In the quarter of a century since three mathematicians and game theorists collaborated to create Winning Ways for Your Mathematical Plays, the book has become the definitive work on the subject of mathematical games. Now carefully revised and broken down into four volumes to accommodate new developments, the Second Edition retains the original's wealth of wit and wisdom. The authors' insightful strategies, blended with their witty and irreverent style, make reading a profitable pleasure. In Volume 4, the authors present a Diamond of a find, covering one-player games such as Solitaire.
Category theory and the work building programming langauges on top of that.
If the whole thing pans out: Langlands Program (unifying most of mathematics).
Wofram Language and the math capability is pretty amazing for such a small team.
Anything that CERN touches, from the web to various quantum theories.
Genetic mapping and science.
The Lambda CDM model, and all the work that goes into constraining their predictions with limited data is pretty amazing.
Some of the things cryptanalysts and hackers do is pretty remarkable. Side channel attacks like Row hammer attacks (not strictly crypto), EM analysis, etc..., and things like hash collisions and Differential cryptanalysis.
Modern materials science is chock full of amazing intellectual achievements.
"Winning ways for your mathematical plays" as a book on game theory is a remarkable achievement by itself.
1. Winning Ways for Your Mathematical Plays
2. A Singular Mathematical Promenade, available for free online: https://perso.ens-lyon.fr/ghys/promenade/
There are many other math books I really like - over the years I've collected a long list of reading recommendations: https://notzeb.com/rec.html (most of them won't fit as answers to this question)
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 I don't think I'd actually get much from reading it (:
In non-Conway recommendations, The Princeton Companion to Mathematics is a huge brick of a volume, but is a very complete math encyclopedia that I love to keep on my desk and thumb through when I feel distracted. You always end up learning something new.
I met him on a few different occasions when I was very young (middle and high school), and he was always extremely generous with his time, especially with an interlocutor not legally old enough to drink, and clearly brilliant in person. One example of his generosity was his collaboration on a book about triangle centers[0] with the late Steve Sigur, who was not a research mathematician but a high school teacher.
Of course the Game of Life is an enduring classic, but I’ll also always have fond memories of Winning Ways for Your Mathematical Plays and Sphere Packings, Lattices and Groups (affectionately known as SPLAG). The mathematical world has truly lost a living legend.
[0] https://books.google.com/books/about/The_Triangle_Book.html?...