1st Edition

The Four Corners of Mathematics A Brief History, from Pythagoras to Perelman

By Thomas Waters Copyright 2025
    288 Pages 229 B/W Illustrations
    by A K Peters/CRC Press

    288 Pages 229 B/W Illustrations
    by A K Peters/CRC Press

    The Four Corners of Mathematics: A Brief History, from Pythagoras to Perelman describes the historical development of the ‘big ideas’ in mathematics in an accessible and intuitive manner. In delivering this bird's-eye view of the history of mathematics, the author uses engaging diagrams and images to communicate complex concepts while also exploring the details of the main results and methods of high-level mathematics. As such, this book involves some equations and terminology, but the only assumption on the readers’ knowledge is A-level or high school mathematics.


    • Divided into four parts, covering Geometry, Algebra, Calculus and Topology
    • Presents high-level mathematics in a visual and accessible way with numerous examples and over 250 illustrations
    • Includes several novel and intuitive proofs of big theorems, so even the non-expert reader can appreciate them
    • Sketches of the lives of important contributors, with an emphasis on often overlooked female mathematicians and those who had to struggle.

    Part I Geometry. 1. The Beginnings. 2. Non-Euclidean Geometry. 3. Curves, surfaces, manifolds. Part II. Algebra. 5. The Beginnings. 6. Complex Numbers. 7. Abstract Algebra. 8. Linear Algebra. Part III. Calculus. 9. The Beginnings. 10. The Solar System. 11. Maxima and Minima. 12. PDE’s. Part IV. Topology. 13. The Beginnings. 14. Degree. 15. Homology. 16. Classification. 


    Thomas Waters was born and grew up in Dublin, Ireland, completing his undergraduate degree and PhD in Mathematics at Dublin City University. This was followed by a post-doc at the University of Strathclyde in Glasgow, then three years as a lecturer at the National University of Ireland, Galway, before becoming a lecturer at the University of Portsmouth, England, in 2010. During his time Thomas has lectured on very many different topics such as Linear Algebra, Differential Geometry, Knot Theory and Analytical Mechanics, to classes large and small, from one student to 300. His research interests go from General Relativity (stability of naked singularities) to Astrodynamics (solar sails in the 3-body problem) to Riemannian Geometry (integrability and the conjugate locus), but a unifying theme would be ordinary differential equations and periodic solutions. Thomas has two daughters, and when he is not being their taxi driver he enjoys long walks in the woods and mountains.