Douglas Hofstadter's book is concerned directly with the nature of “maps” or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity trans…

Shelve Gödel, Escher, Bach: An Eternal Golden Braid

In 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions…

Based on a National Magazine Award-winning article, this masterful biography of Hungarian-born Paul Erdos is both a vivid portrait of an eccentric genius and a layman's guide to some of this century'…

Shelve The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth

For decades, proponents of artificial intelligence have argued that computers will soon be doing everything that a human mind can do. Admittedly, computers now play chess at the grandmaster level, bu…

Shelve The Emperor's New Mind: Concerning Computers, Minds and the Laws of Physics

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 deserv…

Shelve Journey through Genius: The Great Theorems of Mathematics

Anyone who has wondered if free will is just an illusion or has asked 'could I have chosen otherwise?' after performing some rash deed will find this book an absorbing discussion of an endlessly fasc…

Shelve Elbow Room: The Varieties of Free Will Worth Wanting

Clouds are not spheres, mountains are not cones, and lightning does not travel in a straight line. The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ord…

Marvin Minsky -- one of the fathers of computer science and cofounder of the Artificial Intelligence Laboratory at MIT -- gives a revolutionary answer to the age-old question: "How does the mind work…

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and…

Shelve Infinity and the Mind: The Science and Philosophy of the Infinite

"... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vas…

Knuth's classic work has been widely acclaimed as one of the most influential works in the field of computer science. For the first time, these books are available as a boxed, three-volume set. The h…

Shelve The Art of Computer Programming, Volumes 1-3 Boxed Set

This is the classic introduction for the educated lay reader to the richly diverse world of mathematics: its history, philosophy, principles, and personalities.

One of the outstanding voices of his generation, David Foster Wallace has won a large and devoted following for the intellectual ambition and bravura style of his fiction and essays. Now he brings hi…

Shelve Everything and More: A Compact History of Infinity

For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditiona…

Shelve What Is Mathematics?: An Elementary Approach to Ideas and Methods

The revised and updated edition includes three completely new chapters on the prediction and control of chaotic systems. It also incorporates new information regarding the solar system and an account…

Shelve Does God Play Dice?: The New Mathematics of Chaos

This book is about mathematical ideas, about what mathematics means-and why. Abstract ideas, for the most part, arise via conceptual metaphor-metaphorical ideas projecting from the way we function in…

Shelve Where Mathematics Come From: How the Embodied Mind Brings Mathematics into Being

Written in 1940 as his mathematical powers were declining, G.H. Hardy's apology offers an engaging account of the thoughts of a man known for his eccentricities as well as his brilliance in mathemati…

Programming Legend Charles Petzold unlocks the secrets of the extraordinary and prescient 1936 paper by Alan M. TuringMathematician Alan Turing invented an imaginary computer known as the Turing Mach…

Shelve The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine

Most intelligent people today still believe that mathematics is a body of unshakable truths about the physical world and that mathematical reasoning is exact and infallible. Mathematics: The Loss of…

What do Bach's compositions, Rubik's Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientif…

Shelve The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry

Presupposes a knowledge of college level mathematics but is accessible to the average reader through its consistent treatment of mathematical structure with a strict adherence to historical perspecti…