This book provides a philosophy of mathematics that resonates with critical mathematics education. It draws attention to the social complexities that characterise the period of Modernity including the extreme exploitation of manual workers and their families, brutal forms of colonisations, trading of slaves, and the formation of racist ideologies. It portrays Modernity as a period of contradictions and highlights that mathematics is a part of these contradictions. The text interprets mathematics as being indefinite, seeing that mathematics is a part of the ongoing human constructions. It outlines a performative interpretation of mathematics, portraying mathematics as intrinsically connected to actions. Any kind of action, including mathematics-based actions, calls for ethical considerations and this leads to any mathematical practice, either in research, application, or education, to face ethical challenges. It illustrates with examples how a critical philosophy of mathematics can come to be an integral part of classroom practices.

Ole Skovsmose has a special interest in critical mathematics education. His research addresses landscape of investigation, dialogue, students' foreground, inclusive mathematics education, pedagogical imagination, mathematics in action, philosophy of mathematics education, and philosophy of mathematics. He is a professor at the Department of Education, Learning and Philosophy (now Department of Culture and Learning), Aalborg University, Denmark as well as a professor at Universidade Estadual Paulista (Unesp), Brazil. He has recently received the Freudenthal medal of ICMI for his innovative theoretical work.

Part I. Social Complexities.- Chapter 1. Modernity and the Holocaust.- Chapter 2. Glorification of Science and Mathematics.- Chapter 3. Domination by Technology.- Chapter 4. Globalised Exploitation.- Part II. Isolation and Glorification.- Chapter 5. Mathematics as Logical Tautologies.- Chapter 6. Mathematics as Formal Structures.- Chapter 7. Mathematics as Mental Acts.- Chapter 8. Mathematics as Mathematicians' Practice.- Part III. Indefinite Constructions.- Chapter 9. Indefinite with Respect to Concepts and Proofs.- Chapter 10. Indefinite with Respect to Topics and Applications.- Chapter 11. Indefinite with Respect to Power.- Chapter 12. Indefinite with Respect to Culture.- Part IV. Ethical Challenges.- Chapter 13. A Performative Interpretation of Mathematics.- Chapter 14. Performatives.- Chapter 15. Action and Ethics.- Chapter 16. Reflective Inquiries in the Classroom.