Mathematics

This book is a short introduction to mathematics for general readers by Timothy Gowers, a British mathematician, Rouse Ball Professor of Mathematics at Cambridge University, and Fields Medal winner; the original belongs to Oxford University Press's Very Short Introduction series. Rather than focusing on formulas and exercises, the author explains at a philosophical level what fundamental differences exist between advanced mathematics and the mathematics taught in schools. The book begins with models, explaining that mathematical models are simplifications and fictions of the real world, requiring trade-offs among accuracy, simplicity, and explanatory power; it then discusses numbers and abstraction, moving from natural numbers to negative numbers, fractions, real numbers, and complex numbers, and proposes the view that mathematical objects are what they do; it next uses classic cases to show the rigor and ingenuity of mathematical proof, and goes on to address limits and infinity, dimension, geometry, estimation and approximation, closing with a set of common questions that respond to readers' puzzlement over concepts such as infinity, curved space, and imaginary numbers. The book is brief and plain in language, using almost no technical notation, aiming to let readers without a professional mathematical background experience how mainstream mathematics thinks and understand how the mathematical community constructs and tests knowledge. The Chinese edition is translated by Liu Xi, with a preface by Li Daqian, academician of the Chinese Academy of Sciences.