PDF Download Journey through Genius: The Great Theorems of Mathematics
PDF Download Journey through Genius: The Great Theorems of Mathematics
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Journey through Genius: The Great Theorems of Mathematics
PDF Download Journey through Genius: The Great Theorems of Mathematics
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Amazon.com Review
In Journey through Genius, author William Dunham strikes an extraordinary balance between the historical and technical. He devotes each chapter to a principal result of mathematics, such as the solution of the cubic series and the divergence of the harmonic series. Not only does this book tell the stories of the people behind the math, but it also includes discussions and rigorous proofs of the relevant mathematical results.
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Review
"An inspired piece of intellectual history."— Los Angeles Times“It is mathematics presented as a series of works of art; a fascinating lingering over individual examples of ingenuity and insight. It is mathematics by lightning flash.”— Isaac Asimov“Dunham deftly guides the reader through the verbal and logical intricacies of major mathematical questions, conveying a splendid sense of how the greatest mathematicians from ancient to modern times presented their arguments.”—Ivars Peterson, author of The Mathematical Tourist
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Product details
Paperback: 320 pages
Publisher: Penguin Books; 1st edition (August 1, 1991)
Language: English
ISBN-10: 9780140147391
ISBN-13: 978-0140147391
ASIN: 014014739X
Product Dimensions:
5.1 x 0.5 x 7.7 inches
Shipping Weight: 7.2 ounces (View shipping rates and policies)
Average Customer Review:
4.7 out of 5 stars
165 customer reviews
Amazon Best Sellers Rank:
#16,365 in Books (See Top 100 in Books)
I'm not very good at math and I really enjoyed this. About half way through, the specific proofs covered go over my head (darn Newton), so I had to skim those a little and just read the narrative. It's about 3/4 readable text and a fourth walking through theorems, about a third of which were mostly doable for me. It is not necessary to follow all the calculations to benefit greatly from this book and follow it. I learned a lot about how things are calculated; how math developed by person, place, and over time; and feel inspired to try my hand at learning math. This really helped me understand and appreciate the development of math and related scientific fields (which are related) and some brilliant thinkers behind the calculator. For example, find the square root of 3. I can punch this into Exel. These guys had to solve it by hand. I don't feel so "math dumb" now that I understand how some of these difficult calculations came about (which run VERY deep of course). The writing is clear, at a good pace, and interesting (even for someone who grew up hating and struggling with basic math).
I just recently began teaching Math to 7th, 8th, and 10th grades. I bought this book in order to gain further insights into the history, and personalities of mathematics in order to bring some of that to my classes. The book is very well written. To fully appreciate it, you should probably have at least a high school background in mathematics, but it's not so intense that you need college calculus in order to grasp the narrative. Dunham does a great job of telling the story of the mathematician, his life and challenges, how he came up with the theorem, the significance of the theorem, what happens in mathematics and the world because of the theorem (why is it significant), and then walks us thru the different theorems in enough detail so that you get a feel for the brilliance of the thought, but not so much that your eyes glaze over in boredom of getting lost in the numbers.I highly recommend it; it is exactly what the title and review say it is. A leisurely walk/journey through some of the truly remarkable mathematics in human history.
This is a wonderful book. People with a basic grasp of math who are open to the idea that math might be beautiful will be rewarded. But I have a PhD in math and thoroughly enjoyed it, and learned some things along the way. (Because math is taught very ahistorically, Chapter 1 was entirely unfamiliar to me).These are *not* "*The* Great Theorems of Mathematics," as the subtitle suggests, but they certainly are "Great Theorems of Mathematics." Most "Great Theorems" are too technical to be presented in a book of this sort, but Mr. Dunham has done a wonderful job selecting theorems that can be proved with a minimum of prerequisites. In some ways this is a more challenging task than choosing the "greatest" theorems.My main reservation is the fact that at times the proofs get more ponderous than necessary, and can wind up obscuring the simplicity and elegance of the mathematics. The most glaring example is the already-noted proof of Fermat's Little Theorem (p. 226-9). The proof is incomplete, and presented in a very obscure way. The key fact, that (a+b)^p = a^p + b^p (mod p) follows easily and beautifully from the binomial theorem, so a complete proof could be given quite straightforwardly. I had the sense that some of the other theorems could have been presented somewhat more cleanly as well.The story behind Bernoulli's proof of the divergence of the harmonic series is enjoyable, but Bernoulli's proof is complex and unmotivated. Happily Mr. Dunham presents the beautiful proof Nicole Oresme from the 14th century. It is superior to Bernoulli's in every way: shorter, more elegant, and more illuminating, since pursuing his line of thinking makes it clear that the series grows as the log of the number of terms. So it's hard to see why Bernoulli is getting high marks for this particular proof, though he is overall a towering figure in the history of mathematics.Really, all my complaints are nit-picking. This is a wonderful book.I do want to defend Mr. Dunham from one of the other reviews: Euclid can prove (in modern language) that the area of a circle divided by the radius squared is a constant, and he can prove that the circumference divided by the diameter is a constant. But Euclid didn't show that these are the *same* constant, and that is why Archimedes result can fairly be seen as "greater" than Euclid's. Not that those theorems of Euclid's were slouches by any means.
I'm still working through the theorems in the early part of the book. The only way you will gain anything from this book is to work out each step with the text as a companion. That is an enlightening experience in itself.I suppose it's a good thing it was published in 1990 so it can't include Andrew Wiles' 1996 proof of Fermat's most famous conjecture. There is NO way the mathematical layman could follow that!
This was a challenging book for me to read, but only because I don't have the education to be able to absorb all of the formulas and proofs presented. In fact many of the theorems required me to carefully read them so that I could understand them and their implications.That said, I think the content for the book was thoroughly researched and I enjoyed reading about the connections across centuries.I came away with an appreciation of the great mathematicians and admiration for their quest for truth. Mathematics do not have an emotional, political, religious, or artistic component. For the most part, mathematics advances have not been stimulated by the desire to solve practical problems. Ultimately however, our understanding of mathematics help to define truth in everyday life, from cereal box size and nutritional contents to paying income taxes.Though I would be hard pressed to explain any of the theorums, I did find the book inspirational. While most any mathematical relationship (like the ratio of a polygon within a circle) can be found with an internet search, it is fun to try to determine some of these on my own. That describes a great book: it stimulates you to think and expand your horizons long after you've read the last page.
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