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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