If you shut yourself in a room and devise some abstract mathematics for the sake of sheer intellectual fascination, you might not expect your scribblings to have any relevance to the real world. Your parents would probably bug you about what you were doing with your life. And yet time and again, scientists find that the creations of pure thought match what they discover in nature. Does it mean the world at its deepest levels is somehow mathematical? Does it simply mean that scientists are good at cherry-picking the conceptual tools they need? Mathematicians, physicists, philosophers and others debate that question, as astrophysicist Mario Livio describes in the August issue of Scientific American. Whatever the answer may be, we can still marvel at the beauty of mathematical structures.