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The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities 1st Edition
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Top Customer Reviews
Of course, it is impossible to cover the entire range of mathematics in a book such as this but Dunham has chosen well. He sticks mainly to the fundementals of the major fields. In addition, his book reminds us that people with personalities have developed mathematics and that it's not a field created merely to strike fear into the hearts of schoolkids (and adults).
This book will always hold a special place for me: it was the catalyst for an epiphany. I had been teaching high school geometry for a few years when this book came out and I was very good at teaching the modern methods of proof and problem-solving. On the other hand, I didn't really like teaching constructions, because, though I could do them quite well, I didn't truly understand their place and function in geometry and its development. When I first read chapter "G" of this book ("Greek Geometry"), however, it was like a thousand puzzle pieces fell into place and I knew more than how to do constructions, I understood them and was able to teach them more effectively.
If you have any interest in mathematics at all, I recommend this book. It will not disappoint.
As in the previous book, Dunham's descriptions are entertaining and enlightening. The main difference is that this book has broader coverage. As a result, it tends to omit more of the proofs, which I found disappointing, but perhaps that will make it of interest to a wider audience. For people with a deeper interest in mathematics, I recommend you read either "Journey Through Genius" or "Euler: The Master of Us All", another Dunham masterpiece that includes detailed proofs throughout.
The entry on the "Russell Paradox" reads like a hagiography of Bertrand Russell. It makes it appear that Russell ceased working on the Principia Mathematica because he could not find a solution to his paradox--whether a set, all of whose members are not members of themselves, contains itself. According to Dunham, his inability to find a satisfactory solution spelled the end of his quest for the development of a logical foundation for mathematics, which he communicated to Frege, who gave up on his attempts as well. This is pure fiction. The entire Principia Mathematica is based on Russell's theory of ramified types (the stipulation that a set cannot be a member of itself), which he confidently asserted as being the solution to the paradox throughout the work. What put an end to Russell and Whitehead's project, as well as Frege's, was Goedel's incompleteness theorem, totally ignored by Dunham.
Dunham's treatment of Venn diagrams is even worse because it is deprecating of John Venn and his work--and totally wrong. Dunham states that the diagrams that are named after him were Venn's only contribution to mathematics and then makes disparaging remarks about them, particularly that they lacked any originality. Here's the reality: John Venn was an extremely competent mathematician/logician whose many contributions included the furtherance of George Boole's innovations.Read more ›
Most Recent Customer Reviews
Much easier subject matter than some of this author's other books. If you're interested in studying mathematics, you might pick this one up to see what it's about. Read morePublished 21 days ago by Daniel Johnson
Enjoyable as a quick dip into a range of different fields of mathematics. Unfortunately, the Kindle version suffers from many, many typos misformatting in the mathematical... Read morePublished 7 months ago by Rune Mønnike
This book was required for a college math class. It was completely useless. Not worth purchasing AT ALL. It is all about he history of math. Read morePublished 7 months ago by Erica
I think it is a must for everyone, specially for those who dislike math. Writen in an almost coloquial language the author targeted the non-mathematician reader and nicely... Read morePublished 16 months ago by Mario Tanabe
I love the manageable pieces and the choice of topics. A chapter on pi and a chapter on e for example are just what hope find. Read morePublished on February 19, 2014 by Leonard Frieling
Bought it as a christmas gift,never thought someone would like to read about math. This is a really great giftPublished on January 20, 2014 by Karen Edie
What a great book, might have given it four stars, but since it is an interesting, well done math book, I give it five. Read morePublished on January 2, 2014 by William I. Griffith