papers-we-love_papers-we-love/mathematics/README.md

## Mathematics

* [:scroll:](transcendence-of-pi.pdf) [The Transcendence of pi](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/transcendence-of-pi.pdf) by Steve Mayer
* [:scroll:] [Tilings](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/tilings.pdf) by Ardila

  This paper takes programmers out of the domain of what they are familair with counting, and into new terrain.  The paper covers a broad swath of the topic of analysis of tiling, and related strategies.

* [:scroll:] [From Dominoes to Hexagons](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/from-dominoes-to-hexagons.pdf) by Thurston

  A paper on the generalization of tilings across different base planes.

* [:scroll:] [graph isomorphism and representation theory](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/graph-isomorphism-and-representation-theory.pdf) by Daniel Litt

    Programmers work with graphs often (file system, greplin, trees, "graph isomorphism problem").   But have you ever tried to construct a simpler building-block (basis) with which graphs could be built? Or at least a different building block to build the same old things.
    
    This <10 page paper also uses `𝔰𝔩₂(ℂ)` that will be seen to be a simple mathematical object, which leads into an area of real mathematics—rep theory.

* [:scroll:] [Conway's ZIP proof](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/conways-zip-proof.pdf) by George Francis and Jeffrey Weeks

    This paper is good for most knowledge levels because
    * it is pictorial
    * it is about an object you might not have considered mathematical
    * no calculus, crypto, ML, or tough notation
    * it is short
    * it is a classification proof: “How can it be that you know something about _all possible_ `X`, even the `xϵX` you haven’t seen yet?”

* [:scroll:] [packing of spheres](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/packing-of-spheres.pdf) by N. Sloane
  * The role of E8 & Leech lattice in optimal codes
  * An understanding of how mathematically-best compression was never used
  * Ikosahedrons

* [:scroll:] [some underlying geometric notions](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/some-underlying-geometric-notions.pdf)

  This is a higher-level paper, but still a survey (so more readable). It ties together disparate areas like Platonic solids (A-D-E), Milnor’s exceptional fibre, and algebra.

* [:scroll:] [what is a young tableaux?](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/what-is-a-young-tableau.pdf) by Alexander Yong

  Young Tableau appear in many areas of mathematics.  Beyond combinatoric problems, we also see them in representation theory, and the calculus of Grassmannians.
  
  Another common topic is sorting "You do sorting all the time. Are there smart ways to organise sub-sorts?"



### Topology 
* [:scroll:] [Topology of Numbers](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/topology-of-numbers--hatcher.pdf) by hatcher
* [Applied Algebraic Topology and Sensor Networks](https://www.math.upenn.edu/~ghrist/preprints/ATSN.pdf) by Robert Ghrist
* [:scroll:] [Intro to Tropical Algebra Geometry](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/intro-to-tropical-algebraic-geometry.pdf)

  Recently there have been some papers posted about tropical geometry of neural nets. Tropical is also said to be derived from CS. This is a good introduction.

* [:scroll:] [Elements of Algebraic Topology: Sheaves](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/elements-of-algebraic-topology-ch9-sheaves.pdf)

  Seminal writing on topological structures, from one most lauded books 'Elements of Algebraic Topology'