13 Pure Mathematics Books for Physicist's Entertainment

The speaker introduces a series focused on pure math textbooks, contrasting with their other series on mathematical physics. They express a preference for textbooks that emphasize the historical development, computation, and basic ideas of mathematical concepts over a strict focus on rigor. The speaker mentions owning many math textbooks but plans to discuss only a select few that they find enjoyable and educational. The first book highlighted is by Harold M. Edwards, praised for its detailed computations and analysis of Riemann's zeta function, including a 37-page examination of the original paper. The book, though old, is recommended for its depth on complex number theory and analytic number theory.

The speaker continues to discuss Harold M. Edwards' works, emphasizing the author's unique approach to teaching math through history and computation. They recommend a book on Fermat's Last Theorem, which provides a genetic introduction to algebraic number theory and covers proofs up to the 1850s. The book is appreciated for its detailed computations and explanations of unique factorization in number fields. Another book by Edwards on Galois theory is also recommended for its accessibility and comprehensive coverage of the topic, despite its graduate-level status. The speaker then mentions other books on number theory, including one that provides an undergraduate-level proof of the prime number theorem and another that discusses factorization techniques and the RSA cryptosystem.

The speaker shifts focus to more advanced topics, such as the proof of Fermat's Last Theorem, which is outlined in a book that provides a broad view of the mathematical areas involved in the proof. They also discuss books on set theory and logic, recommending a book by Enderton for its thorough and easy-to-understand approach to set theory and another for mathematical logic that includes detailed proofs of Gödel's theorem. The speaker appreciates these books for not skipping details and for their historical context. They also mention a book by Manning that covers a range of topics in mathematical logic, including computability and model theory.

The speaker recommends a book on non-Euclidean geometry that provides a comprehensive look at the development of geometric principles, including the axiomatization following Hilbert and the history of the first parallel postulate. They appreciate the book's coverage of elliptic, hyperbolic, and spherical geometries, as well as its extension into Klein's Erlangen program. Turning to analysis, the speaker praises a book by Corner that offers a wide range of topics, including Fourier analysis and its applications, and another book that provides a historical perspective on the development of integration theory, including Lebesgue's theory.

The speaker discusses books on probability theory, including a short book with interesting models and a more philosophical work by James that delves into the interpretations and controversies surrounding probability. They also mention a two-volume work on applied mathematics that covers a range of topics from games theory to complexity theory and a book on experimental mathematics that explores the use of computers in discovering and verifying mathematical formulas and theorems.

In the final paragraph, the speaker recommends a book by Stillwell that combines the history of mathematics with proofs and discoveries across various fields of mathematics. They emphasize the enjoyment derived from reading these books, which are meant for entertainment rather than strict academic study. The speaker concludes by encouraging viewers to explore these enjoyable math books for a less painful and more engaging learning experience.