Tuesday, July 24, 2012

Great Feuds in Mathematics















Title: Great Feuds in Mathematics – Ten of the Liveliest Disputes Ever
Author: Hal Hellman
Publisher:  John Wiley, 2006 (First)
ISBN: 978-0-471-64877-2
Pages: 217

Hal Hellman is the author of a series of books on Great Feuds in Science, Medicine and Technology. This is the fourth in the series, centred on mathematics. He has published articles in the major newspapers and magazines of the U.S. Mathematics is an area of science, ruled by cold, logical discipline where questions are decided objectively and decisively. Naturally we would consider the possibility of feuds and disputes that should arise between mathematicians to be very remote. People often assign characteristics pertaining to the field of study on to the behaviour of its practitioners. In this respect, mathematics is a field of study which brooks no quarrels or simmering tensions because of the logical nature of its subject matter. But, mathematicians are also human beings and questions of primacy, originality and deceit arise among them too. Just as you won’t expect zoologists to be unruly and wild, you can’t expect mathematicians to be logical and straightforward.

This book describes in detail, ten of the liveliest quarrels, starting from 16th century Italian mathematicians Tartaglia and Cordano on solving cubic equations right up to the 20th century, with the vigorous dispute between absolutists/platonists and fallibilists/constructivists. As the centuries unfold before our eyes, we understand the platonic shift that has taken place between the practitioners. In those early ages, information was a hidden treasure. If you chance upon a novel way of solving a particular class of equations, you keep the method to your bosom. Your chances of survival in an unsure world may depend on your ability to reproduce it effectively before an enlightened audience or a rich sympathiser. This has radically changes in modern times, the slogan metamorphizing to ‘Publish or Perish’. Whatever you have – even precocious ideas – is to be put before your peers lest others get there in front of you.

The most energetic and arresting dispute among them all is that took place between Isaac Newton and Wilhelm Gottfried Leibniz. Newton developed rudiments of calculus, the most widely used mathematical tool today, be it in pure science or in technology. In 1665, he called it method of fluxions, but delayed publication for several years. Leibniz independently found it in 1673 but published ‘soon after’, in 1684. Newton withheld publication till 1704. When they both appeared, the question of primacy naturally ensued, with both sides obtaining the support of their compatriots and sympathizers who didn’t have sole mathematical considerations in their hearts. Leibniz had followers in the continent, while Newton had Britishers on his side and the Royal Society, whose president he was. Both sides accused the other of plagiarism, but Newton’s increasing stature and Leibniz’ failing luck decided the matter. Newton emerged the clear winner, but later events proved that Leibniz’ method and notation was easier and versatile. The modern world uses it. So it may be said that Leibniz lost the battle, but won the war.

Personal feuds even crossed family ties, as exemplified by the tussle between Jakob and Johan Bernoullie. Johan was the younger who was tutored by his elder brother. They soon quarrelled over the use of calculus, both accusing each other of stealing from their work. When the time period enters the 19th century, the mathematics get more complicated and uninteresting making the book tedious and a great bore. Chapters on mathematical logicism and philosophy is really punishing the readers. The issues that burnt between Cantor and Kronecker, Russell and Poincare, and Hilbert and Brouwer are simply unworthy to be mentioned in a book targeting the general reader.

Hellman lacks the authority to seal the issue at hand. Whatever he has written is clearly second-hand material, those scavenged from biographies and incidents reproduced somewhere else and taken without much ‘value addition’ by the author. Being no mathematician himself, what he has succeded in producing are half-baked opinions like such and such commented such and such on this particular issue. Except the first three-four chapters, the book is thoroughly unappealing and taxes heavily on the reader’s patience.

The book is recommended only for the heavily mathematically inclined.

Rating: 2 Star

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