Mathematics, form and function
by Saunders Mac Lane · first published 1986
86% recommend14% neutral
Why HN recommends it
Broad, high-level tour of all of undergraduate-level mathematics by a respected 20th-century mathematician; useful for autodidacts and applied people who want to see how the subjects fit together.
Summarised by Claude from recommending comments
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…how they fit together. It's definitely targeted at an advanced reader though. A book describing the large-scale structure of modern mathematics and its fundamental concepts at an undergraduate level is Mathematics, Form and Function by Saunders Mac Lane. If you like this paper but feel like it's currently out of your reach, you might like this book. Something deep about mathematics that I feel has only begun to be explored in the…
on “A View of Mathematics (2005) [pdf]” ↗The best overview I've seen is Mathematics: Form and Function by Saunders Mac Lane: http://www.amazon.com/dp/0387962174/ It has the benefit of being written by one of the top mathematicians of the 20th century. There are downloadable copies in the series of tubes.
on “Logic and Mathematics - an overview.” ↗Mathematics and Logic by Mark Kac and Stan Ulam (1992 Dover paperback, ISBN 978-0486670850) [1] Mathematics, Form and Function by Saunders Mac Lane (1986 Springer-Verlag hardcover, ISBN 0-387-96217-4) [2] [1]: https://www.cut-the-knot.org/books/kac/index.shtml [2]: https://en.wikipedia.org/wiki/Mathematics,_Form_and_Function
on “Ask HN: Are there books for mathematics like Feynman's lectures on physics?” ↗This year I either read, or started to read the following interesting books: Mathematics: Form and Function by Saunders Mac Lane. This is one of my favorite books concerning the "build-up" of mathematics (it also contains nice diagrams of "relatedness" of subjects). On HN somebody once recommended Mathematics:…
on “Ask HN: Best books you read in 2012” ↗…which does just what I said above and tells a lightly fictionalized "just so" story of the "history and development" of mathematics as an excuse to introduce everything in a motivated fashion is MacLane's Mathematics: Form and Function which I just recommend endlessly. https://www.amazon.com/Mathematics-Form-Function-Saunders-Ma...
on “Linear Algebra Done Right – 4th Edition” ↗Time to read "Mathematics: Form and Function" by Saunders Mac Lane, my friend.
on “Why are mathematicians so bad at arithmetic? (2017)” ↗…programs http://www.htdp.org/2003-09-26/Book/curriculum-Z-H-1.html#no... I think I will add something that I am interested in, it is not of interest to programmers, but heck, we are hackers! All the Math you missed: Thomas A Garrity Mathematics: Form and function. Mac Lane. These are the first 2 books I would buy if I am interested in math and want to know more. These books are simply index books. They go over the land mark concepts in mathematics along with…
on “News.YC Library” ↗Since you mentioned you already have a strong applied math background, try Mathematics: Form and Function by Saunders MacLane for a broad portrait of mathematics that might get you excited to read more deeply into a given subtopic. Note that while this book surveys a broad swathe of mathematics, it depends…
on “Great books about mathematics” ↗If you can find a way to get a hold of it, Saunders MacLane's Mathematics: Form and Function is a tremendous book for understanding how math arises from the world and reflects it. What's written here is a lot more specific than that, of course, but if this illustration interests you then it might…
on “Striking parallels between mathematics and software engineering” ↗Given everyone recommending books for math autodidacts interested in learning the "breadth" of mathematics, I cannot recommend more highly Saunder's MacLane's "Mathematics, Form and Function". It reads as a high level false-historical account of how math might have been developed, in its entirety, if it unfolded in the most direct and logical way from the human experiences we all share (guided…
on “A Software Engineer’s Adventures in Learning Mathematics” ↗I really enjoy Saunders MacLane's Mathematics Form and Function for sight at the "answers" this article seeks. MacLane's argument is that mathematics arises from a relatively small number of meaningful forces and "good" mathematics arises when those forces all align…
on “Is there something mysterious about mathematics?” ↗Probably not a perfect book for someone at the HS level, but just a bit past that I would HIGHLY recommend MacLane’s Mathematics Form and Function. It’s a revisionist history of mathematics aimed to demonstrate how ideas flow from one to another. He eliminates a lot of dead-ends and takes a perspective as to one “ought” to move from one subject…
on “Ask HN: How to self-learn math?” ↗mathematics form and function by Mac Lane (sweeping coverage of all of math at about the undergrad math major level by one of the best mathematicians of the 20th) and the power broker by Caro (no clue really - Robert Moses was the…
on “Ask HN: What are you reading?” ↗…interesting entries I know about: * Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being by George Lakoff and Rafael Nunez * The Mathematician's Mind by Jacques Hadamard * Mathematics Form and Function by Saunders MacLane * On the Brink of Paradox: Highlights from the Intersection of Philosophy and Mathematics by Agustin Rayo The preface and chapter 1 of A Book of Abstract Algebra by Charles C. Pinter…
on “Philosophy of mathematics – a reading list (2020)” ↗Mathematics: Form and Function by Saunders McLane
on “Ask HN: Books with a high signal to noise ratio?” ↗