This recreational math book takes the reader on a fantastic voyage into the world of natural numbers. From the earliest discoveries of the ancient Greeks to various fundamental characteristics of the natural number sequence, Clawson explains fascinating mathematical mysteries in clear and easy prose. He delves into the heart of number theory to see and understand the exquisite relationships among natural numbers, and ends by exploring the ultimate mystery of mathematics: the Riemann hypothesis, which says that through a point in a plane, no line can be drawn parallel to a given line.While a professional mathematician's treatment of number theory involves the most sophisticated analytical tools, its basic ideas are surprisingly easy to comprehend. By concentrating on the meaning behind various equations and proofs and avoiding technical refinements, Mathematical Mysteries lets the common reader catch a glimpse of this wonderful and exotic world.

    But the dot, though perfect in every way, only had eyes for a wild and unkempt squiggle. All of the line's romantic dreams were in vain, until he discovered...angles! Now, with newfound self-expression, he can be anything he wants to be--a square, a triangle, a parallelogram....And that's just the beginning!First published in 1963 and made into an Academy Award-winning animated short film, here is a supremely witty love story with a twist that reveals profound truths about relationships--both human and mathematical--sure to tickle lovers of all ages.

      “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.”—Nina MacLaughlin, Boston Globe “Engaging, eminently readable . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.”—Judith Goodstein, American Scientist  Harvard geometer and Fields medalist Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers readers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.

    BooklistLearn to use the most important codes and methods of secret communication in use since ancient times. Cipher and decipher codes used by spies. Explore the famous codes that changed the fate of nations and political leaders. And enjoy hours of fun experimenting with cryptography ― the science of secret writing. Beginning with simple letter substitutions and transposition ciphers, world-famous science writer Martin Gardner explains how to break complicated polyalphabetical ciphers and codes worked with grids, squares, triangles, and charts. You'll learn codes that are keyed to typewriters and telephone dials . . . even codes that use playing cards, knots, and swizzle sticks. Experiment with invisible writing ― inks that glow in black light and turn red under heat ― and explore the possibilities of sending messages through outer space to unknown worlds. Using this book, you can solve the historically famous Playfair Cipher used by Australia in World War II, the Pigpen Cipher used by Confederate soldiers during the Civil War, Thomas Jefferson's Wheel Cipher, the Beaufort system used by the British Royal Navy, codes devised by authors for heroes in literature ― Sherlock Holmes, Captain Kidd, and the Shadow. And you will enjoy experimenting with bizarre methods of message sending ― the Dot Code, Knot Code, Swizzle Code, and more. Young cryptanalysts, cipher fans, and puzzlists of all ages will find hours of intrigue and challenge in Codes, Ciphers and Secret Writing. "A stimulating must for the intermediate cryptographer." ― The Kirkus Reviews

    "A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.