Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.
Dunham is especially reverent toward Leonhard Euler and Georg Cantor, two incredibly prolific mathematicians who push the boundaries of theoretical math despite physical and mental challenges. Overall I would recommend the book. Dunham presents highlights from math history as great works of art.
If you are willing to do a little work in following the proofs, there is much to appreciate. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.
Theorems are presented without any indicator of where they are headed. He carries this analogy through the book consistently, for example identifying Georg Cantor as the mathematical parallel of his contemporary Vincent van Gogh. Looking for candidates to replace them, though, gives a good idea of why they were chosen.
It is mathematics by lightning flash. Dunham takes a chronological path through the subject, beginning with the ancient Greeks and the thinkers centered in Alexandria, the site of the greatest collection of learning in the ancient world. Dunham has done an excellent job of selecting exemplary theorems that can be explained to an interested reader having no special mathematical training, that are associated with the most greatest mathematicians of all time, and that influenced the future of mathematics.
After receiving his Ph. The Great Theorems of Mathematics is a survey of twelve great theorems selected by author William Dunham for the importance to the field of mathematics as well as for how they represent the prevailing ideas and ideals of the times in which they appear.
Now William Dunham gives them the attention they deserve. In addition to the "great theorems," he finds time to describe many other masterpieces. Dunham ably describes how theoretical math is often at the forefront, and how ideas that seem too bizarre to publish in one era come to have practical significance in another once science and technology have caught up.
Some of it is good and some not so good. I recommend this book to a general reader interested in the history of mathematics, and particularly to undergraduate students of mathematics: These three mathematicians have an impact so great nobody approaches their advances for many centuries.
He describes the contentious Bernoulli brothers, Johann and Jakob, who despite their bickering manage to transform the mathematics of their day.
Dunham picks up the thread in the 16th century with the eccentric and superstitious Gerolamo Cardano who is jailed for heresy at one point but manages to solve equations once thought unsolvable.
Dunham keeps promising that the formula will eventually be derived, but I gave up beforehand. He describes the reluctance of mathematicians to divulge their discoveries, sometimes out of fear of having their precious assets taken from them, but also sometimes because of a fear that some more theoretical ideas might not be accepted among their colleagues.
Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor.
The mathematical exposition is uneven.
May 13, James Swenson rated it really liked it The title is a fair description: Rather than drill the math, Dunham wishes to present the theorems in a setting that enhances their historical importance and it is not necessary to completely comprehend each theorem to grasp their influence.
Add to Cart About Journey through Genius Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever.Buy a cheap copy of Journey through Genius: The Great book by William Dunham.
In Journey through Genius, author William Dunham strikes an extraordinary balance between the historical and technical. He devotes each chapter to a principal Free shipping over $ Journey Through Genius: The Great Theorems of Mathematics Summary & Study Guide includes detailed chapter summaries and analysis, quotes, character descriptions, themes, and more.
ACKNOWLEDGMENT. chapter 1 Hipocrates' quadrature of the Lune (ca. B.C.) 1. The Appearance of Demonstrative Mathematics 1 Some Remarks on Quadrature 11 Great Theorem 17 Epilogue 20 chapter 2 Euclid's Proof of the Pythagorean Theorem (ca.
B.C.) Journey through Genius – William Dunham Preface Acknowledgments Chapter 1. Hippocrates’ Quadrature of the Lune (ca. B.C.) The Appearance of Demonstrative Mathematics Some Remarks on Quadrature Great Theorem Epilogue Chapter 2.
Euclid’s Proof of the Pythagorean Theorem (ca.
B.C.). Journey Through Genius THE GREAT THEOREMS OF MATHEMATICS WILLIAM DUNHAM WILEY objects of study. Books are written and courses are taught on precisely Each chapter of Journey Through Genius has three primary components: The first is its historical emphasis.
The "great theorems" on the. Journey through Genius: Great Theorems of Mathematics / Edition 1 Praise for William Dunham s 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 5/5(1).Download