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100 Great Problems of Elementary Mathematics
Problems that beset Archimedes, Newton, Euler, Cauchy, Gauss, Monge and other greats, ready to challenge today's would-be problem solvers. Among them: How is a sundial constructed? How can you calculate the logarithm of a given number without the use of logarithm table? No advanced math is required. Includes 100 problems with proofs.
416 pages, Paperback
First published June 1, 1965
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Displaying 1 - 7 of 7 reviews
April 3, 2017
2.5 stars.
First of all, this is a book for mathematicians (I am one myself), with full, detailed proofs of theorems (not problems) making its core. I actually enjoyed the selection of theorems (4 stars), but I do not know what "elementary mathematics" means to the author; here we have infinite series, Buffon's needle problem, the impossibility of solving the quintic, the Hermite-Lindemann transcendence theorem... interspersed with easier problems.
In fact, this is a book more about proofs than about the problems they arise from, which are concisely stated in one line or two -sometimes too much concisely. You could not use this book as a problem book for gifted students or math-olympiad participants, because a) most "problems" are really hard theorems and b) they are not sufficiently explained by their statements.
I also have complains about both the writing and general scheme of this work: the explanations seem obscure and difficult to me (even those about things I know well), which is the real pitfall of the book: I found myself skipping most of the paragraphs; the notation is more proper of the beginning of the 20th century (this is no surprise, the bulk of the book was written before 1932); several proofs are lacking rigour (e.g. introducing a variable X such that (X-1)^2=X^2, (X-1)^3=X^3); there are confounding mistakes (e.g. using i where it should be -1); and several results should had been presented in reverse order for them to make sense.
In short: A book that lies a lot in its title ("elementary" does not check, "problems" does not check, "solutions" should not be relegated to the second title line); a book to check for wonderful problems and some good proving ideas, but not worthy of being thoroughly studied.
First of all, this is a book for mathematicians (I am one myself), with full, detailed proofs of theorems (not problems) making its core. I actually enjoyed the selection of theorems (4 stars), but I do not know what "elementary mathematics" means to the author; here we have infinite series, Buffon's needle problem, the impossibility of solving the quintic, the Hermite-Lindemann transcendence theorem... interspersed with easier problems.
In fact, this is a book more about proofs than about the problems they arise from, which are concisely stated in one line or two -sometimes too much concisely. You could not use this book as a problem book for gifted students or math-olympiad participants, because a) most "problems" are really hard theorems and b) they are not sufficiently explained by their statements.
I also have complains about both the writing and general scheme of this work: the explanations seem obscure and difficult to me (even those about things I know well), which is the real pitfall of the book: I found myself skipping most of the paragraphs; the notation is more proper of the beginning of the 20th century (this is no surprise, the bulk of the book was written before 1932); several proofs are lacking rigour (e.g. introducing a variable X such that (X-1)^2=X^2, (X-1)^3=X^3); there are confounding mistakes (e.g. using i where it should be -1); and several results should had been presented in reverse order for them to make sense.
In short: A book that lies a lot in its title ("elementary" does not check, "problems" does not check, "solutions" should not be relegated to the second title line); a book to check for wonderful problems and some good proving ideas, but not worthy of being thoroughly studied.
September 13, 2020
Mathematical problems have beset people for centuries. The 100 Great Problems of Elementary Mathematics collects various puzzles and their solutions. The book is fascinating. It covers a wide range of topics in six major categories. Some of the standout problems are the Hermite-Lindemann Transcendence Problem, the Fermat Equation, and the Heptadecagon Construction.
February 17, 2014
An absolutely wonderful resource for mathematics teachers, students and enthusiasts. Each problem is interesting by itself, be it in a historically and/or conceptually way, and the proofs are clearly presented. This book is an excellent addition to any library, as it is not only a mathematics book, but also a general cultural resource that will delight readers. Anyone interested in how major mathematical problems were first posed and eventually solved, be them arising from a practical need or from a purely intellectual exercise, will enjoy this book.
June 17, 2019
In general, hard to understand/follow. This may be due to the fact that it was translated, but nonetheless, I was rather unsatisfied.
November 24, 2025
100 Great Problems of Elementary Mathematics is presented as a collection of interesting "apparently simple" problems and "surprising and enlightening" solutions. Unfortunately it is nothing like that. The problems aren't particularly interesting in themselves, often consisting of great blurbs of algebraic manipulations, and the solutions are presented in an exceptionally tedious way, quite similar to a Wikipedia article on mathematics.
The book consists of poorly explained problems, followed by a dive into details which very quickly becomes extremely tedious to read, the kind of "drunk on mathematics" waffling that 100 years after this book was produced is still seen in online forums, or the ludicrously unreadable mathematics articles on Wikipedia. Very little attempt is made to interest or even enlighten the reader.
For example, on page 36 we have "Cauchy's Mean Theorem". The entire explanation of what this is, is "The geometric mean of several positive numbers is smaller than the arithmetic mean of these numbers". The author doesn't even bother to explain what either an arithmetic or a geometric mean is, or even to give an example, but in true Wikipediot style, immediately dives into "The proof of the theorem that will be presented..." Of course it is completely useless unless you know what an arithmetic and geometric mean are, and the proof given is not even the simple and enlightening one, but tedious pages of algebra.
I definitely don't recommend this book to anyone looking for a collection of amusing or interesting recreational mathematics problems, and if you just want to dive into proofs of theorems, there are much more satisfactory books than this one too.
The book consists of poorly explained problems, followed by a dive into details which very quickly becomes extremely tedious to read, the kind of "drunk on mathematics" waffling that 100 years after this book was produced is still seen in online forums, or the ludicrously unreadable mathematics articles on Wikipedia. Very little attempt is made to interest or even enlighten the reader.
For example, on page 36 we have "Cauchy's Mean Theorem". The entire explanation of what this is, is "The geometric mean of several positive numbers is smaller than the arithmetic mean of these numbers". The author doesn't even bother to explain what either an arithmetic or a geometric mean is, or even to give an example, but in true Wikipediot style, immediately dives into "The proof of the theorem that will be presented..." Of course it is completely useless unless you know what an arithmetic and geometric mean are, and the proof given is not even the simple and enlightening one, but tedious pages of algebra.
I definitely don't recommend this book to anyone looking for a collection of amusing or interesting recreational mathematics problems, and if you just want to dive into proofs of theorems, there are much more satisfactory books than this one too.
September 19, 2023
Cool book, and it’s certainly aimed at a specific target audience, presumably higher education. Definitely above my education level but I still enjoyed reading through it and the problems that were selected. The very liberal use of greek letter notations in paragraphs mixed in with text, was sometimes confusing and difficult to read.
There is some history in here too as the author chose some problems to be those that were drastic breakthroughs of their time and what their purpose and underlying reasoning was. It could also be called 100 influential discoveries, or proofs that impacted our society.. etc.
There is some history in here too as the author chose some problems to be those that were drastic breakthroughs of their time and what their purpose and underlying reasoning was. It could also be called 100 influential discoveries, or proofs that impacted our society.. etc.
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July 12, 2017Oops, bit off more than I can chew. I'm choking. Help.
Displaying 1 - 7 of 7 reviews