- Hellman, Hal.
Great Feuds in Mathematics.
Hoboken, NJ: John Wiley & Sons, 2006.
ISBN 0-471-64877-9.
-
Since antiquity, many philosophers have looked upon
mathematics as one thing, perhaps the only thing,
that we can know for sure, “the last fortress
of certitude” (p. 200). Certainly then,
mathematicians must be dispassionate
explorers of this frontier of knowledge, and
mathematical research a grand collaborative endeavour,
building upon the work of the past and weaving the
various threads of inquiry into a seamless intellectual
fabric. Well, not exactly….
Mathematicians are human, and mathematical research is
a human activity like any other, so regardless of the
austere crystalline perfection of the final product,
the process of getting there can be as messy, contentious,
and consequently entertaining as any other enterprise
undertaken by talking apes. This book chronicles ten of
the most significant and savage disputes in the history
of mathematics. The bones of contention vary from the
tried-and-true question of priority (Tartaglia vs.
Cardano on the solution to cubic polynomials, Newton
vs. Leibniz on the origin of the differential and
integral calculus), the relation of mathematics to
the physical sciences (Sylvester vs. Huxley), the
legitimacy of the infinite in mathematics
(Kronecker vs. Cantor, Borel vs. Zermelo), the
proper foundation for mathematics (Poincaré vs.
Russell, Hilbert vs. Brouwer), and even
sibling rivalry (Jakob vs. Johann Bernoulli).
A final chapter recounts the incessantly disputed question
of whether mathematicians discover structures
that are “out there” (as John D. Barrow
puts it, “Pi in the Sky”)
or invent what is ultimately as much a human construct
as music or literature.
The focus is primarily on people and events, less so on the
mathematical questions behind the conflict; if you're unfamiliar with
the issues involved, you may want to look them up in other
references. The stories presented here are an excellent antidote to
the retrospective view of many accounts which present mathematical
history as a steady march forward, with each generation building upon
the work of the previous. The reality is much more messy, with the
directions of inquiry chosen for reasons of ego and national pride as
often as inherent merit, and the paths not taken often as interesting
as those which were. Even if you believe (as I do) that mathematics
is “out there”, the human struggle to discover and figure
out how it all fits together is interesting and ultimately inspiring,
and this book provides a glimpse into that ongoing quest.
December 2007 