An eloquent exposition of what Dunham (Mathematics/Hanover) calls
"the Mona Lisas or Hamlets" of mathematics - 12 classic theorems
ranging from Hippocrates' quadrature of the lunes (c. 440 B.C.) and
Euclid's proof of the Pythagorean theorem (c. 300 B.C.) to Georg
Cantor's theorem of the non-denumerability of the continuum (1874)
and his crowning achievement, Cantor's Theorem (1891), which, as
Dunham puts it, "pushed mathematics into unexplored territory where
it began to merge into the realms of philosophy and metaphysics."
Dunham brackets his explanation of each theorem with an accessible
discussion of the state of mathematics - and of the world - prior
to the theorem, and relevant biographical information about the
mathematicians. The theorem explanations themselves, for all their
elegance, require a current familiarity with high-school-level
math; while not for many of us, then, Dunham's fine tour through
the best of mathematics will prove a treat for those who know the
difference between a finite cardinal and an infinite one. (Kirkus
Reviews)
Praise for William Dunhams 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 from ancient to modern times presented their
arguments." Ivars Peterson Author, The Mathematical Tourist
Mathematics and Physics Editor, Science News
"It is mathematics presented as a series of works of art; a
fascinating lingering over individual examples of ingenuity and
insight. It is mathematics by lightning flash." Isaac Asimov
"It is a captivating collection of essays of major mathematical
achievements brought to life by the personal and historical
anecdotes which the author has skillfully woven into the text. This
is a book which should find its place on the bookshelf of anyone
interested in science and the scientists who create it." R. L.
Graham, AT&T Bell Laboratories
"Come on a time-machine tour through 2,300 years in which Dunham
drops in on some of the greatest mathematicians in history. Almost
as if we chat over tea and crumpets, we get to know them and their
ideasideas that ring with eternity and that offer glimpses into the
often veiled beauty of mathematics and logic. And all the while we
marvel, hoping that the tour will not stop." Jearl Walker, Physics
Department, Cleveland State University Author of The Flying Circus
of Physics
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