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Sean Broderick 4 years ago
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## 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: [The Transcendence of Pi](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
* :scroll: [Tilings](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
* :scroll: [From Dominoes to Hexagons](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
* :scroll: [Graph Isomorphism and Representation Theory](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()` as a simple mathematical object that leads into the area of real mathematics—represention theory.
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.
* :scroll: [Conway's ZIP proof](https://www.maths.ed.ac.uk/~v1ranick/papers/francisweeks.pdf) by George Francis and Jeffrey Weeks
A short paper, it also shows how to use `𝔰𝔩₂()` as a simple mathematical object that leads into the area of real mathematics—represention theory.
This paper presents a classification proof: "How can it be that you know something about _all possible_ `X`, even the `xϵX` you havent seen yet?" The well-diagramed discussion requires no calculus, crypto, ML, or dense notation, making it good for most knowledge levels.
* [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 havent seen yet?" The well-diagramed discussion requires no calculus, crypto, ML, or dense notation, making it good for most knowledge levels.
* [Packing of Spheres](http://neilsloane.com/doc/Me109.pdf) by N. Sloane
* :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
* [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), Milnors exceptional fibre, and algebra.
* :scroll: [What is a Young Tableaux?](https://www.ams.org/notices/200702/whatis-yong.pdf) by Alexander Yong
* [What is a Young Tableaux?](https://www.ams.org/notices/200702/whatis-yong.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.
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
* [Topology of Numbers](https://pi.math.cornell.edu/~hatcher/TN/TNbook.pdf) by hatcher
### Topology
* :scroll: [Topology of Numbers](https://pi.math.cornell.edu/~hatcher/TN/TNbook.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)
* :scroll: [Intro to Tropical Algebra Geometry](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://www.math.upenn.edu/~ghrist/EAT/EATchapter9.pdf) by Ghrist
* [Elements of Algebraic Topology: Sheaves](https://www.math.upenn.edu/~ghrist/EAT/EATchapter9.pdf) by Ghrist
Seminal writing on topological structures, from one most lauded books 'Elements of Algebraic Topology'
Seminal writing on topological structures, from one most lauded books 'Elements of Algebraic Topology'

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