Surreal numbers
how two ex-students turned on to pure mathematics and found total happiness : a mathematical novelette
by Donald Knuth · first published 1974
66% recommend34% neutral
Why HN recommends it
Short, playful math story told as a dialogue between two characters who discover surreal numbers themselves; it teaches by making the reader explore, and suits the curious who want an unusual, fun math read.
Summarised by Claude from recommending comments
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Another trivia point is he's the inventor of surreal numbers, which 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…
on “Sprouts Explained” ↗You might get a kick out of "Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness, 1974, ISBN 0-201-03812-9." by Knuth. Yeah, that Knuth. I haven't read it in a decade or two but it was enjoyable and on…
on “Hyperreal numbers: infinities and infinitesimals” ↗What no love for Knuth's Surreal numbers? https://cs.stanford.edu/~knuth/sn.html I think if you're not into sci fi, you've discovered what most call the distinction between hard and soft sci fi. Soft sci fi is the usual boring eternal "human…
on “Science Fiction by Scientists” ↗Then John H. Conway's Surreal Numbers might be of interest to you. Donald Knuth wrote a book about the subject and it's actually in the form of a story with dialogue, not your typical math book. I'll attempt a summary. It is possible to…
on “Foundations of Mathematics (2015) [pdf]” ↗…Hackers by Stephen Levy (problematic as it may be) and Journey Through Genius by William Dunham. They led me into deeper dives and other books which rooted my knowledge in some chronological perspective. - Surreal Numbers by Donald Knuth, a “fiction” book about Conway’s surreal numbers. Holy cow, this shifts your perspective on what a number can be. - Godel Escher Bach by Hofstadter, recommended by others, as a mind bending…
on “Ask HN: Life Changing Books?” ↗…leave it in? To really get some feeling for the content of the text, it seems to be really essential that the reader explores the content a bit herself. This is illustrated quite well in Don Knuth's "Surreal Numbers". Knowing this is probably the key to learning to read mathematics. One can try to write all this out, but that will make the text harder to read for the mathematician, who now has to find the important…
on “How to Read Mathematics” ↗…it depends on your friends, but I'll support the parent's case of some of those being great in-person discussion books, especially Knuth. And lots of great math books. Knuth's little "romance novel", Surreal Numbers, is a great example of a highly discussable math book.
on “The Books We Talk About (and Those We Don’t)” ↗Check out Knuth's book "Surreal Numbers: How two ex-students turned on to pure mathematics and found total happiness". It's a book about discovering new mathematics, in this case Conway's Surreal Numbers. http://www-cs-faculty.stanford.edu/~knuth/sn.html
on “Communicating Advanced Mathematics to Kids” ↗Barely qualifying as fiction, but very focused on the beauty and entertainment value of mathematics: "Surreal Numbers" by Donald Knuth.
on “MathFiction: Alex Recommends” ↗Speaking of Life, a few years back I ran across a photo of Conway confronting a different form of Life that made me laugh out loud: https://imgur.com/a/L4JGQN6 Always enjoyed Knuth's book _Surreal Numbers_ on Conway's work. It's a very unusual math tutorial.
on “John Conway has died” ↗…Winning Ways for your Mathematical Plays is really fun to thumb through. The Book of Numbers is fantastic and something I would gift to any mathematically curious, somewhat independent, child. Knuth's Surreal Numbers is also a great read. Got On Numbers and Games coming in the mail, and am trying to track down a reasonably priced copy of The Symmetries of Things. I'm tempted to get the Atlas for my collection, but…
on “Ask HN: What kind of math do you study in your free time?” ↗Surreal Numbers by Knuth is great, although not related to analyis/calculus: https://www.amazon.com/Surreal-Numbers-Donald-Knuth/dp/02010...
on “Ask HN: Recommend a maths book for a teenager?” ↗For what little it's worth, I am not a religious person, but I found Knuth's Surreal Numbers perfectly reasonable, much more on the tongue-in-cheek side than the proselytizing side. And the surreal numbers are over of my favorite things in mathematics, so I'd say they're worth it :)
Knuth has a nice book on Surreal numbers. https://www-cs-faculty.stanford.edu/~knuth/sn.html This interview is excellent https://www.youtube.com/watch?v=mPn2AdMH7UQ He wrote the book in less than a week, the book was just flowing for days…
on “Surreal Numbers – An Introduction (2019) [pdf]” ↗…of books that are simply "collected papers" makes it easy to focus on something much narrower. For impractical, you may want to start from Selected Papers on Fun and Games. And then he has books like Surreal Numbers, which is written as a story of a couple discovering mathematical notation and deriving a whole system...
on “Ask HN: Most interesting, mildly impractical, well-written books on software?” ↗