According to G. H. Hardy, the “real” mathematics of the greats, such as Fermat and Euler, is “useless,” and thus the work of mathematicians should not be judged on its applicability to real-world problems. Yet, mysteriously, much of mathematics used in modern science and technology was derived from this “useless” mathematics. Cell phone technology is based on trig functions, which were invented centuries ago. Newton observed that the Earth’s orbit is an ellipse, a curve discovered by ancient Greeks in their futile attempt to double the cube. It is as if some magic hand had guided the ancient mathematicians, so their formulas were perfectly fitted for the sophisticated technology of today. Using anecdotes and witty storytelling, this book explores that mystery. Through a series of fascinating stories of mathematical effectiveness, including Planck’s discovery of quanta, mathematically curious readers will get a sense of how mathematicians develop their concepts.