Great Feuds In Mathematics

Praise for Hal Hellman Great Feuds in Mathematics "Those who think that mathematicians are cold, mechanical proving machines will do well to read Hellman's book on conflicts in mathematics. The main characters are as excitable and touchy as the next man. But Hellman's stories also show how scientific fights bring out sharper formulations and better arguments." -Professor Dirk van Dalen, Philosophy Department, Utrecht University Great Feuds in Technology "There's nothing like a good feud to grab your attention. And when it comes to describing the battle, Hal Hellman is a master." -New Scientist Great Feuds in Science "Unusual insight into the development of science . . . I was excited by this book and enthusiastically recommend it to general as well as scientific audiences." -American Scientist "Hellman has assembled a series of entertaining tales . . . many fine examples of heady invective without parallel in our time." -Nature Great Feuds in Medicine "This engaging book documents [the] reactions in ten of the most heated controversies and rivalries in medical history. . . . The disputes detailed are . . . fascinating. . . . It is delicious stuff here." -The New York Times "Stimulating." -Journal of the American Medical Association

From Descartes battling Fermat for the honour of inventing analytic geometry, to Poincaré wrangling with Russell over the logical foundations of mathematics, this text provides a fascinating look behind the numbers game.

Most science chronicles present a triumphant march through time, with revolutionary thinkers and their discoveries following in orderly progression. The truth, however, is somewhat different. Scientific Feuds is a collection of the most vicious battles among the greatest minds of our time. It features such contests as Huxley and Wilberforce's debate on Darwin's theory of evolution, Franklin and Wilkins' fight over the discovery of DNA, and the “War of Currents” between Tesla and Edison (which ended with Edison electrocuting dogs and horses in a vain attempt to discredit Tesla's work). From passionate competition to vindictive sniping, these rivalries prove that the world of science is far from cold and methodical.

Containing a large and varied set of problems, this rich resource will allow students to stretch their mathematical abilities beyond the school syllabus, and bridge the gap to university-level mathematics. Many proofs are provided to better equip students for the transition to university. The author covers substantial extension material using the language of sixth form mathematics, thus enabling students to understand the more complex material. Exercises are carefully chosen to introduce students to some central ideas, without building up large amounts of abstract technology. There are over 1500 carefully graded exercises, with hints included in the text, and solutions available online. Historical and contextual asides highlight each area of mathematics and show how it has developed over time.

This book provides a fundamental reassessment of mathematics education in the digital era. It constitutes a new mindset of how information and knowledge are processed by introducing new interconnective and interactive pedagogical approaches. Math education is catching up on technology, as courses and materials use digital sources and resources more and more. The time has come to evaluate this new dynamic, which transcends all previous use of ancillary devices to supplement classroom math instruction. Interactivity and interconnectivity with the online world of math and math texts (such as television programs and internet sites) can be integrated with our traditional modes for delivery of math instruction. This book looks at how this integration can unfold practically by applying these relevant pedagogical principles to elementary topics such as numeration, arithmetic, algebra, story problems, combinatorics, and basic probability theory. The book further exemplifies how mathematics can be connected to topics in popular culture, information technologies, and other such domains.

Mathematics plays an important role in mechanics and other human endeavours. Validating examples in this first volume include, for instance: the connection between the golden ratio (the “divine proportion" used by Phidias and many other artists and enshrined in Leonardo's Vitruvian Man, shown on the front cover), and the Fibonacci spiral (observable in botany, e.g., in the placement of sunflower seeds); is the coast of Tuscany infinitely long?; the equal-time free fall of a feather and a lead ball in a vacuum; a simple diagnostic for changing your car's shocks; the Kepler laws of the planets; the dynamics of the Sun-Earth-Moon system; the tides' mechanism; the laws of friction and a wheel rolling down a partially icy slope; and many more. The style is colloquial. The emphasis is on intuition - lengthy but intuitive proofs are preferred to simple non-intuitive ones. The mathematical/mechanical sophistication gradually increases, making the volume widely accessible. Intuition is not at the expense of rigor. Except for grammar-school material, every statement that is later used is rigorously proven. Guidelines that facilitate the reading of the book are presented. The interplay between mathematics and mechanics is presented within a historical context, to show that often mechanics stimulated mathematical developments - Newton comes to mind. Sometimes mathematics was introduced independently of its mechanics applications, such as the absolute calculus for Einstein's general theory of relativity. Bio-sketches of all the scientists encountered are included and show that many of them dealt with both mathematics and mechanics.

This book is a mathematical potpourri. Its material originated in classroom presentations, formal lectures, sections of earlier books, book reviews, or just things written by the author for his own pleasure. Written in a nontechnical fashion, this book expresses the unique vision and attitude of the author towards the role of mathematics in society. It contains observations or incidental remarks on mathematics, its nature, its impacts on education and science and technology, its personalities and philosophies. The book is directed towards the math buffs of the world and, more generally, towards the literate and interested public. Philip Davis is known for his work in numerical analysis and approximation theory, as well as his investigations in the history and philosophy of mathematics. Currently a Professor Emeritus from the Division of Applied Mathematics at Brown University, Davis is known for his books both in the areas of computational mathematics and approximation theory and for books exploring certain questions in the philosophy of mathematics and the role of mathematics in society.

The dramatic stories of ten historic feuds: How they altered the course of discovery-and shaped the modern world Hall Hellman tells the lively stories of ten of the most outrageous and intriguing disputes from the seventeenth to the twentieth centuries. Bringing the cataclysmic clash of ideas and personalities to colorful life, Hellman explores both the science and the spirit of the times. Along the way, he reveals that scientific feuds are fueled not only by the purest of intellectual disagreements, but also by intransigence, ambition, jealousy, politics, faith, and the irresistible human urge to be right. Unusual insight into the development of science . . . I was excited by this book and enthusiastically recommend it to general as well as scientific audiences. -American Scientist Hellman has assembled a series of entertaining tales. . . . many fine examples of heady invective without parallel in our time. -Nature An entertaining and informative account of the unusual personalities and sometimes bitter rivalries of some of the world's greatest scientific minds. -Publishers Weekly A fascinating new book which details some of the most famous disputes of the ages.-Courier Mail Dry science history turns into entertaining reading without sacrificing historical accuracy. -The Christchurch Press Great Feuds in Science is wonderful history, as the reader learns how scientists had to fight with religious leaders and other scientists to get their work recognized, accepted, and even get the credit for it! -Bookviews