What Is Mathematics?

What Is Mathematics? is a foundational mathematics text that serves as both an introduction for students and an accessible overview for general readers. The book covers fundamental mathematical concepts across number theory, geometry, topology, and calculus. First published in 1941 by Oxford University Press, the work emerged from Richard Courant's course materials, with significant contributions from Herbert Robbins. A 1996 second edition features an additional chapter by Ian Stewart on recent mathematical developments. The text approaches complex mathematical ideas through clear explanations and practical examples, maintaining rigor while remaining accessible to non-specialists. The authors present both historical context and modern applications for key mathematical principles. The book's enduring influence stems from its ability to bridge the gap between elementary and advanced mathematics, revealing the field's underlying unity and beauty. Its philosophical approach to mathematical thinking has shaped how mathematics is taught and understood.

Readers describe this as a challenging but rewarding exploration of mathematical concepts. The explanations build gradually and connect different areas of mathematics in ways that create deeper understanding. Liked: - Clear progression from basic to advanced topics - Historical context and real-world applications - Detailed illustrations and diagrams - Suitable for self-study with practice problems - Accessible to readers with high school math background Disliked: - Dense and difficult for beginners - Some sections require multiple readings - Occasional jumps in difficulty level - Old-fashioned writing style - Limited coverage of modern mathematics Ratings: Goodreads: 4.24/5 (1,089 ratings) Amazon: 4.5/5 (168 ratings) Notable comments: "Takes work but rewards patience" - Goodreads reviewer "Not for casual reading, requires pencil and paper" - Amazon reviewer "Changed how I view mathematics" - Mathematics Stack Exchange user "Worth the effort for serious math students" - Reddit r/math comment

Mathematics: Its Content, Methods and Meaning by Aleksandr Danilovich Aleksandrov A comprehensive exploration of mathematics from its foundations to advanced concepts, written by three master mathematicians from the Soviet mathematical tradition.

The Nature of Mathematics by Philip E. B. Jourdain The book traces mathematical concepts through history, connecting mathematical discoveries with the fundamental questions that motivated them.

Mathematics and Its History by John Stillwell This text presents mathematical concepts in their historical context while showing the connections between different branches of mathematics.

Mathematical Thought from Ancient to Modern Times by Morris Kline The development of mathematical ideas is traced from ancient civilizations through modern times, emphasizing the evolution of mathematical thinking.

Journey through Genius by William Dunham The book examines twelve mathematical theorems through history, presenting both the mathematical content and the historical context of each breakthrough.

⭐ Written during Courant's exile from Nazi Germany, the book emerged from his experiences teaching mathematics to American students at New York University. ⭐ Albert Einstein praised the book, writing a recommendation that called it "a lucid representation of the fundamental concepts and methods of the whole field of mathematics." ⭐ The co-author, Herbert Robbins, was just 26 years old when he collaborated with Courant on this project, and went on to become a renowned statistician. ⭐ The book's unique approach influenced the "New Math" movement of the 1960s, which sought to reform mathematics education in American schools. ⭐ Despite being over 80 years old, the book remains in print and is used in mathematics education worldwide, having been translated into at least 13 languages.