The Calculus Gallery: Masterpieces from Newton to Lebesgue

About this book

More than three centuries after its creation calculus remains a dazzling intellectual achievement and the gateway into higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth--mathematicians whose achievements are comparable to those of Bach in music or Shakespeare in literature. William Dunham lucidly presents the definitions theorems and proofs. "Students of literature read Shakespeare; students of music listen to Bach " he writes. But this tradition of studying the major works of the "masters" is if not wholly absent certainly uncommon in mathematics. This book seeks to redress that situation. Like a great museum The Calculus Gallery is filled with masterpieces among which are Bernoullis early attack upon the harmonic series (1689) Eulers brilliant approximation of pi (1779) Cauchys classic proof of the fundamental theorem of calculus (1823) Weierstrasss mind-boggling counterexample (1872) and Baires original "category theorem" (1899). Collectively these selections document the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough rigorous and unflinching--a story of genius triumphing over some of the toughest most subtle problems imaginable. Anyone who has studied and enjoyed calculus will discover in these pages the sheer excitement each mathematician must have felt when pushing into the unknown. In touring The Calculus Gallery we can see how it all came to be.