Conceptual Mathematics

One approach to mathematics is to regard it as comprising distinct aspects: algebra – the manipulation of symbols, geometry – dealing with shape and position, and logic – making arguments. Conceptual mathematics, or category theory, combines all of these. It is about the structure of arguments, and deals with algebra geometrically. While category theory only succeeds in making small portions of mathematics easy — these are the portions that lie closest to the core of the subject, the part that illuminates the rest. It lies at the heart of a revolution in how pure mathematicians do research.

Since the turn of the century category theory has developed direct applications in ecological diversity, engineering, biology, chemistry, theoretical physics, computer science and informatics. Cheng argues in her new book, The Joy of Abstraction, that by forcing clear thinking about contentious issues, such as social justice and gender, it can contribute to a more constructive political culture. The Tizard project applies conceptual mathematics to the symbiosis of school mathematics and informatics.