Customer Rating: 
Summary: A nice book
Comment: This is a very nice and elegantly written book. The proofs of the theorems selected as great are presented in simple terms. They require no more then high school mathematics(although some of these proofs are not rigorous, for example on the summation of infinite series). The only problem I can see is with the choice of the theorems (too many from geometry) but of course that is a matter of taste. I would have given the book five stars if there had been a chapter on Godel's theorem in it.
Customer Rating:
Summary: Excellent history of great mathematical minds
Comment: William Dunham is the author of several books on the history of mathematics.
In this brief history of mathematics and mathematicians, the author, rather than writing a little bit about a large number of mathematicians, has provided longer treatments of a few. The 'few', naturally, being the most talented/famous from the earliest days. To include:
Hippocrates
Euclid
Archimedes
Heron
Cardano
Newton
The Bernoullis
Leibniz
Euler
Cantor
This book spends some time building and describing mathematical problems and concepts in ways that the average reader will understand. He also relates biographical information about the people who worked on them. Some of the history is quite fascinating, such as the practice in the middle ages of public challanges between mathematicians to solve problems, much like a gun fight of the Wild West.
This would make a good volume in any library.
Math teachers should own (and read) this.
Customer Rating:
Summary: Journey through Genius
Comment: I think this book is a masterpiece! W. Dunham describes the history of mathematics by going over some of the most remarkable theorems and ideas along with their inventors and proofs. The book begins on Hippocrates' quadrature of the lune and ends on Cantor's infinite sets and one may just stand and wonder at the genius and creativity of people described in the book. The book is fun to read as it includes aspects satisfiable to all kind of readers and knowledge seekers. It talks about theorems, etc. providing lot of insight into problem solving and tools present in math. It describes biographies of key mathematicians in the history along with many stories. The book is also able to inspire people who would like to occupy a place in history, as I'm pretty sure the creativeness and inventivenss of people included may be very inspiring for others.
Customer Rating:
Summary: nice look at mathematics and important theorems
Comment: Dunham has done an excellent job of taking us through the history of mathematics providing a context with the civilization of the time. He shapes his production around what he considers to be the great theorems of mathematics.
The order of presentation is chronological. Early on we see great admiration for Euclid and his "Elements" as two of Euclid's theorems appear on the list, a proof of the Pythagorean theorem and the proof that there are infinitely many primes. Euler and Cantor are also honored with two theorems included among the collection.
However there is more to Dunham's presentation than just the proofs. We find other related results by these masters and other great mathematicians that were their contemporaries. He shows reverence for Newton. Gauss and Weierstrass and others are mentioned but none of their theorems are highlighted.
It is not his intention to slight these great mathematicians. Rather, Dunham's criteria seems to be to present the theorems that have simple and elegant proofs but often surprising results. His coverage of Cantor is particularly good. It seems that he is most knowledgeable about Cantor's mathematics of transfinite numbers and the related axiomatic set theory.
For a detailed description of the chapters in this work, look at the detailed review by Shard here at Amazon. I found this book to be well written and authoritative and learned a few things about Euler and number theory that I hadn't known from my undergraduate and graduate training in mathematics. Yet I did not give the book five stars.
There are a couple of omissions that I find reduce it to a four star rating. My main objection is the slighting of Evariste Galois. Galois was the great French mathematician who died in a duel at the early age of 21 in the year 1832. Yet, in his short life he developed a theory of abstract algebra seemingly unrelated to the great unsolved questions about constructions with straight edge and compass due to the Greeks and yet his theory resolved many of these questions. I was very impressed in graduate school when I learned the Galois theory and came to realize that problems such as a solution to the general 5th degree equation by radicals and the trisection of an arbitrary angle with straight edge and compass were impossible.
Now, Galois theory is certainly beyond the scope of this book but so is non-Euclidean geometry and aspects of number theory and set theory that Dunham chooses to mention. He spends a great deal of time on Euclid's work and the various possible constructions with straight edge and compass.
Also, in the chapter on Cardano's proof of the general solution to the cubic, he also presents the solution to the quartic and refers to Abel's result on the impossibility of the general solution to the quintic equation. This would have been the perfect place to introduce Galois who independently and at the same time in history proved the impossibility of solving the general quintic equation by radicals. Oddly Galois is never once mentioned in the entire book.
In discussing number theory and Euler's contributions, the theorems and conjectures of Fermat are mentioned. This book was written in 1991 and it presents Fermat's last theorem as an unproven conjecture.
Andrew Wiles presented a proof of Fermat's last theorem to the mathematical community in 1993 and after some needed patchwork to the proof, it is now agreed that Fermat's last theorem is true. There are a number of books written on Fermat's last theorem including an excellent book by Simon Singh. It seems that Dunham's book is popular and has been reprinted at least 10 times since the original printing in 1991. It would have been appropriate to modify the discussion of Fermat's last theorem in one of these reprintings.
Customer Rating:
Summary: Christmas gift
Comment: This is a great book for a math nerd. My daughter is pursuing her advanced degree in mathematics and this was a special request from her. She loves it!
Summary: A nice book
Comment: This is a very nice and elegantly written book. The proofs of the theorems selected as great are presented in simple terms. They require no more then high school mathematics(although some of these proofs are not rigorous, for example on the summation of infinite series). The only problem I can see is with the choice of the theorems (too many from geometry) but of course that is a matter of taste. I would have given the book five stars if there had been a chapter on Godel's theorem in it.
Customer Rating:
Summary: Excellent history of great mathematical minds
Comment: William Dunham is the author of several books on the history of mathematics.
In this brief history of mathematics and mathematicians, the author, rather than writing a little bit about a large number of mathematicians, has provided longer treatments of a few. The 'few', naturally, being the most talented/famous from the earliest days. To include:
Hippocrates
Euclid
Archimedes
Heron
Cardano
Newton
The Bernoullis
Leibniz
Euler
Cantor
This book spends some time building and describing mathematical problems and concepts in ways that the average reader will understand. He also relates biographical information about the people who worked on them. Some of the history is quite fascinating, such as the practice in the middle ages of public challanges between mathematicians to solve problems, much like a gun fight of the Wild West.
This would make a good volume in any library.
Math teachers should own (and read) this.
Customer Rating:
Summary: Journey through Genius
Comment: I think this book is a masterpiece! W. Dunham describes the history of mathematics by going over some of the most remarkable theorems and ideas along with their inventors and proofs. The book begins on Hippocrates' quadrature of the lune and ends on Cantor's infinite sets and one may just stand and wonder at the genius and creativity of people described in the book. The book is fun to read as it includes aspects satisfiable to all kind of readers and knowledge seekers. It talks about theorems, etc. providing lot of insight into problem solving and tools present in math. It describes biographies of key mathematicians in the history along with many stories. The book is also able to inspire people who would like to occupy a place in history, as I'm pretty sure the creativeness and inventivenss of people included may be very inspiring for others.
Customer Rating:
Summary: nice look at mathematics and important theorems
Comment: Dunham has done an excellent job of taking us through the history of mathematics providing a context with the civilization of the time. He shapes his production around what he considers to be the great theorems of mathematics.
The order of presentation is chronological. Early on we see great admiration for Euclid and his "Elements" as two of Euclid's theorems appear on the list, a proof of the Pythagorean theorem and the proof that there are infinitely many primes. Euler and Cantor are also honored with two theorems included among the collection.
However there is more to Dunham's presentation than just the proofs. We find other related results by these masters and other great mathematicians that were their contemporaries. He shows reverence for Newton. Gauss and Weierstrass and others are mentioned but none of their theorems are highlighted.
It is not his intention to slight these great mathematicians. Rather, Dunham's criteria seems to be to present the theorems that have simple and elegant proofs but often surprising results. His coverage of Cantor is particularly good. It seems that he is most knowledgeable about Cantor's mathematics of transfinite numbers and the related axiomatic set theory.
For a detailed description of the chapters in this work, look at the detailed review by Shard here at Amazon. I found this book to be well written and authoritative and learned a few things about Euler and number theory that I hadn't known from my undergraduate and graduate training in mathematics. Yet I did not give the book five stars.
There are a couple of omissions that I find reduce it to a four star rating. My main objection is the slighting of Evariste Galois. Galois was the great French mathematician who died in a duel at the early age of 21 in the year 1832. Yet, in his short life he developed a theory of abstract algebra seemingly unrelated to the great unsolved questions about constructions with straight edge and compass due to the Greeks and yet his theory resolved many of these questions. I was very impressed in graduate school when I learned the Galois theory and came to realize that problems such as a solution to the general 5th degree equation by radicals and the trisection of an arbitrary angle with straight edge and compass were impossible.
Now, Galois theory is certainly beyond the scope of this book but so is non-Euclidean geometry and aspects of number theory and set theory that Dunham chooses to mention. He spends a great deal of time on Euclid's work and the various possible constructions with straight edge and compass.
Also, in the chapter on Cardano's proof of the general solution to the cubic, he also presents the solution to the quartic and refers to Abel's result on the impossibility of the general solution to the quintic equation. This would have been the perfect place to introduce Galois who independently and at the same time in history proved the impossibility of solving the general quintic equation by radicals. Oddly Galois is never once mentioned in the entire book.
In discussing number theory and Euler's contributions, the theorems and conjectures of Fermat are mentioned. This book was written in 1991 and it presents Fermat's last theorem as an unproven conjecture.
Andrew Wiles presented a proof of Fermat's last theorem to the mathematical community in 1993 and after some needed patchwork to the proof, it is now agreed that Fermat's last theorem is true. There are a number of books written on Fermat's last theorem including an excellent book by Simon Singh. It seems that Dunham's book is popular and has been reprinted at least 10 times since the original printing in 1991. It would have been appropriate to modify the discussion of Fermat's last theorem in one of these reprintings.
Customer Rating:
Summary: Christmas gift
Comment: This is a great book for a math nerd. My daughter is pursuing her advanced degree in mathematics and this was a special request from her. She loves it!