William DunhamCritiques

I thought I wouldn't learn anything new about the Lincoln assassination, since I have read a lot on the subject and watched quite a few documentaries...but Bill fooled me. I did learn some new things, and was riveted by the tale as if I had not heard it ever before.
I was interested in his take on both Mary Surratt and Dr. Mudd, since I have visited both their homes and you get a different leaning on their parts there.
Overall a pleasing experience. I am anxious to read "Killing Kennedy", since I was alive for that event and remember it well.

7/7/22

Got me interested in some things I wasn't familiar with before. A good balance between between math and background info, and the proofs are easy to follow in most chapters.

This is a brilliant intellectual journey through some of the great theorems of mathematics. The author writes very clearly and evocatively--then, there is the math. I am not a mathematician, and I frequently get lost in the rows after rows of numbers that go into the proofs of each theorem. Still, through Dunham's excellent explanations, I am able at least to grasp the gist of what is being said and to understand the intellectual achievement involved. I learned a lot reading this book about the beauty of mathematics and how geniuses--because that is the apt word here--have unraveled some of its mysteries over the centuries. This is not a long book, and while the math can be dense, and the ideas themselves may verge on giving you a headache as you struggle to understand them, the journey through genius (great title) is actually a very pleasant one for anyone with a bit of curiosity about a subject they may feel they don't understand well enough. This book will certainly increase your understanding of mathematics a bit--but it will increase your understanding and appreciation of mathematicians a LOT.½

I completely enjoyed this book. Beautiful mathematics exquisitely presented. Provocative discussion of deeper meaning of theorem and the creative development of conceptual ideas.

It's a retelling of several historic math discoveries. Interesting, but not much new, since I'd read a lot of other books covering the same topics.

It felt great reading this book because it took me back to my school days where we learned these concepts/theorems along with their proofs.

The book brings history and mathematics together which was an interesting read. I specifically liked reading about how Archimedes proved the area of a circle and how Limits were introduced as a result of finding the area of irregular shapes.

This book is recommended for anyone who has even the slightest interest in Mathematics.

Need A level maths to follow this excellent book about Euler and his maths. What a guy!

Viaje a través de los genios es un viaje apasionante por la historia de las matemáticas y de los matemáticos. William Dunham expone en 12 capítulos, 12 grandes teoremas matemáticos. Lo hace explicando las vidas de los matemáticos que los pensaron y el momento de la historia en el que lo hicieron. Con gran entusiasmo y admiración hacia estos genios. Dunham tiene el acierto de incluir las demostraciones de estos teoremas, a la vez que lo hace de manera clara y comprensible. No sólo explica la historia de las matemáticas y de los matemáticos, explica matemáticas. Seguramente muchas de las personas que dicen que no les gustan las matemáticas cambiarán de opinión al leer este libro.

De Hipócrates a Cantor, de la demostración geométrica del teorema de Pitágoras tal como la hizo Euclides a la relación de Cantor con el infinito. Hipócrates, Euclides, Arquímedes, Herón, Cardano, Fermat, Newton, Leibniz, Bernoulli, Euler, Gauss, Cantor... Como personajes de una novela, sus vidas y sus teoremas van llenando los capítulos de este libro, siempre estructurados de la misma forma: en primer lugar una introducción histórica o de los avances anteriores para el tema central del capítulo, después el teorema central que protagoniza el capítulo y, finalmente, un epílogo en el que se explica el impacto que tuvo el teorema en matemáticos posteriores.

El único aspecto negativo a destacar es la de la traducción castellana de Editorial Pirámide, que presenta errores de todo tipo: tipográficos, ortográficos y errores de transcripción de las fórmulas matemáticas.

Un gran libro para los amantes de las matemáticas y para que los que no lo son aún lo acaben siendo.

Excellent balance of historical background and real-life proofs. Although at times the material is too simple, it is presented briskly and the author's tone is pleasant.

I read this book while I was in the hospital recovering from surgery. It held my morphined attention. 'Nuff said? Probably not.

I'm coming to consider truly substantive "popular" scientific exposition to be a high art, indeed: many attempt it & few are successful. This book is one of the rare successes. It does not dumb down, but it speaks warmly and invitingly to the reader.

A total treat & one to keep. I want to re-read it in a more lucid state.

A wonderful book that samples Euler’s work in several areas of mathematics. This is not a traditional biography focusing on Euler’s life, but rather a tour through a small portion of Euler’s amazing work. A first year course in Calculus would be helpful, but most of the mathematics can be followed with a college level algebra class. Each chapter covers several of Euler’s most impressive contributions to a specific branch of mathematics. While Euler contributed to every major area of the mathematics of his time, this book limits itself to eight (Number Theory, Logarithms, Infinite Series, Analytic Number Theory, Complex Variables, Algebra, Geometry, and Combinatorics). The chapters begin with a brief background of the area before Euler, then describe Euler’s contribution, and end with an epilogue that traces Euler’s impact forward in history.

What stands out in this book is how Dunham artfully takes the reader through the mathematics. Proofs are presented in a very approachable way that highlights Euler’s surprising twists and leaps of genius. Unlike the traditional (dry) way that proofs are usually presented, the author stays with you through the proofs, explaining key steps and commenting on Euler’s overall strategy. I was so impressed with how the author pulled this off that I immediately ordered his book “The Calculus Gallery”.

This is one of the most interesting books on the history of Calculus that I have ever read. It does require a moderate amount of mathematical knowledge (although not more than the standard first year undergraduate Analysis courses), but it is written with such a brilliance that one reads it with the eagerness more frequently experienced when reading a good thriller. But then, the history of Mathematical Analysis is, when we look at it in the proper way, one of the most fascinating and thrilling episodes in the intellectual history of mankind. This book is but one of the different stories that can be written: not being the history of Calculus, not even a history, it is, as the title indicates, a gallery, like an art gallery: reading along it we travel from the founding fathers Newton and Leibitz, until the pinacle of rigor and generality (and beauy!!) attained in the beginning of the 20th Century by Baire and Lebesgue. Along the way we visit some of the brilliant ideas of the Bernoulli brothers, Euler, Cauchy, Riemann, Liouville, Weierstrass, Cantor, and Volterra, and we see how, in two and a half centuries, the combined work of these (and others) outstanding minds shaped one of the most beautiful and powerful of all human creations. Like in any art gallery, a lot of names, some of then genius, are missing, but what is there is enough to tell a story, to disquiet and to awe the visitor. All in all, this is a magnificent book that all teachers and students of mathematics should read. It is also a work that should sadden us for the beauty herein is not likely to be appreciated by many more. It comes to mind the following famous poem by Fernando Pessoa, one of the most celebrated of all portuguese poets (in my loose translation): Newton's binomial is as beautiful as the Venus of Milo. The trouble is that few people can be aware of this. And the (generalized) Newton's binomial expansion is just the beginning: it is the very first section of the first chapter in this book...

Easily the best expostion on mathematics I've ever read. No, it's not all-inclusive; Dunham picks out some of the salient sojourns in mathematics and describes them and their beauty beautifully. Great.

Reading Euler's story is inspiring!

Professor William Dunham writes about one of the greatest mathematicians who has lived. Leonhard Euler (pronounced "oiler" or "OILa") lived from 1707 to 1783 and produced a massive volume of papers and books on mathematics, physics, and other subjects. His influence on mathematics is incalculable and considerd by modern mathematicians as one of the greatest minds ever. This work is one in a series that was chartered by the American Mathematical Association with the purpose of "furthering the ideal of execellence in mathematical exposition". This book provides the student of mathematics an appreciation of the man behind the math and some good exercises in the math itself. It also gives those with more general interest an appreciation of the mind of a great thinker whose works fundamentally influence great thinkers today.

This book is not, and is not meant to be, anything close to a biography or even a history. Dunham clearly wants the reader to develop a reverant appreciation for the man who almost single-handedly pushed math into the modern era. He allows one to glimpse, in less than 200 pages, the works that are still to this day being published in what will likely be 25,000+ pages (those actually written by Euler).

Get your pencil and paper and follow along with this one. You will get an inkling of the way one of the great minds worked, and you might even learn some math!½

A delightful tour of some of the intellectual highlights or mathematics. Not as focussed as the author's even better "Calculus gallery", but gives a wider range, though the book stops with Cantor's investigations into infinity. The stories in this book have been told many times, but they are told well here.½

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 maths, but it also includes discussions and rigorous proofs of the relevant mathematical results.

Praise for William Dunhams Journey Through Genius The Great Theorems of Mathematics "Dunham deftly guides the reader through the verbal and logical intricacies of major mathematical questions and proofs, conveying a splendid sense of how the greatest mathematicians from ancient to modern times presented their arguments." -Ivars Peterson Author, The Mathematical Tourist Mathematics and Physics Editor, Science News

"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

"It is a captivating collection of essays of major mathematical achievements brought to life by the personal and historical anecdotes which the author has skillfully woven into the text. This is a book which should find its place on the bookshelf of anyone interested in science and the scientists who create it." -R. L. Graham, AT&T Bell Laboratories

"Come on a time-machine tour through 2,300 years in which Dunham drops in on some of the greatest mathematicians in history. Almost as if we chat over tea and crumpets, we get to know them and their ideas-ideas that ring with eternity and that offer glimpses into the often veiled beauty of mathematics and logic. And all the while we marvel, hoping that the tour will not stop." -Jearl Walker, Physics Department, Cleveland State University Author of The Flying Circus of Physics

Exceptional explanatory mathematical work.½