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/ardila.tilings.0501170.pdf) by Ardila

  Programmers are used to counting boring things. Why not count something more interesting for a change?

* [:scroll:] [graph isomorphism and representation theory](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/daniel litt. graph isomorphism and representation theory. graphs-sl2.pdf) by Daniel Litt

    Programmers work with graphs often (file system, greplin, trees, "graph isomorphism problem" (who cares) ).   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)`, a simple mathematical object you haven’t heard of, but which is a nice lead-in to an area of real mathematics—rep theory—that (1) contains actual insights (1a) that you aren’t using (2) is simple (3) isn’t pretentious.

* [:scroll:] [Conway's ZIP proof](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/francis + weeks ZIP proof.pdf) by francis + weeks

    This paper can be shown to college freshmen because
    * it’s pictorial
    * it’s about an object you mightn’t have considered mathematical
    * no calculus, crypto, ML, or pretentious notation
    * it’s short
    * it’s a classification proof: “How can it be that you know something about _all possible_ `X`, even the `xϵX` you haven’t seen yet?’

* [: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:] [On Invariants](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/OnOnInvariants.pdf) by Bar-Natan

  2 pages about how notation and algorithms are inferior to clarity and simplicity.

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

* [:scroll:] [some underlying geometric notions](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/some-underlying-geometric-notions.pdf)
* [:scroll:] [triality in so(4,4) characteristic classes, D4 G2 singularities](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/triality.in.so(4,4).characteristic.classes.d4.g2.singularities.1311.0507.pdf) by Mikosz and Weber

  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.

  It has pictures and you’ll get a better sense of what mathematics is like from skimming it.

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

  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-algebra-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:] [EAT: Sheaves](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/EAT-chapter9-sheaves.pdf)

  Varying your dimensionality across a space. But also — distributed robots!