Mathematics: Its Content, Methods and Meaning

Dover has released all three volumes of the original in an affordable single volume paperback. Although the book is necessarily uninformed by developments since the 1960s, it is a solid and challenging introduction to mathematics useful to the motivated high-school student. It is consciously informed by a Marxist philosophy of mathematics which may be unfamiliar to some readers. The authors believe that mathematics is less about an ideal world of forms and more emergent from daily work. For this reason they reference their examples to practical examples of the sort popular in the Soviet Union in the 1960s taken from heavy industry. The section on computer technology, of course is useful primarily to the antiquarian. Because the authors are not excessively formal in the Western mode the student has to do extra work to derive results they illustrate with physical metaphors in some cases. There's also a certain motivation here to sing the praises of Russian mathematicians which is fortunately subordinated to the truth. As such, the book is a document from a period when Russia's greatness was based on its prowess in science and mathematics, prowess based on a universal availability of public education. This resource has been sold to Western investors for pennies on the dollar with no plan to reproduce it for the next generation, which is rather sad.

I whole-heartedly agree with the other positive reviews offered here. There are only a few things I would like to add:(1) Popular math and science has become quite popular lately. I'm sure that there are many pop-math/pop-sci readers who would like a more 'meatier' treatment of math that still has an accessible style. If you're in that group, then this book is for you.It basically requires recollection of high school algebra and a willingness to wade through and learn some challenging material. I should add that the book looks intimidating in size but this is mostly due to the fact that Dover has bound 3 volumes as 1 (which is actually a great deal for readers).(2) I can't think of too may books that can, with effort, take a novice through the bulk of a college/university level math curriculum.(3) This book contains material by 2 of the greatest mathematicians/scientists of all time: Andrei Kolmogorov (famous for his work on probability and information theory as well as Kolmogorov Complexity/Algorithmic Information Theory) and I. M. Gelfand (for his work on mathematical physics). The book is worth buying for that reason alone.

It is a wonderful book. It reminds me of "The Feynman Lectures" in that it focuses on understanding, is (relatively) accessibly, has an incredible depth, and in that it covers an amazing amount. It includes "real" instruction, and you would be able to "do problems" after reading the book, although the real focus is more on understanding/ conceptual stuff.

In addition to my previous review, concerning the contents, here are a few additions on physical aspects.This 1999 paperback edition has all three volumes in one binding. The paper is thinner so the book is less bulky. Page number resets at the beginning of volume 2 and 3. (not renumbered.) Thus the book content is not altered from the 2nd edition (three volumes set) from MIT Press in 1969.One major change is that there is one index at the end of the book which covers all three volumes. The volume is indicated together with the page number. This improves the convenience.

Many mathematics and engineering books today require "relatively modest background and mathematical maturity," and the text goes with mathematical formalism and compact descriptions. However, this series (three books) is a collection of chapters on single topic, written by top Russian mathematicians in plain language and vivid illustrations. Bright high school students should be able to read them, but the material is no kids stuff, in a sense that every chapter gives at least some real feeling of the topic. I recommend this series only to those who are seriously interested in mathematics but looking for the friendly version of the real mathematics. I think the title describes this.Among the three books, I like Volume 2 the best, because Chapter 10 is on prime numbers (Mardzanisvili and Postnikov), 11 on probability theory (Kolmogorov), 12 and 13 on approximation of functions and numerical aspects, and these match with my interests the best. This volume also includes differential equations, culculus, complex analysis, etc.Volume 1 and 3 contain analysis, topology, algebra, geometry, etc. At this paper edition price, all three are worth keeping.A small caveat is that my review and contents description is based on the original edition by MIT press in 1960s. I assumed that second edition did not reorganize the general construction of the books.