JOURNEY THROUGH GENIUS: The Great Theorems of Mathematics

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.