Elements
by Euclid · first published 1482
27% recommend70% neutral4% critical
Why HN recommends it
Concise axiom-to-theorem geometry showing how rigorous proof is built from a few definitions and postulates; recommended for self-study, math beginners, and anyone wanting the origins of geometry.
Summarised by Claude from recommending comments
The classic Heath translation, in a completely new layout with plenty of space and generous margins. An affordable but sturdy student and teacher sewn softcover edition in one volume, with minimal notes and a new index/glossar
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Interesting and pleasant to read. I find it inspiring that some people today (but more a couple of generations ago) still learn geometry from (usually translations of) Euclid’s Elements. I just love the idea that people still study math from a book more than 2,000 years old.
on “Who Said Nobody Read Isaac Newton?” ↗(Someone already posted How to Solve It which would be my first recommendation on this forum.) The Zhuangzi, probably at least two translations. The Elements (that is, Euclid's). Process and Reality has had the most impact on my thinking but it's one of the most unapproachable things I've ever read. Get there eventually.
on “Ask HN: Books that teach you to think” ↗There’s a very nice book about the Poincaré conjecture, going from the roots of geometry in Euclid’s Elements to Perelman’s proof: http://books.google.com/books?id=kM8fAQAAIAAJ At least for me it hit the sweet spot between a rigorous math paper and a good story book.
on “Math genius Grigori Perelman explains why he turned down $1 million prize” ↗…very important object lessons in it). Surely Plato and Aristotle deserve some attention! The contents of the latter's Rhetoric is essential for when you can't reach people with dialectic. Euclid's Elements is still about as good as you can get for what it teaches. Plutarch is great, but I really like that period of history. To it I would add reading some of the earlier bits of Livy. Read, or better yet…
on “Ask HN: Books with a high signal to noise ratio?” ↗…sight of which techniques to reach for or appreciate how a superficially complex-looking thing is simple but being expressed very tersely. Other books I found worth reading over the years: Euclid's Elements, because you can't be too good at geometry and the proofs are so concise you can treat them as warm-up exercises Hofstadter's Godel, Escher, Bach: An Eternal Golden Braid, which uses humor, poetry, art,…
on “Ask HN: How to learn mathematical proofs from scratch?” ↗Read and understand the thirteen books of the Elements by Euclid, preferably in the original Greek. This ought to be sufficient for a fundamental understanding of the mathematical method, its power and application--all generated from a handful of axioms and…
on “2021 Revision of the Mathematics Framework for California Public Schools” ↗For a nicely illustrated and colored text of Euclid's Elements see: Byrne: Six Books of Euclid : https://smile.amazon.com/gp/product/3836559382
on “Euclid's Elements (1997)” ↗I spent a year in a "Great Books" college, where there are no textbooks, no lectures, etc., just primary sources progressing roughly chronologically. For first year math, you go through Elements almost entirely front-to-back. I have mixed feelings about the Great Books programs in general, but the Euclid class was remarkable. It tends not to be a math-heavy group of students, but even those who…
on “Euclid's Elements (1997)” ↗…to resolve all proofs down to postulates. I would recommend finding an area that you are interested in and then finding a famous problem. My favorite books are: * Euler: Master of us all * Euclid's Elements * Hardy and Wright: Introduction to a Theory of Numbers * Jonathan Stillwell: Yearning for the Impossible * Ash and Gross: Fearless Symmetry * Jean-Pierre Tignol: Galois' Theory of Algebraic Equations…
on “Learning Math” ↗Invalidates? Absolutely none. Good mathematics is eternal and the Elements has some beautiful mathematics. What I meant to say is that in the fullness of time they have been expanded on and surpassed. You can still learn good and valid mathematics from Euclid, but you can…
on “Ask HN: Best Mathematics book for complete noobie?” ↗I thought he meant Euclid's Elements - now that's an awesome book. http://en.wikipedia.org/wiki/Euclids_Elements (the link doesn't work because HN removes the apostrophe from hyperlinks for some reason)
on “The Elements - A Perfect Coffee Table Book for Nerds” ↗…equivalent of compass and straightedge geometrical construction[1]. It's about starting with fundamental and simple components and building higher-level abstractions upon these firm foundations. Euclid's Elements, which heavily relied on this approach and made it famous, was arguably the most influential mathematical text ever written. By combining simple constructs according to simple rules, you can be certain…
on “The Lambda Calculus for Absolute Dummies (2012)” ↗…them are helpful in your case, since they show you proof construction in action. Pick a classic, something that everyone is familiar with but at the time of its writing it was revolutionary. Euclid's The Elements come to mind.
on “Hilbert's 24th problem” ↗…will not recognise the crux of the proof, but will simply see something ends up being equal to something else in some identity without understanding how that relates to what was being proved. Euclid's Elements (an ancient Greek textbook on Geometry) is a good model in this regard. He first states what he is to prove. He then starts from the assumptions and finishes with what he was to prove. Each step in between…
on “Pixar in a Box – Khan Academy” ↗…into propositions, and certain paragraphs into arguments. This work is the purest form of that, a true paragon with enviable succinctness. Even if you're not into math, try picking up a copy of Euclid's Elements to see how articulate thoughts _can_ be.
on “Euclid's Elements (1997)” ↗