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Map The Matics

This document provides a visual representation of the relationships between various fields of mathematics. It shows mathematics subjects as nodes connected by arrows to indicate connections and quotients between the fields. At the center is a gray shape loosely representing various aspects of geometry, surrounded by fields like topology, analysis, algebra, and number theory.

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fcc3
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457 views1 page

Map The Matics

This document provides a visual representation of the relationships between various fields of mathematics. It shows mathematics subjects as nodes connected by arrows to indicate connections and quotients between the fields. At the center is a gray shape loosely representing various aspects of geometry, surrounded by fields like topology, analysis, algebra, and number theory.

Uploaded by

fcc3
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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a biased, not fully faithful geometric representation of mathematics

arrows indicate how to take the quotient


finance maths
by axel sarlin and innokentij zotov measure-theoretic
PDE ergodic theory probability theory
updated 2017-02-08 21:10
harmonic analysis dynamical systems
measure theory
analysis
quantum physics functional analysis geometric measure theory
complex analysis
quantum symplectic *
riemannian geometry
information theory lie theory geometry
differential geometry **
representation differential topology
theory alg. and top. K-theory top. graph
commutative algebra theory
homological algebra topology knot theory
non-commutative algebraic geometry
computational algebra algebra and geometry low-dimensional topology
arithmetic and algebraic topology
algebra tropical
diophantine geometry

geometry algebraic number theory homotopy theory

group theory category theory topos theory ***


homotopy type theory * the gray shape is supposed to
cryptography algebraic combinatorics loosely represent various
logic aspects of geometry
combinatorics
model theory
discrete maths proof theory
decision theory ** many physical subjects, such as
gauge theory, 4-manifolds and
discrete probability computability theory relativity could be placed around
theory graph theory here
set theory

representation theory is hard to place: it has many connections to e.g. *** the n-lab perspective on modern physics
number theory, differential geometry, harmonic analysis, combinatorics... would end up in here somewhere
whilst not really a research subject on its own, linear algebra would fit in here. Some still
active aspects of it could be considered computational or commutative algebra...

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