Ten Questians and their Answers

Abstract

Abstract Many things in the world have a mathematical side to them and it is the business of mathematics to try to understand that facet of their nature. Mathematical reasoning can often explain things that otherwise remain obscure or baffling, and sometimes the reasoning involved is easy to understand once it is presented to you. This introductory chapter consists of a series of examples meant to prove my point. If you feel yourself any the wiser after reading them through, I invite you to read on. This book makes no claim to great depth, but through it I hope to convey the flavour of modern mathematics. It may also serve to clarify some aspects of school algebra and geometry, and even arithmetic, about which you may have always felt somewhat uneasy. It is perfectly possible, for instance, for anyone to understand the theorem of Pythagoras as well as a professional mathematician; the level of difficulty encountered is only that met when assembling a jigsaw puzzle of half a dozen pieces. There is no reason why such genuinely interesting aspects of mathematics need remain a mystery-indeed, most thoughtful people, with a little patience, can understand such things completely. Even some profound aspects of twentieth-century mathematics are quite accessible, and I hope to give the reader the satisfaction of seeing some parts of the mathematical world that were never revealed to even the greatest minds of the past.