E. T. Bell

Men of Mathematics (eBook, ePUB)

• Format: ePub

Produktbeschreibung

From one of the greatest minds in contemporary mathematics, Professor E.T. Bell, comes a witty, accessible, and fascinating look at the beautiful craft and enthralling history of mathematics.

Men of Mathematics provides a rich account of major mathematical milestones, from the geometry of the Greeks through Newton's calculus, and on to the laws of probability, symbolic logic, and the fourth dimension. Bell breaks down this majestic history of ideas into a series of engrossing biographies of the great mathematicians who made progress possibleand who also led intriguing, complicated, and often surprisingly entertaining lives.

Never pedantic or dense, Bell writes with clarity and simplicity to distill great mathematical concepts into their most understandable forms for the curious everyday reader. Anyone with an interest in math may learn from these rich lessons, an advanced degree or extensive research is never necessary.

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Produktdetails

• Verlag: Simon + Schuster LLC
• Seitenzahl: 608
• Erscheinungstermin: 31. März 2014
• Englisch
• ISBN-13: 9781476784250
• Artikelnr.: 40653451

Autorenporträt

E.T. Bell was the former President of the Mathematical Association of America and a former Vice President of the American Mathematical Society of the American Association for the Advancement of Science. He won the Bôcher Prize of the American Mathematical Society for his research work. His twelve published books include The Purple Sapphire (1924), Algebraic Arithmetic (1927), Debunking Science, and Queen of the Sciences (1931), Numerology (1933), and The Search for Truth (1934). Dr. Bell died in December 1960, just before the publication of his latest book, The Last Problem.

Inhaltsangabe

Contents
1. INTRODUCTION
For the reader's comfort. The beginning of modern mathematics. Are
mathematicians human? Witless parodies. Illimitable scope of mathematical
evolution. Pioneers and scouts. A clue through the maze. Continuity and
discreteness. Remarkable rarity of common sense. Vivid mathematics or vague
mysticism? Four great ages of mathematics. Our own the Golden Age.
2. MODERN MINDS IN ANCIENT BODIES
Zeno (fifth century B.C.), Eudoxus (408-355 B.C.), Archimedes (287?-212
B.C.)
Modern ancients and ancient moderns. Pythagoras, great mystic, greater
mathematician. Proof or intuition? The taproot of modern analysis. A
bumpkin upsets the philosophers. Zeno's unresolved riddles. Plato's needy
young friend. Inexhaustible exhaustion. The useful conics. Archimedes,
aristocrat, greatest scientist of antiquity. Legends of his life and
personality. His discoveries and claim to modernity. A sturdy Roman. Defeat
of Archimedes and triumph of Rome.
3. GENTLEMAN, SOLDIER, AND MATHEMATICIAN
Descartes (1596-1650)
The good old days. A child philosopher but no prig. Inestimable advantages
of lying in bed. Invigorating doubts. Peace in war. Converted by a
nightmare. Revelation of analytic geometry. More butchering. Circuses,
professional jealousy, swashbuckling, accommodating lady friends. Distaste
for hell-fire and respect for the Church. Saved by a brace of cardinals. A
Pope brains himself. Twenty years a recluse. The Method. Betrayed by fame.
Doting Elisabeth. What Descartes really thought of her. Conceited
Christine. What she did to Descartes. Creative simplicity of Ms geometry.
4. THE PRINCE OF AMATEURS
Fermat (1601-1665)
Greatest mathematician of the seventeenth century. Fermat's busy, practical
life. Mathematics his hobby. His flick to the calculus. His profound
physical principle. Analytic geometry again. Arithmetica and logistica.
Fermat's supremacy in arithmetic. An unsolved problem on primes. Why are
some theorems "important"? An intelligence test. "Infinite descent."
Fermat's unanswered challenge to posterity.
5. "GREATNESS AND MISERY OF MAN"
Pascal (1625-1662)
An infant prodigy buries his talent. At seventeen a great geometer.
Pascal's wonderful theorem. Vile health and religious inebriety. The first
calculating Frankenstein. Pascal's brilliance in physics. Holy sister
Jacqueline, soul-saver. Wine and women? "Get thee to a nunnery.!" Converted
on a spree. Literature prostituted to bigotry. The Helen of Geometry. A
celestial toothache. What the post-mortem revealed. A gambler makes
mathematical history. Scope of the theory of probability. Pascal creates
the theory with Fermat. Folly of betting against God or the Devil.
6. ON THE SEASHORE
Newton (1642-1727)
Newton's estimate of himself. An uncertified youthful genius. Chaos of his
times. On the shoulders of giants. His one attachment. Cambridge days.
Young Newton masters futility of suffering fools gladly. The Great Plague a
greater blessing. Immortal at twenty four (or less). The calculus. Newton
unsurpassed in pure mathematics, supreme in natural philosophy. Gnats,
hornets, and exasperation. The Principia. Samuel Pepys and other fussers.
The flattest anticlimax in history. Controversy, theology, chronology,
alchemy, public office, death.
7. MASTER OF ALL TRADES
Leibniz (1646-1716)
Two superb contributions. A politician's offspring. Genius at fifteen.
Seduced by the law. The "universal characteristic." Symbolic reasoning.
Sold out to ambition. A master diplomat. Diplomacy being what it is, the
diplomatic exploits of the master are left to the historians. Fox into
historian, statesman into mathematician. Applied ethics. Existence of God.
Optimism. Forty years of futility. Discarded like a dirty rag.
8. NATURE OR NURTURE?
The Bernoullis (seventeenth-and eighteenth centuries)
Eight mathematicians in three generations. Clinical evidence for heredity.
The calculus of variations.
9. ANALYSIS INCARNATE
Euler (1707-1783)
The most prolific mathematician in history. Snatched from theology. Rulers
foot the bills. Practicality of the unpractical. Celestial mechanics and
naval warfare. A mathematician by chance and foreordination. Trapped in St.
Petersburg. The virtues of silence. Half blind in his morning. Flight to
liberal Prussia. Generosity and boorishness of Frederick the Great. Return
to hospitable Russia. Generosity and graciousness of Catherine the Great.
Total blindness at noon. Master and inspirer of masters for a century.
10. A LOFTY PYRAMID
Lagrange (1736-1813)
Greatest and most modest mathematician of the eighteenth century. Financial
ruin his opportunity. Conceives his masterpiece at nineteen. Magnanimity of
Euler. Turin, to Paris, to Berlin: a grateful bastard aids a genius.
Conquests in celestial mechanics. Frederick the Great condescends.
Absent-minded marriage. Work as a vice. A classic in arithmetic. The
Mécanique analytique a living masterpiece. A landmark in the theory of
equations. Welcomed in Paris by Marie Antoinette. Nervous exhaustion,
melancholia, and universal disgust in middle life. Reawakened by the French
Revolution and a young girl. What Lagrange thought of the Revolution. The
metric system. What the revolutionists thought of Lagrange. How a
philosopher dies.
11. FROM PEASANT TO SNOB
Laplace (1749-1827)
Humble as Lincoln, proud as Lucifer. A chilly reception and a warm welcome.
Laplace grandiosely attacks the solar system. The Mécanique céleste. His
estimate of himself. What others have thought of him. The "potential"
fundamental in physics. Laplace in the French Revolution. Intimacy with
Napoleon. Laplace's political realism superior to Napoleon's.
12. FRIENDS OF AN EMPEROR
Monge (1746-1818), Fourier (1768-1830)
A knife grinder's son and a tailor's boy help Napoleon to upset the
aristocrats' applecart. Comic opera in Egypt. Monge's descriptive geometry
and the Machine Age. Fourier's analysis and modern physics. Imbecility of
trusting in princes or proletarians. Boring to death and bored to death.
13. THE DAY OF GLORY
Poncelet (1788-1867)
Resurrected from a Napoleonic shambles. The path of glory leads to jail.
Wintering in Russia in 1812. What genius does in prison. Two years of
geometry in hell. The rewards of genius: stupidities of routine. Poncelet's
projective geometry. Principles of continuity and duality.
14. THE PRINCE OF MATHEMATICIANS
Gauss (1777-1855)
Gauss the mathematical peer of Archimedes and Newton. Humble origin.
Paternal brutality. Unequalled intellectual precocity. His chance, at ten.
By twelve he dreams revolutionary discoveries, by eighteen achieves them.
The Disquisitiones Arithmeticae. Other epochal works summarized. The Ceres
disaster. Napoleon, indirectly robbing Gauss, takes second best.
Fundamental advances in all branches of mathematics due to Gauss too
numerous for citation: see the account given. A sage of sages. Unwelcome
death.
15. MATHEMATICS AND WINDMILLS
Cauchy (1789-1857)
Change in nature of mathematics with nineteenth century. Childhood in the
French Revolution. Cauchy's early miseducation. Lagrange's prophecy. The
young Christian engineer. Prophetic acuteness of Malus. The theory of
groups. In the front rank at twenty seven. One of Fermat's enigmas solved.
The pious hippopotamus. Butted by Charles the Goat. Memoirs on astronomy
and mathematical physics. Sweetness and obstinacy invincible. The French
Government makes a fool of itself. Cauchy's place in mathematics. Drawbacks
of an irreproachable character.
16. THE COPERNICUS OF GEOMETRY
Lobatchewsky (1793-1856)
The widow's mite. Kazan. Appointed professor and spy. Universal ability.
Lobatchewsky as an administrator. Reason and incense combat the cholera.
Russian gratitude. Humiliated in his prime. Blind as Milton, Lobatchewsky
dictates his masterpiece. His advance beyond Euclid. Non-Euclidean
geometry. A Copernicus of the intellect.
17. GENIUS AND POVERTY
Abel ( 1802-1829)
Norway in 1802. Smothered by clerical fecundity. Abel's awakening.
Generosity of a teacher. A pupil of the masters. His lucky blunder. Abel
and the quintic. The Government to the rescue. Abel's grand tour of
mathematical Europe not so grand. French civility and German cordiality.
Crelle and his Journal. Cauchy's unpardonable sin. "Abel's Theorem."
Something to keep mathematicians 500 years. Crowning a corpse.
18. THE GREAT ALGORIST
Jacobi (1804-1851)
Galvanoplastics versus mathematics. Born rich. Jacobi's philological
ability. Dedicates himself to mathematics. Early work. Cleaned out. A goose
among foxes. Hard times. Elliptic functions. Their place in the general
development. Inversion. Work in arithmetic, dynamics, algebra, and Abelian
functions. Fourier's pontification. Jacobi's retort.
19. AN IRISH TRAGEDY
Hamilton (1805-1865)
Ireland's greatest. Elaborate miseducation. Discoveries at seventeen. A
unique university career. Disappointed in love. Hamilton and the poets.
Appointed at Dunsink. Systems of rays. The Principia of optics. Prediction
of conical refraction. Marriage and alcohol. Fields. Complex numbers. The
commutative law repealed. Quaternions. Mountains of paper.
20. GENIUS AND STUPIDITY
Galois (1811-1832)
An all-time world record in stupidity. Galois' childhood. The pedagogues
surpass themselves, At sixteen Galois repeats Abel's mistake. Politics and
education. Examinations as arbiters of genius. Hounded to death by a
priest. More academic ineptitude. Absent-minded Cauchy again. Driven to
rebellion. A master mathematician at nineteen. "A carcase to stir up the
people." The foulest sewer in Paris. Patriots rush to the field of honor.
Galois' last night. The riddle of equations solved. Buried like a dog.
21. INVARIANT TWINS
Sylvester (1814-1807); Cayley (1821-1895)
Cayley's contributions. Early life. Cambridge. Recreations. Called to the
Bar. Fourteen years in the law. Cayley meets his collaborator. Sylvester's
stormier life. Hamstrung by religion. Cayley and Sylvester contrasted.
Sylvester's mission to the Virginians. Further false steps. The theory of
invariants. Called to Johns Hopkins University. Inextinguishable vitality.
"Rosalind." cayley's unification of geometry. Space of n dimensions.
Matrices. Oxford endorses Sylvester. Respectable at last.
22. MASTER AND PUPIL
Weierstrass (1815-1897); Sonja Kowalewski (1850-1891)
The father of modern analysis. Relations of Weierstrass to his
contemporaries. The penalties of brilliance. Forced into law, forces
himself out. Beer and broadswords. A fresh start. Debt to Gudermann.
Fifteen years in the mud. Miraculous extrication. Weierstrass' life
problem. Too much success. Sonja storms the master. His favorite pupil.
Their friendship. A woman's gratitude. Repenting, Sonja wins Paris prize.
Weierstrass universally honored. Power series. Arithmetization of analysis.
Doubts.
23. COMPLETE INDEPENDENCE
Boole (1815-1864)
British mathematics. Damned at birth by snobbery. Boole's struggle for
education. False diagnoses. Providence intervenes. Discovery of invariants.
What is algebra? A philosopher attacks a mathematician. Frightful carnage.
Boole's chance. "The Laws of Thought." Symbolic logic. Its mathematical
significance. Boolean algebra. Dead in his prime.
24. THE MAN, NOT THE METHOD
Hermite (1822-1901)
Old problems and new methods. Hermite's masterful mother. His detestation
of examinations. Instructs himself. Higher mathematics sometimes easier
than elementary. Educational disasters. Letters to Jacobi. A master at
twenty one. Revenge on his examiners. Abelian functions. Pestered by
Cauchy. Hermite's mysticism. Solution of the general quintic.
Transcendental numbers. A hint to circle-squarers. Hermite's
internationalism.
25. THE DOUBTER
Kronecker (1823-1891)
Legend of an American saint. Lucky Kronecker. School triumphs. Great gifts.
Algebraic numbers. Battles with Weierstrass. Kronecker's business career.
Returns rich to mathematics. The Galois theory. Kronecker's lectures. His
skepticism his most original contribution.
26. ANIMA CANDIDA
Riemann (1826-1866)
Poor but happy. Riemann's chronic shyness. Destined for the church. Saved.
A famous hypothesis. Career at Göttingen. "A new mathematic." Physical
researches. Application of topology to analysis. Epoch-making essay on
foundations of geometry. Gauss enthusiastic. The. blessings of poverty. A
root of tensor analysis. Quest for health. Under a fig tree. Riemann's
landmark in geometry. Curvature of space. Pathbreaking for relativity.
27. ARITHMETIC THE SECOND
Kummer (1810-1893), Dedekind (1831-1916)
Aged in the wood. Napoleonic warp to Kummer's geniality. Equally gifted in
the abstract and the concrete. What Fermat's Last Theorem started. Theory
of ideal numbers. Kummer's invention comparable to Lobatchewsky's. Wave
surface in four dimensions. Big of body, mind, and heart. Dedekind, last
pupil of Gauss. First expositor of Galois. Early interest in science. Turns
to mathematics. Dedekind's work on continuity. His creation of the theory
of ideals.
28. THE LAST UNIVERSALIST
Poincare (1854-1912)
Poincaré's universality and methods. Childhood setbacks. Seized by
mathematics. Keeps his sanity in Franco-Prussian war. Starts as mining
engineer. First great work. Automorphic functions. "The keys of the
algebraic cosmos." The problem of n bodies. Is Finland civilized?
Poincare's new methods in celestial mechanics. Cosmogony. How mathematical
discoveries are made. Poincare's account. Forebodings and premature death.
29. PARADISE LOST?
Cantor (1845-1918)
Old foes with new faces. Rotting creeds. Cantor's artistic inheritance and
father-fixation. Escape, but too late. His revolutionary work gets him
nowhere. Academic pettiness. Disastrous consequences of "safety first." An
epochal result. Paradox or truth? Infinite existence of transcendentals.
Aggressiveness advances, timidity retires. Further spectacular claims. Two
types of mathematicians. Insane? counter-revolution. The battle grows
fiercer. Cursing the enemy. Universal loss of temper. Where stands
mathematics today? And where will it stand tomorrow? lnvictus.
INDEX