This is a personal notebook from a conceptual travel. But, in a different sense, it also represents a report on travelling. The main part of the manuscript was written in Brazil, Denmark and England, whilst notes have also been inspired by visits to other countries. So, the book not only represents conceptual travel, it also reflects seasons of real travelling. In Part 1, the book comments on the critical position of mathematics education, and also indicates some concerns of critical mathematics education. Part 2 comments on mathematics in action, and considers the discussion of mathematics as an applied discipline in the contexts of technology, management, engineering, economics, etc. In Part 3, the book comments on mathematics and science in general. These comments are then generalised into a discussion of 'reason' and of the 'apparatus of reason'. Finally, Part 4 returns to the discussion of mathematics education, and comments on notions that could become 'sensitive' to the critical position of mathematics education.Ole Skovsmose is also travelling between different academic fields. He touches upon mathematics and mathematics education, the philosophy of mathematics, technology and science, as well as sociological issues, glancing over issues such as globalisation, ghettoising, learning society, and risk society. Travelling with the author, the reader will become aware of connections between many of these different issues. This very personal and warm academic book should inspire anyone active in the field of mathematics education or education in general.