Connecting Humans to Equations: A Reinterpretation of the Philosophy of Mathematics presents some of the most important positions in the philosophy of mathematics, while adding new dimensions to this philosophy. Mathematics is an integral part of human and social life, meaning that a philosophy of mathematics must include several dimensions. This book describes these dimensions by the following four questions that structure the content of the book: Where is mathematics? How certain is mathematics? How social is mathematics? How good is mathematics? These four questions refer to the ontological, epistemological, social, and ethical dimension of a philosophy of mathematics. While the ontological and epistemological dimensions have been explored in all classic studies in the philosophy of mathematics, the exploration of the book is unique in its social and ethical dimensions. It argues that the foundation of mathematics is deeply connected to human and social actions and that mathematics includes not just descriptive but also performative features. This human-centered and accessible interpretation of mathematics is relevant for students in mathematics, mathematics education, and any technical discipline and for anybody working with mathematics
Part I. Where is Mathematics? -- Chapter 1: Mathematics in Eternity -- Chapter 2: Mathematics in Nature -- Chapter 3: Mathematics in Mind -- Part II: How Certain is Mathematics? -- Chapter 4: A Solid House of Cards -- Chapter 5: The Magnificent Disaster -- Chapter 6: Mathematics without Content -- Part III: How Social is Mathematics? -- Chapter 7: Mathematics as Intuition -- Chapter 8: Mathematics as Dialogue -- Chapter 9: Mathematics as Grammar -- Part VI: How Good is Mathematics? -- Chapter 10: Beyond the isolation of Mathematics -- Chapter 11: Beyond the Neutrality of Mathematics -- Chapter 12: What is the Philosophy of Mathematics?