Proofs from the book
by Martin Aigner · first published 1998
61% recommend35% neutral4% critical
Why HN recommends it
Short, elegant proofs of famous results, from the infinitude of primes to the art gallery problem. Shows proofs can be more interesting than their conclusions; suits the mathematically curious with some background.
Summarised by Claude from recommending comments
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…writing. Seriously, he can make the axiomatic construction of the real number system read like a novel; open https://web.archive.org/web/20190813160507/https://www.dpmms... on any page and you will see. Proofs from the BOOK by Aigner and Ziegler is a cross-section of some of the nicest proofs in reasonably elementary (read: undergrad-comprehensible) maths. Might be a bit too advanced, though (the writing is terse and a lot…
on “Ask HN: Recommend a maths book for a teenager?” ↗See also "Proofs from the Book" by Martin Aigner & Günter M. Ziegler, illustrated by Karl H. Hofmann. http://www.amazon.co.uk/Proofs-THE-BOOK-Martin-Aigner/dp/3642008550 Stuffed with beautiful short proofs. Each section starts…
on “Algorithms from the “Book”” ↗…recommendation already: - Carl B. Boyer - A History of Mathematics - William Dunham - Journey Through Genius - Philip J. Davi & Reuben Hersh - The Mathematical Experience - Martin Aigner & Günter M. Ziegler - Proofs from the Book - Imre Lakatos - Proofs and Refutations - Robert M. Young - Excursions in Calculus: An Interplay of the Continuous and the Discrete - Courant & Robbins - What is Mathematics? - George Pólya - How to Solve…
on “Ask HN: How or where to begin learning mathematics from first principles?” ↗Proofs from the Book looks superb but does anyone know of another introduction to proofs or compendium of simple proofs suitable for young mathematicians?
on “Classic Mathematics Books for Lifelong Learners” ↗I don't think this is completely true. There may not be tons of "proofs without words" in it, but the book Proofs from the Book is a great example of a nice collection of elegant proofs of elementary propositions that convince at a level that's much more effective than a pure, logical demonstration. Sure, you won't find these…
on “Proofs without words” ↗The wonderful book, Proofs from THE BOOK, http://www.amazon.com/Proofs-BOOK-Martin-Aigner/dp/364200855... discusses the art gallery problem, among many interesting mathematical problems, and then exemplifies the playful spirit of mathematical…
on “The Art Gallery Problem” ↗Béla Bollobás "The Art of Mathematics" has a very nice treatment of this problem (the history, multiple proofs) as problem number 33. And Aigner, Zeigler "Proofs from THE BOOK" also has a good treatment.
on “A computing scientist's approach to a once-deep theorem of Sylvester's (1988)” ↗For more random interesting theorems with outrageously clever and beautiful proofs, the "Proofs from THE BOOK" [1] book is a fantastic collection. As a curiosity, "THE BOOK" in the title comes from Erdos, who often referred to the book in which God keeps nice proofs of math theorems :) [1]: https://www.amazon.com/Proofs-BOOK-Martin-Aigner/dp/36420085...
on “Theorem of the Day” ↗There's a wonderful book, by the way, Proofs from THE BOOK, of, well, simple beautiful proofs. The book is named after > mathematician Paul Erdős, who often referred to "The Book" in which God keeps the most elegant proof of each mathematical theorem. During…
on “Statistician Proves Gaussian Correlation Inequality” ↗A great book in a similar vein is Proofs from THE BOOK by Martin Aigner, Karl H. Hofmann, Günter M. Ziegler. It's a reference to Paul Erdős and his notion of "The Book" in which God had written down the most beautiful and elegant proofs.
on “Some Fundamental Theorems in Mathematics” ↗Likely listed elsewhere, from the article for convenience: Zero: The Biography of a Dangerous Idea - Charles Seife Measurement - Paul Lockhart Prelude to Mathematics - W. W. Sawyer Proofs from The Book - Aigner and Ziegler The Joy of x - Steven Strogatz Things to Make and Do in the Fourth Dimension - Matt Parker What is Mathematics? - Courant and Robbins A History of PI - Petr Beckmann An Imaginary…
on “Classic Mathematics Books for Lifelong Learners” ↗There is a wonderful book called Proofs from THE BOOK, highly recommended if you like maths. Can't say it better than Wikipedia: > Proofs from THE BOOK is a book of mathematical proofs by Martin Aigner and Günter M. Ziegler. The book is dedicated to the…
on “The Mathematical Nomad, Paul Erdős” ↗I first encountered that one in Proofs from the Book, which, BTW, is a beautiful book in every sense of the word.
on “Furstenberg and Margulis awarded 2020 Abel Prize” ↗+1 for Proofs from the BOOK, Visual Group Theory, and Flatland, already recommended by others. -1 for Polya's How to Solve it - I don't remember a damned thing from it.
on “Ask HN: Recommend a maths book for a teenager?” ↗Incarnated as the wonderful Proofs from THE BOOK by Martin Aigner and Günter M. Ziegler. https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK > During a lecture in 1985, Erdős said, "You don't have to believe in God, but you should believe in The Book."
on “The Real Book” ↗