Journey Through Genius: The Great Theorems of Mathematics
Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve.\ Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician...
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Explores the ``masterpieces'' of mathematics, seventeen landmarks spanning 2,300 years and representing ten mathematicians. Each of these landmarks, to some degree, changed the way the world was perceived. Each theorem is presented with a description of the state of mathematics at the time, the development of the theorem, a biographical sketch of the mathematician and an outline of the proof with explanation.
Hippocrates' Quadrature of the Lune (ca440 B.C.)Euclid's Proof of the Pythagorean Theorem (ca300 B.C.)Euclid and the Infinitude of Primes (ca300 B.C.)Archimedes' Determination of Circular Area (ca225 B.C.)Heron's Formula for Triangular Area (caA.D75)Cardano and the Solution of the Cubic (1545)A Gem from Isaac Newton (Late 1660s)The Bernoullis and the Harmonic Series (1689)The Extraordinary Sums of Leonhard Euler (1734)A Sampler of Euler's Number Theory (1736)The Non-Denumerability of the Continuum (1874)Cantor and the Transfinite Realm (1891)AfterwordChapter NotesReferencesIndex
