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

## Mathematics

* :scroll: [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

  The paper covers a broad swath of the topic on 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

    The *graph isomorphism problem* shows how to construct graphs using a simple building-block ("basis").  The same method applies to finding different building blocks to construct the same things.  This technique can be applied to file systems, greplin, trees, virtual DOM, etc.
    
    A short paper, it also shows how to use `𝔰𝔩₂(ℂ)` as a simple mathematical object that leads into the area of real mathematics—represention theory.

* :scroll: [Conway's ZIP proof](https://www.maths.ed.ac.uk/~v1ranick/papers/francisweeks.pdf) by George Francis and Jeffrey Weeks

    This paper presents a classification proof: "How can it be that you know something about _all possible_ `X`, even the `xϵX` you haven’t seen yet?"  The well-diagramed discussion requires no calculus, crypto, ML, or dense notation, making it good for most knowledge levels.

* :scroll: [Packing of Spheres](http://neilsloane.com/doc/Me109.pdf) by N. Sloane
  Discusses the role of E8 & Leech lattices in optimal codes for mathematically-ideal compression. Ikosahedrons, a tool in this investigation, are also presented.

* :scroll: [Some Underlying Geometric Notions](https://pi.math.cornell.edu/~hatcher/AT/AT.pdf) by Hatcher

  High-Level survey which relates disparate topics, e.g. 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 combinatoric problems, representation theory, and the calculus of Grassmannians.  Another common topic is sorting, and smarter 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'