The Mathematical Universe
From the simple elegance of the Pythagorean theorem to the looking-glass world of Russell's Paradox and the summed infinities of integral calculus, experience the beauty and majesty of the mathematical universe. William Dunham, author of the popular Journey Through Genius, will give you a rare sampling of its joys. Writing in his trademark razor-sharp style, Dunham introduces a tantalizing selection of the great proofs, notorious disputes, and intriguing unsolved mysteries. Subjects range from the golden age of Greek geometry to the furthest frontier of infinite series. In chapters spanning the field from A to Z, discover the marvels of the Monte Carlo Method and the ancient riddle of Dido's Problem. Scale the heights of the Himalayas with famed surveyor Sir George Everest and puzzle over the fascinating conundrum of Fermat's Last Theorem. Dunham explores more than five thousand years of mathematical history, digging into the earliest records in Egypt, Babylon, India, and China, and turning up surprising tales and tidbits from modern times.. All along the way, Dunham portrays the great masters of math at their work. In colorful anecdotes, the brilliant - often eccentric - luminaries chart the course of mathematical progress.
Stats for nerds
3recommend
4mentions
4people
2022–2024years
75% recommend25% neutral
Mentions per year
What Hacker News says
- I'm a mathematician (PhD in numnber theory...) and I took a look. It's a basic textbook about some concepts like functions, relations, and basic proof techniques. It seems okay. I was expecting something different from the title, though. It's not too different from many basic books introducing such concepts but obviously a lot of effort was put into it.
Personally, I think if you want an introduction to the "art" of mathematics, it would be a lot better to pick up a more idiosyncratic book that doesn't aim to cover the basics of the standard curriculum in a textbook-style way, which in my opinion is rather tedious. That could either be a more high-level book like Ian Stewart's "From Here to Infinity" or one of Raymond Smullyan's fun texts on logic.
Or for a more basic book, something like "The Mathematical Universe" by William W. Dunham is a much more interesting introduction to the "art" of mathematics than a textbook-style intro.
- I can recommend the following:
John Derbyshire's Unknown Quantity - A real and imaginary history of algebra
David Well's The Penguin Dictionary of Curious and Interesting Numbers
William Dunham's The Mathematical Universe - An Alphabetical Journey Through the Great Proofs, Problems and Personalities
Alex Bello's Alex's Adventures in The Numberland - Dispatches from the wonderful world of mathematics
- Great introductory books along with videos:
- Mathematics and Its History (John Stillwell) - Journey through Genius: The Great Theorems of Mathematics (William Dunham) - Proofs Without Words: Exercises in Visual Thinking (Roger B. Nelsen) - The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities (William Dunham) - Odds & Ends: Introducing Probability & Decision with a Visual Emphasis (Jonathan Weisberg) - Introduction to Probability (Joseph K. Blitzstein, Jessica Hwang) - The Secret Life of Equations: The 50 Greatest Equations and How They Work (Richard Cochrane) - Euler's Gem: The Polyhedron Formula and the Birth of Topology (David S. Richeson) - 3Blue1Brown Essence of Linear Algebra: https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab - 3Blue1Brown Differential Equations: https://www.youtube.com/playlist?list=PLZHQObOWTQDNPOjrT6KVlfJuKtYTftqH6 - Dynamics: The Geometry of Behavior (Ralph Abraham, Christopher Shaw) - Geometry, Relativity and the Fourth Dimension (Rudolf Rucker) - 3Blue1Brown Essence of Calculus: https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr - Calculus for the Practical Man (J.E. Thompson) - Div, Grad, Curl, and All That: An Informal Text on Vector Calculus (Harry M. Schey) - Who Is Fourier? a Mathematical Adventure - Physics, Topology, Logic and Computation: A Rosetta Stone (John C. Baez, Mike Stay) - An Illustrated Guide to Relativity (Tatsu Takeuchi) - The Mathematics Of Quantum Mechanics (Martin Laforest) - A Student's Guide to Maxwell's Equations (Daniel Fleisch) or if you're also interested in a visual guide, I wrote one as well: https://github.com/photonlines/Intuitive-Guide-to-Maxwells-Equations - Introduction to Elementary Particles (David J. Griffiths) - An Invitation to Applied Category Theory: Seven Sketches in Compositionality (Brendan Fong, David I Spivak) - Solving Mathematical Problems: A Personal Perspective (Terence Tao) - William Dunham's "The Mathematical Universe" was already mentioned but I actually came to suggest his earlier work "Journey Through Genius".
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