The Little Book Of Mathematical Principles, Theories, & Things, by Robert Solomon
This book is a quintessential example of the sort of odd and quirky writings on mathematics and the principles of mathematics that I greatly enjoy . Written by someone who has an obvious appreciation of how odd mathematics is and how mathematicians are human beings just like everyone else, this book is the sort of work that makes for excellent reading for someone who wants to get a basic understanding of the chronology of mathematical discovery. Most of the writing is on a basic level, but some of it is a bit more technical, and the author shows himself to be fond of certain topics relating to prime numbers, the nature of axioms and postulates, and the importance of wrestling with conjectures and having a sound logical basis for mathematical enterprise in the face of contradictions. This book may not be of interest to everyone, but for those people who are interested in the subject material of the book, there is much to enjoy here in a small package of just over 200 quarto-sized pages, much worthwhile information to serve as a thought-provoking read or as a reference.
In terms of its contents, this book consists of a variety of mathematical principles, theories, and other things that were discovered or published organized in a roughly chronological fashion. Each of these entries includes the place and time when it was published or discovered, a title, the name(s) of the person or people involved with the discovery, a short summary of the matter, and then a short explanation full of details and sometimes drawings and figures and equations that takes up a page or two. The topics chosen show certain interests that the author has, including a contrast between the graphical approach of the ancient Babylonians and the algebraic approach of the Arabs, quarrels over what mathematical notation was viewed as legitimate (negative numbers and i and irrational and transcendental numbers among those aspects of mathematics viewed with some suspicion over history). The author also talks about the quirks of mathematicians and the way in which mathematics found itself involved in matters of public policy, showing the field to be far more relevant than is often viewed to be the case by a large proportion of the population who has little interest in mathematics, especially the more esoteric aspects of it.
For those who do find this book to be of interest, though, there is much that is worthy of investigation. For example, the author notes that there are seven millennium problems, one of which (the Poncarè conjecture) has been proven, and some of which involve fluid dynamics and quantum theory as well as the probablistic resources required to solve issues of public interest. This last one is something that the author appears a bit ignorant about, as the “traveling salesman problem” is one that has received a great deal of interest from logistic companies and is something I have personal experience in and will likely discuss at some point in greater detail. As someone who is perhaps a bit more of a math nerd than most people, I suppose, I found it worthwhile that the author’s interest in mathematical problems intersected not only my own interests but also my own personal experience and expertise, which was greatly pleasing to me. If you have a high degree of interest in and knowledge of mathematics, this is likely a book whose witty and humane touch will likely greatly please you as well, if you are anything like I am, at least.
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