15 Popular Mathematics Books

Mark Weitzman introduces the theme of the video, focusing on popular mathematics books not typically textbooks. He acknowledges having previously covered physics books and now wishes to delve into the realm of mathematics. He mentions a classic book 'Mr. Tompkins' which uses cartoon characters to explain complex concepts like relativity and nuclear physics. The video script outlines his intention to highlight authors known for their quality work in mathematics literature, such as Devlin, Klein, Nahin, Peterson, and Conway. The session aims to review classic books, discuss specific theorems and problems, and explore areas like history, philosophy, and biographies related to mathematics.

The paragraph delves into classic mathematics books and biographies of renowned mathematicians. It starts with the all-time classic 'Gödel, Escher, Bach' which explores logic, recursion, art, and music. 'The World of Mathematics' is highlighted for its comprehensive coverage of various mathematical topics. 'A Mathematician's Apology' by G. H. Hardy is mentioned for its famous statement on the uselessness of number theory, a view that contrasts with its later applications in cryptography. 'The Man of Mathematics' by E. T. Bell, despite being controversial, is recognized as a classic. The paragraph also emphasizes the importance of reading biographies of top physicists of the 20th century.

This section of the script focuses on books that deal with specific mathematical conjectures and problems. 'The P versus NP Problem and the Quest for the Millennium Bug' is recommended as a favorite, providing a step-by-step proof of the Banach-Tarski paradox in an accessible manner. The speaker also mentions books on the Riemann Hypothesis, Fermat's Last Theorem, and Kepler's Conjecture, each offering insights into these famous mathematical challenges. The discussion includes the book 'Symmetry and the Monster' which explores the classification of finite simple groups and the Monster group's connection to string theory.

The script moves on to discuss the Millennium Prize Problems, seven of the most significant unsolved mathematical problems with a $1 million prize for each. 'Millennium Problems' by Keith Devlin is highlighted for its coverage of these problems. The paragraph also touches on the history of mathematical concepts, including the work of Abel on the unsolvability of fifth-degree algebraic equations, and the Four Color Theorem, which was resolved by a computer-assisted proof. The Poincaré conjecture and its solution by Grigori Perelman in the field of topology are also mentioned.

The paragraph discusses books that provide a historical and philosophical perspective on mathematics, as well as biographies of mathematicians. 'The Loss of Certainty' by Cline is noted for its examination of the shaky foundations of mathematics, including the development of set theory. The speaker also recommends a three-volume work on the history of mathematics from ancient times to the modern era. Books on the philosophy of mathematics, including the nature of mathematical understanding and the work of famous mathematicians, are also highlighted, providing a deeper dive into the subject.

This section of the script explores books on specific mathematical topics and theories. It mentions 'Penrose Tiles to Trapdoor Ciphers' by Martin Gardner, who is celebrated for his 'Mathematical Games' column. The speaker also discusses books on the history of pi, the geometry of higher dimensions, and the work of Calabi and Yau in relation to string theory. 'On Numbers and Games' by Conway is highlighted for its exploration of various types of numbers, including those invented by Conway himself.

The script continues with a focus on books that delve into the concepts of numbers, infinity, and set theory. Nahin's books on specific mathematical topics, often requiring a background in calculus, are mentioned. Other books discussed include those on the constant e, the imaginary number i, and the pursuit and evasion problems. The paragraph also covers books on the mathematical constant gamma, the randomness in financial markets, and infinity in the context of set theory.

This paragraph discusses books that explore group theory, puzzles, and mathematical recreations. It mentions 'Group Theory in the Bedroom and Other Mathematical Diversions' for its non-technical exploration of group theory with relatable analogies. The speaker also talks about 'Rubik's Cube' and its connection to group theory, permutations, and combinatorics. The paragraph includes a recommendation for 'The Best Writing on Mathematics,' an annual collection of essays, and various other essay books on mathematics.

The final paragraph wraps up the discussion by mentioning recent developments in mathematics covered in books like 'Mathematics in the New Golden Age' by Keith Devlin. It also highlights 'Love and Math' by a Russian mathematician, focusing on the intersection of mathematics, physics, and geometry. The speaker expresses intent to review books on engineering, computers, weapons, atomic bombs, and public policy in future videos, concluding the series on popular books.