robbins taught him, way back in high-school, complex variable! Also my former Temple colleague, the brilliant Donald J. Newman, is mentioned very favorably, and confirmed what I already knew, that he was grossly under-rated. Also my great hero, I.J. Good (Jack Good) is raved about, as well as other people I knew and respected: Steve Maurer, Gene Golub, and Peter Henrici (whose gorgeous "formal" proof of Lagrange inversion I exposited here).
But perhaps even more interesting were the last few pages, where he laments that computational mathematicians are still underdogs, and the "cool crowd" (that garner Fields and Turing and Able prizes) consists mostly of pure people. That's why Rob Corless said that this is an important book for "working philosophers of science". He is probably right, but sociologists of mathematics should also pay attention, since mathematicians are humans (and hence mammals), and they have their own (distorted) pecking order.
Not that computational mathematicians are saints. Many of them are "pure mathematicians wannabees", and very narrow minded. (see e.g. here)
One thing I strongly disagree with Nick is his identifying himself as a "continuous mathematician". Whether he likes it or not, he is discretian (and hence, in my value system, one of the "good guys"). On page 15 he defines Numerical Analysis as follows
"Numerical analysis is the study of algorithms for the problems of continuous mathematics."
Just because you apply it to so-called continuous mathematics, does not make you continuous! Anyone who develops algorithms (for digital computers) is a discrete mathematician. Also Linear Algebra, SVD notwithstanding, is part of discrete mathematics, even if it is over the so-called real numbers.
Nick laments about the indifference of "pure" mathematicians to numeric mathematics, but I was also disappointed that such a great Numerical Giant seems oblivious, and has so little use for, the (at least as) equally important part of computational mathematics, called symbolic computation, that I am sure numerical people can use to improve their algorithms.
But the most disappointing part of this wonderful book is that it is so hard to find. I can easily afford 36 dollars, but poor undergraduate and graduate students, may not, and they should benefit the most from this gem. Since I feel very strongly about it, and until SIAM and/or Nick will make it "open access", I went through the trouble of producing a scanned copy. [Olivier Gerard noticed that pages 2 and 3 were missing: they are here.]
If you like it, and can afford 36 dollars, you should get the nice paperback, not just an ugly printout! Enjoy!
Added June 20, 2023: Read Mizan Khan's insightful remarks