What we're about
We will be reading "Mathematics: Its Content, Methods, and Meaning" — A historical, anthropological, philosophical, and mathematical take on mathematics. It is a major survey of mathematics written in the Soviet Union in the 1950s. The explicit goal of the authors was to “acquaint a sufficiently wide circle of the ... intelligentsia with the various mathematical disciplines, their content and methods, the foundations on which they are based, and the paths along which they have developed.” No mathematical background necessary, just a curious and clever mind!
Each chapter covers a major branch of mathematics, but focuses on the fundamental concepts and most important results rather than upon detailed proofs. Importantly, there is a significant focus on the historical background to the development of a mathematical branch as well as the philosophical implications of the its major results. (Notably, in the chapter on Probability Theory: Andrey Kolmogorov, one of the greatest mathematicians of the 20th century, waxes philosophical for a few pages on the nature of “true” randomness.)
What others have to say about this book.
From the MIT Press: “This book undertakes the ultimate task of mathematical exposition, outlining the history and cultural significance of mathematical ideas and their continuous development from the earliest beginnings of history to the present day.”
Roger S. Pinkham from American Scientist: “The high quality of exposition, the unparalleled breadth, and the emphasis on concept rather than proof for proof's sake should do much to raise the level of mathematical literacy everywhere.”
What will be discussed during meetups?
We will discuss one chapter (or less) each meeting. Some of the questions we’ll discuss in our meetings: How did this branch of mathematics emerge? What were the historical conditions? How does this branch of mathematics relate to the ones that came before — where does it fit on the family tree of mathematics? What are the major ideas/theorems in the branch of mathematics and what are their philosophical implications? What applications arise out of this branch?
Perhaps we’ll go into some mathematical details if needed and desired, however that won’t be the focus (unlike in university math courses, where proofs of major theorems typically make up the bulk of learning material).
Who is this book for? How accessible?
"The intelligentsia of laymen who care to tackle more than today's popular magazine articles on mathematics will find many rewarding introductions to subjects of current interest." — The Mathematics Teacher
"There are proofs in these volumes, but usually they are presented only for the most important results, and even then to emphasize key areas and to illustrate the kind of methodology employed. . . . It is hard to imagine that any intelligent American with a curious mind and some good recollection of his high school and college mathematics would not find many entrancing discoveries in the intellectual gold mine that is this work." — The New York Times Book Review
It is highly accessible for motivated enthusiasts.
Now, those that are acquainted with a lot of the factual information in this book should also get some use out of this reading group. Since the book offers a very high-level overview of its subject matter, it may “perhaps help to remove a certain narrowness of outlook occasionally to be found in some of our younger mathematicians” (from the preface to the Russian edition of the book).
Where can you buy the book?
This is quite an easy book to find thanks to the English version being published by Dover Publishers (a fantastic publishing house for many reasons, one of them being their continuous effort to publish out-of-print masterful math books at very low prices). I found my copy at an Indigo several years ago. A lot of bookstores, if they have a mathematics section, will have a section for Dover books.
You can also buy online:
Also, a lot of the chapters are free to view on Google books: