Topics in mathematics
An alphabetical list of mathematical topics is available; together with the "Watch links" feature, this list is useful to track changes in mathematics articles. The following list of subfields and topics reflects one organizational view of mathematics.
Quantity
Numbers -- Natural numbers -- Integers -- Rational numbers -- Real numbers -- Complex numbers -- Hypercomplex numbers -- Quaternions -- Octonions -- Sedenions -- Hyperreal numbers -- Surreal numbers -- Ordinal numbers -- Cardinal numbers -- p-adic numberss -- Integer sequences -- Mathematical constants -- Number names -- Infinity
Change
Arithmetic -- Calculus -- Vector calculus -- Analysis -- Differential equations -- Dynamical systems and chaos theory -- Fractional calculus -- List of functions
Structure
Abstract algebra -- Number theory -- Algebraic geometry -- Group theory -- Monoids -- Analysis -- Topology -- Linear algebra -- Graph theory -- Universal algebra -- Category theory
Space
Topology -- Geometry -- Trigonometry -- Algebraic geometry -- Differential geometry -- Differential topology -- Algebraic topology -- Linear algebra -- Fractal geometry
Discrete mathematics
Combinatorics -- Naive set theory -- Probability -- Theory of computation -- Finite mathematics -- Cryptography -- Graph theory -- Game theory
Applied Mathematics
Mechanics -- Numerical analysis -- Optimization -- Probability -- Statistics -- Financial mathematics
Famous Theorems and Conjectures
Fermat's last theorem -- Riemann hypothesis -- Continuum hypothesis -- P=NP -- Goldbach's conjecture -- Twin Prime Conjecture -- Gödel's incompleteness theorems -- Poincaré conjecture -- Cantor's diagonal argument -- Pythagorean theorem -- Central limit theorem -- Fundamental theorem of calculus -- Fundamental theorem of algebra -- Fundamental theorem of arithmetic -- Four color theorem -- Zorn's lemma -- "The most remarkable formula in the world
Foundations and Methods
Philosophy of mathematics -- Mathematical intuitionism -- Mathematical constructivism -- Foundations of mathematics -- Set theory -- Symbolic logic -- Model theory -- Category theory -- Theorem-proving -- Logic -- Reverse Mathematics -- Table of mathematical symbols
History and the World of Mathematicians
History of mathematics -- Timeline of mathematics -- Mathematicians -- Fields medal -- Abel Prize -- Millennium Prize Problems (Clay Math Prize) -- International Mathematical Union -- Mathematics competitions -- Lateral thinking
Mathematics and other fields
Mathematics and architecture
Mathematical tools
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Quotes
Referring to the axiomatic method, where certain properties of an (otherwise unknown) structure are assumed and consequences thereof are then logically derived, Bertrand Russell said:
- Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
This may explain why John Von Neumann once said:
- In mathematics you don't understand things. You just get used to them.