papers-we-love_papers-we-love/mathematics

Mathematics

• 📜 The Transcendence of pi by Steve Mayer

• [📜] Tilings by Ardila

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

• [📜] [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.

• [📜] [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?’

• [📜] from dominoes to hexagons by Thurston

• [📜] On Invariants by Bar-Natan

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

• [📜] packing of spheres by Sloane

  • role of E8 & Leech lattice in optimal codes
  • mathematically best compression was never used
  • ikosahedron

• [📜] some underlying geometric notions

• [📜] triality in so(4,4) characteristic classes, D4 G2 singularities 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.

• [📜] [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

• [📜] topology of numbers by hatcher

• Applied Algebraic Topology and Sensor Networks by Robert Ghrist

• [📜] intro to tropical algebra geometry

  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.

• [📜] EAT: Sheaves

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