Why Beauty Is Truth: The History of SymmetryAt the heart of relativity theory, quantum mechanics, string theory, and much of modern cosmology lies one concept: symmetry. In Why Beauty Is Truth, world-famous mathematician Ian Stewart narrates the history of the emergence of this remarkable area of study. Stewart introduces us to such characters as the Renaissance Italian genius, rogue, scholar, and gambler Girolamo Cardano, who stole the modern method of solving cubic equations and published it in the first important book on algebra, and the young revolutionary Evariste Galois, who refashioned the whole of mathematics and founded the field of group theory only to die in a pointless duel over a woman before his work was published. Stewart also explores the strange numerology of real mathematics, in which particular numbers have unique and unpredictable properties related to symmetry. He shows how Wilhelm Killing discovered "Lie groups" with 14, 52, 78, 133, and 248 dimensions-groups whose very existence is a profound puzzle. Finally, Stewart describes the world beyond superstrings: the "octonionic" symmetries that may explain the very existence of the universe. |
From inside the book
Results 1-5 of 70
Page ix
... physics, in the quantum world of the very small and the relativistic world of the very large. It may even provide a route to the long-sought “Theory of Everything,” a mathematical unification of those two key branches of modern physics ...
... physics, in the quantum world of the very small and the relativistic world of the very large. It may even provide a route to the long-sought “Theory of Everything,” a mathematical unification of those two key branches of modern physics ...
Page x
... physics unchanged. These concepts, and more recent ones at the frontiers of today's physics, could not have been discovered without a deep mathematical un- derstanding of symmetry. This understanding came from pure mathemat- ics; its ...
... physics unchanged. These concepts, and more recent ones at the frontiers of today's physics, could not have been discovered without a deep mathematical un- derstanding of symmetry. This understanding came from pure mathemat- ics; its ...
Page xii
... physics but to mathematical constants like π (the Greek letter pi). The speed of light, for instance, might in principle be anything, but it happens to be 186,000 miles per second in our universe. On ... physics. Physicists have xii PREFACE.
... physics but to mathematical constants like π (the Greek letter pi). The speed of light, for instance, might in principle be anything, but it happens to be 186,000 miles per second in our universe. On ... physics. Physicists have xii PREFACE.
Page xiii
... Physicists have long wondered why space has three dimensions and time one—why we live in a four-dimensional space-time. The theory of superstrings, the most recent attempt to unify the whole of physics into a single coherent set of laws ...
... Physicists have long wondered why space has three dimensions and time one—why we live in a four-dimensional space-time. The theory of superstrings, the most recent attempt to unify the whole of physics into a single coherent set of laws ...
Page 23
... Physicists , engineers , and astronomers tend to view proofs with disdain , as a kind of pedantic appendage , because they have an effective substitute : observation . For instance , imagine an astronomer trying to calculate the ...
... Physicists , engineers , and astronomers tend to view proofs with disdain , as a kind of pedantic appendage , because they have an effective substitute : observation . For instance , imagine an astronomer trying to calculate the ...
Contents
1 | |
17 | |
3 The Persian Poet 33 | 33 |
4 The Gambling Scholar 45 | 45 |
5 The Cunning Fox 63 | 63 |
6 The Frustrated Doctor and the Sickly Genius 75 | 75 |
7 The Luckless Revolutionary 97 | 97 |
8 The Mediocre Engineer and the Transcendent Professor 125 | 125 |
11 The Clerk from the Patent Office 173 | 173 |
12 A Quantum Quintet 199 | 199 |
13 The FiveDimensional Man 221 | 221 |
14 The Political Journalist 243 | 243 |
15 A Muddle of Mathematicians 259 | 259 |
16 Seekers after Truth and Beauty 275 | 275 |
Further Reading 281 | 281 |
Index 283 | 283 |
Other editions - View all
Common terms and phrases
Abel aether Albert angle atom Babylonian beauty became calculations called Cardano circle complex numbers construction cube root cubic decimal dimensions discovered discovery Einstein electromagnetic electron equations Euclid Euclidean Évariste Galois exactly exceptional Lie groups exist father Fermat primes field force formula fundamental Galois Galois’s Gamesh Gauss geometry gravity Greek group theory Hamilton Heisenberg idea Killing’s known Lagrange later Lie algebras light look mathe mathematicians mathematics matics method moving multiplication negative numbers Newton Niels normed division algebra number system octonions particles permutations physicists physics plane polygons problem proof proton proved quadratic quantum theory quarks quartic quaternions quintic quintic equation radicals real numbers relativity rotation Ruffini sack simple Lie algebras solution solve space space-time spin square root string theory structure subgroup superstrings supersymmetry symbols symmetry group Tartaglia tells theorem Theory of Everything thing tion transformations triangle trisect turned universe waves Wigner wrote
Popular passages
Page v - O Attic shape! Fair attitude! with brede Of marble men and maidens overwrought, With forest branches and the trodden weed; Thou, silent form, dost tease us out of thought As doth eternity: Cold Pastoral! When old age shall this generation waste, Thou shalt remain, in midst of other woe Than ours, a friend to man, to whom thou say'st, "Beauty is truth, truth beauty," — that is all Ye know on earth, and all ye need to know.
Page 33 - WAKE ! For the Sun, who scatter'd into flight The Stars before him from the Field of Night, Drives Night along with them from Heav'n, and strikes The Sultan's Turret with a Shaft of Light. ii Before the phantom of False morning died, Methought a Voice within the Tavern cried, "When all the Temple is prepared within, "Why nods the drowsy Worshipper outside?
Page 38 - And lately, by the Tavern Door agape, Came shining through the Dusk an Angel Shape Bearing a Vessel on his Shoulder; and He bid me taste of it; and 'twas — the Grape!
Page 43 - IS-NOT' though. with Rule and Line And 'UP-AND-DOWN' by logic I define, Of all that one should care to fathom, I Was never deep in anything but - Wine.
Page 44 - We are no other than a moving row Of Magic Shadow-shapes that come and go Round with the Sun-illumined Lantern held In Midnight by the Master of the Show...
Page 38 - Is-not' though with Rule and Line And 'Up-and-down' by Logic I define, Of all that one should care to fathom, I Was never deep in anything but — Wine.
Page 24 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.
Page 38 - Come, fill the Cup, and in the fire of Spring Your Winter-garment of Repentance fling: The Bird of Time has but a little way To flutter — and the Bird is on the Wing.