This unique text by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. The first describes questions and issues about mathematics that have motivated philosophers almost since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in such thinkers as Plato, Aristotle, Kant, and Mill. The third section covers the three major positions, and battle lines, throughout the twentieth century: that mathematics is logic (logicism), that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV looks at contemporary positions and work which brings the reader up-to-date on the discipline. Thinking about Mathematics is accessible to those with little background in either mathematics or philosophy. It is aimed at students and professionals in mathematics who have little contact with academic philosophy and at philosophy students and other philosophers who forgot much of their mathematics.

斯圖爾特·夏皮羅(stewart shapiro)，俄亥俄州立大學的哲學教授，同時也是蘇格蘭聖·安德魯斯大學的定期訪問教授。他是當今一位重要的數學哲學傢，其思想屬於結構主義，認為數學的研究對象是結構而不是個體。這種思想被認為是源自德國偉大的數學傢理查德·戴德金，是當代數學哲學中較為有影響的一派。夏皮羅的主要著作包括《數學哲學：結構與本體論》、《數學哲學：對數學的思考》，以及《沒有基礎主義的基礎：一個二階邏輯的案例》。他還是《牛津數學哲學與邏輯手冊》的主編。