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Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is.
Paul Erdős (1913–1996)This book is about beautiful mathematical concepts and creations.
Some people believe that mathematics is the language of nature, others that it is an abstract game with symbols and rules. Still others believe it is all calculations. Plato equated mathematics with “the good.” My approach to mathematics is as an art form, like painting, sculpture, or music. While the artist works in a tangible medium, the mathematician works in a medium of numbers, shapes, and abstract patterns. In mathematics, as in art, there are constraints. The most stringent is that mathematical results must be true; others are conciseness and elegance. As with other arts, mathematical ideas have an esthetic appeal that can be appreciated by those with the willingness to investigate.
I hope that this book will inspire readers with the beauty of mathematics. I present mathematical topics in the categories of words, images, formulas, theorems, proofs, solutions, and unsolved problems. We go from complex numbers to arithmetic progressions, from Alcuin's sequence to the zeta function, and from hypercubes to infinity squared. Who should read this book? I believe that there is something new in it for any mathematically-minded person.
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