Reddit mentions of On Numbers and Games

Your post has too little context/content for anyone to give you particularly relevant or specific advice. You should list what you know already and what you’re trying to learn. I find it’s easiest to research a new subject when I have a concrete problem I’m trying to solve.

But anyway, I’m going to assume you studied up through single variable calculus and are reasonably motivated to put some effort in with your reading. Here are some books which you might enjoy, depending on your interests. All should be reasonably accessible (to, say, a sharp and motivated undergraduate), but they’ll all take some work:

(in no particular order)
Gödel, Escher, Bach: An Eternal Golden Braid (wikipedia)
To Mock a Mockingbird (wikipedia)
Structure in Nature is a Strategy for Design
Geometry and the Imagination
Visual Group Theory (website)
The Little Schemer (website)
Visual Complex Analysis (website)
Nonlinear Dynamics and Chaos (website)
Music, a Mathematical Offering (website)
QED
Mathematics and its History
The Nature and Growth of Modern Mathematics
Proofs from THE BOOK (wikipedia)
Concrete Mathematics (website, wikipedia)
The Symmetries of Things
Quantum Computing Since Democritus (website)
Solid Shape
On Numbers and Games (wikipedia)
Street-Fighting Mathematics (website)

But also, you’ll probably get more useful response somewhere else, e.g. /r/learnmath. (On /r/math you’re likely to attract downvotes with a question like this.)

You might enjoy:
https://www.reddit.com/r/math/comments/2mkmk0/a_compilation_of_useful_free_online_math_resources/
https://www.reddit.com/r/mathbooks/top/?sort=top&t=all

It doesn’t seem to be grounded in philosophy. I would argue Jon Conways writings on games and numbers are a clear influence.
https://www.amazon.com/Numbers-Games-John-H-Conway/dp/1568811276

Linear programming:

• Vanderbei, Linear Programming: Foundations and Extensions
  
  Combinatorial optimization:
  
  
• Papadimitriou and Steiglitz, Combinatorial Optimization: Algorithms and Complexity
  
• Cook, Cunningham, Pulleyblank, and Schrijver, Combinatorial Optimization
  
  Game theory:
  
  
• Fudenberg and Tirole, Game Theory
  
• Osborne and Rubinstein, A Course in Game Theory
  
  Combinatorial game theory:
  
  
• Berlekamp, Conway, and Guy, Winning Ways for Your Mathematical Plays (volume 1, volume 2, volume 3, volume 4)
  
• Berlekamp, The Dots and Boxes Game: Sophisticated Child's Play
  
• Albert, Nowakowski, and Wolfe, Lessons in Play: An Introduction to Combinatorial Game Theory
  
• Conway, On Numbers and Games

Cardinal subtraction:
> k1-k2=k3 iff k1+k3 =k2

In this case, k1=k2 so we need to find the value(s) of k3 that don't change k1 when added. Unfortunately this includes all the finite numbers and k1. It does however give you a family of answers that satisfy the equation, so in a sense any answer you take from that set is correct. Maro can basically give any ruling and it won't "break math".

Once we get to Omnific Integers we can start to give nice answers (You can do similar things with Ordinals, but the math is not as nice since you don't have negatives among other things). The first infinity is ω, and:

> ω-ω=0.

In fact, the omnific integers satisfy all the basic laws of arithmetic. ω+1 > ω > ω - 1> 0 in this setting.
You can divide and multiply as well, so if I have ω+18 life and cast a [[Dire Fleet Ravager]], I will have ω/3+6 life after the effect resolves. Knuth wrote a small book about Surreal numbers, which are used to construct to construct the omnific integers. On numbers and games is a more in depth look at this number system.