In a previous post I quoted C. S. Lewis on the value of reading old books. He argued that every generation has its blind spots, and one way to see past the contemporary blind spots is to read old books. In that spirit, here are some of my favorite old math books.

- Inequalities by Hardy, Littlewood, and Pólya. First published in 1934, second edition 1952.
- A course in modern analysis by Whittaker and Watson. First published 1902, fourth edition 1927.
- An Introduction to Probability Theory and Its Applications by William Feller. First edition 1950, third edition 1968.

These books contain useful facts hard to find elsewhere. More importantly, they embody an approach to mathematics that has fallen out of fashion. I believe the latter is what Lewis had in mind, not merely reference books but books that encapsulate the perspective of an earlier generation.

I don’t know the first two books but I have the Feller book. It comes as two volumes, one on discrete distributions and one on continuous distributions. Both are peppered with very interesting examples that make make the reader think.

A couple of weeks ago, I found some nice gems from a book sale at our public library. The Hamilton County Public Library (Cincinnati area) is reputed to be in the top three busiest public libraries, which made for a great treasure trove. I don’t have anything quite 1900 vintage, but among others I found

How to Study, How To Solveby Dadourian, which focuses on profitable behavior and discipline generally, and specific to studying mathematics. To quote:>More importantly, they embody an approach to mathematics that has fallen out of fashion.

Would you elaborate, John? I’m wondering what you had in mind.

Sue, part of what I had in mind was “hard analysis” versus “soft analysis.” Hard analysis looks at specific functions and studies them in detail, produces quantitative estimates, etc. Soft analysis is more abstract and existential. Hard analysis likes to strengthen conclusions. Soft analysis likes to weaken hypotheses. (See Jenga mathematics.) The books I listed are on the hard side whereas soft analysis has been more fashionable, though the pendulum is starting to move back toward the hard side.

I read your Jenga math post and the comments there. This sort of thing makes me feel like I’m not a “real mathematician”. It’s above my head… If you have an example you think I’d get, I am interested in how math books have changed over time.

Sue, here’s an example. Two thirds of the book “A course in modern analysis” listed above is about special functions: the gamma function, Bessel functions, etc. Years ago it was common for math students to study that book cover to cover. Now most math majors no nothing about special functions, except maybe the gamma function, but they probably do know something about basic topology, groups, etc. It’s important that students learn these abstract unifying concepts, but it’s a shame that a lot of classical mathematics isn’t taught any more.

That sounds like a bit of a split between ‘engineering/applied math’ and ‘pure math’, or do I have the dimension wrong? I got a math BA (pure, not applied) at U of Michigan in 79. Don’t know if that tells anything about my background or not.

I have a very cool old mathematics book you may like . Fabulous cover showing an Arab on a camel – with palm trees. It is embossed on the cloth. Background is Black. Title of the book is First Course in THE NEW MATHEMATICS by Edgerton and Carpenter. The letters and the scene are in red and green. Hardback, dated 1934. In really good condition.

If you are interested, I will send you a picture.

I have found an old Math book at a charitable yard sale. Was curious if there was a market for it.

‘Ray’s Mathematical, Ray’s New Higher Arithmetic’

Copyright 1880

Preface marked as Cinninnati, July, 1880

If you know where I might get some information on this book, or others, please let me know.

Thank you,

Carol Cook

I believe that book is popular in some homeschool circles, perhaps in modern editions.

Helen Plum Library, here in Lombard, Illinois got rid of all their old math books except for one: ‘Mathematics for the Million’ by Hogben. It seems like the rest were published within the last fifteen or twenty years. Old books can be better, perhaps because the authors didn’t grow up watching TV. Newton N. Minow referred to television as a “vaste wasteland.” However, if you want to learn about new technology or the latest discoveries in science, try something more current.

The math we learn in school is about 100 back. Grad students get to move up a few more decades eventually getting to the now.

Those old math books know nothing of computers or calculators. One of my kids was taught fractions on a calculator. Please don’t do this to a kid. It ruins them.

I have all three and would add the collection of problems by Polya and Szego.