On numbers and games
by John Horton Conway · first published 1976
79% recommend21% neutral
Why HN recommends it
The original source for surreal numbers, with a gorgeous treatment of infinities and numbers built from games. Suits readers with some math maturity; Winning Ways is the gentler companion.
Summarised by Claude from recommending comments
"By defining numbers as the strengths of positions in certain games, the author arrives at a new class, the surreal numbers, that includes both real numbers and ordinal numbers. These surreal numbers are applied in the author's mathematical analysis of game strategies."--Cover.
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…Share with others what you learn. Learn from others when they share it. I'd add a few of books to your list: Graph Theory by W. T. Tufte: http://www.chapters.indigo.ca/en-ca/books/product/9780521794... On Numbers and Games by John H. Conway: http://www.amazon.com/On-Numbers-Games-John-Conway/dp/156881... And for good re-introduction to geometry and it's practical application to computer graphics: http://www.amazon.com/Primer-Graphics-Development-Wordware-L...…
on “A Software Engineer’s Adventures in Learning Mathematics” ↗John Conway's On Numbers and Games has a great overview of infinities. And since it's about games it'll be great for teaching kids too!
on “How to explain infinity to kids” ↗…Knuth (yeah, that Knuth not some other Knuth) wrote an enjoyable little semi-fictional novel about in the 70s. I thought it was a fun book, its not intense like TAOCP. Conway's also the author of ONAG. On Numbers And Games. You'll probably run into that acronym in serious discussion about game theory, like computer game design or RPG system design. Its a pretty intense book. From memory its one of those "$50 for 100…
on “Sprouts Explained” ↗My brain is absolutely hopeless at top-10-like things. But here are a few gems from some of those categories. Mathematics: John Conway's "On Numbers and Games". (If you've run across the term "surreal numbers", this is the original source. Absolutely gorgeous, but heavy going if you aren't actually a mathematician.) David McKay's "Information theory, inference,…
on “Ask HN: How big is your personal library?” ↗Of course you can always use Conway's surreal numbers (http://en.wikipedia.org/wiki/Surreal_number). I can only recommend reading his book 'On Numbers and Games': "On Numbers and Games is a mathematics book by John Horton Conway. The book is a serious mathematics book, written by a preeminent mathematician, and is directed at other mathematicians. The material…
on “Infinity is Not a number” ↗…True *Game> half * 1 == half True *Game> half * (one + one) > 1 False The best resources for learning are both by Conway: "Winning Ways for your Mathematical Plays" (WW) and "On Numbers and Games" (ONAG). WW is more accessible and introduces you to numbers via games, whereas ONAG is more of a hard-core math book that explains games via numbers. WW is probably better if you don't have a strong…
on “Infinity Is Not a Number - It's a Free Man” ↗…Theory of Transfinite Numbers which gives essentially the original development of ordinal numbers, which is based on (Cantor's own) development of set theory. Another original I recommend is Conway's On Numbers and Games, although that field (surreal numbers) has not been as influential. I think it's underrated. About Lockhart's Lament: This guy sounds a bit angry about things. I'd love to see change in math education,…
on “Math reading list” ↗…Frankenstein by Mary Shelley mainly for it's deftly abridged version and preface which gave a new dimension to the story for me. Non-fiction would either be Mortality by the late Christopher Hitchens or "On Numbers and Games" by John H. Conway.
on “Ask HN: What book changed your life in 2014?” ↗"On Numbers and Games" is a great book but it can be tough. "Winning Ways for your Mathematical Plays" by Berlekamp, Conway & Guy is a gentler introduction to surreal number. It's also very fun.
on “A Software Engineer’s Adventures in Learning Mathematics” ↗I cannot recommend On Numbers and Games by John H. Conway enough. He demonstrates the surreal numbers by proof which is a wonderful introduction to proofs. The latter section of the book is highly entertaining. He also worked on cool stuff…
on “John Conway's Life in Games” ↗…21st Century C: Amazing! Finally a practical book about C. The modern tool-set available, the notable language features of C99 and C11, and a few in-depth projects to pull it all together. Great book. On Numbers And Games: A fabulous book by one of my mathematical heroes. Well worth getting through it. Frankenstein: Mary Shelley's classic. I started collecting the new Penguin Classics line and the introductions are really…
on “Ask HN: Books you read in 2015?” ↗Conway's On Numbers And Games has this feature too - I knew I'd love it when I saw that was the first page.
on “Abstract Algebra (2016) [pdf]” ↗…formal (not looking for pop science). But it would be good if it is relatively self-contained (doesn't require too much prior knowledge, it establishes some foundations and builds from them). I'm a fan of On Numbers and Games by Conway for instance, and the more literary Surreal Numbers by Knuth (written earlier but inspired by Conway's research before publication).
on “Ask yourself dumb questions and answer them (2020)” ↗(Apparently I was extremely unclear with this text. For clarity: if you want to actually understand surreal numbers, go and read On Numbers and Games, by Conway, which is a delightful book; or get an LLM to talk you through Wikipedia. Original text follows.) It’s a terrible explanation. A surreal number is defined as a pair of sets of surreal numbers…
on “I vibed a proof of Conway's conjecture” ↗Both "Surreal Numbers" and "On Numbers and Games" do a not-terrible job of presenting surreal numbers to a (relatively) non-technical audience.
on “Trapping A Transcendental - Finding numbers that aren't solutions to polynomials” ↗