Originally published: London : Jonathan Cape, 2004.

Includes bibliographical references (p. 1050-1085) and index.

1. The roots of science -- 2. An ancient theorem and a modern question -- 3. Kinds of number in the physical world -- 4. Magical complex numbers -- 5. Geometry of logarithms, powers, and roots -- 6. Real-number calculus -- 7. Complex-number calculus -- 8. Riemann surfaces and complex mappings -- 9. Fourier decomposition and hyperfunctions -- 10. Surfaces -- 11. Hypercomplex numbers -- 12. Manifolds of n dimensions -- 13. Symmetry groups -- 14. Calculus on manifolds -- 15. Fibre bundles and gauge connections -- 16. The ladder of infinity -- 17. Spacetime -- 18. Minkowskian geometry -- 19. The classical fields of Maxwell and Einstein -- 20. Lagrangians and Hamiltonians -- 21. The quantum particle -- 22. Quantum algebra, geometry, and spin -- 23. The entangled quantum world -- 24. Dirac's electron and antiparticles -- 25. The standard model of particle physics -- 26. Quantum field theory -- 27. The Big Bang and its thermodynamic legacy -- 28. Speculative theories of the early universe -- 29. The measurement paradox -- 30. Gravity's role in quantum state reduction -- 31. Supersymmetry, supra-dimensionality, and strings -- 32. Einstein's narrower path; loop variables -- 33. More radical perspectives; twistor theory -- 34. Where lies the road to reality?

"What Roger Penrose accomplishes in this book is threefold. First, he gives us an overall narrative description of our present understanding of the universe and its physical behaviors - from the unseeable, minuscule movement of the subatomic particle to the journeys of the planets and the stars in the vastness of time and space." "Second, he evokes the extraordinary beauty that lies in the mysterious and profound relationships between these physical behaviors and the subtle mathematical ideas that explain and interpret them." "Third, Penrose comes to the arresting conclusion - as he explores the compatibility of the two grand classic theories of modern physics - that Einstein's general theory of relativity stands firm while quantum theory, as presently constituted, still needs refashioning." "Along the way, he talks about a wealth of issues, controversies, and phenomena; about the roles of various kinds of numbers in physics, ideas of calculus and modern geometry, visions of infinity, the big bang, black holes, the profound challenge of the second law of thermodynamics, string and M theory, loop quantum gravity, twistors, and educated guesses about science in the near future."--BOOK JACKET.