Mathematical logic

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.

Quotes

  • Frege's development began with... "an epoch-making little book" called Begriffsschrift, translated as Concept Script or Conceptual Notation... Just as Aristotle's Prior Analytics is the foundation of traditional or syllogistic logic—the logic of the categorical three-term syllogism, Frege's Begriffsschrift is the keystone of modern or mathematical logic.
    • Michael Losonsky, Linguistic Turns in Modern Philosophy (2006) pp. 148-149.
  • In 1920 logic was mostly a philosopher's garden. There were also a few mathematicians there, cultivating the logical roots of the mathematical tree. Today, Recursion Theory, Set Theory, Model Theory and Proof Theory, logic's major subdisciplines, have become full-fledged branches of mathematics.
    • Anil Nerode; Richard Shore (17 January 1997). Logic for Applications. Springer Science & Business Media. p. 1. ISBN 978-0-387-94893-5. 

Mathematics
Mathematicians
(by country)

Abel • Anaxagoras • Archimedes • Aristarchus of Samos • Aryabhata • Averroes • Arnold • Banach • Bhāskara I • Bhāskara II • Brahmagupta • Cantor • Cartan • Chern • Cohen • Descartes • Diophantus • Erdős • Euclid • Euler • Fourier • Gauss • Gödel • Grassmann • Grothendieck • Hamilton • Hilbert • Hypatia • Lagrange • Laplace • Leibniz • Milnor • Newton • von Neumann • Noether • Penrose • Perelman • Poincaré • Pólya • Pythagoras • Ramanujan • Riemann • Russell • Schwartz • Serre • Tao • Tarski • Thales • Turing • Weil • Weyl • Wiles • Witten

Numbers

1 • 23 • 360 • e • π • Fibonacci numbers • Fraction • Irrational number • Negative number • Number • Prime number • Quaternion • Octonion • Sedenion

Concepts

Abstraction • Algorithms • Axiomatic system • Completeness • Deductive reasoning • Differential equation • Dimension • Ellipse • Elliptic curve • Exponential growth • Infinity • Integration • Geodesic • Induction • Proof • Partial differential equation • Principle of least action • Prisoner's dilemma • Probability • Randomness • Theorem • Topological space • Wave equation

Results

Euler's identity • Fermat's Last Theorem

Pure math

Abstract algebra • Algebra • Analysis • Algebraic geometry (Sheaf theory) • Algebraic topology • Arithmetic • Calculus • Category theory • Combinatorics • Commutative algebra • Complex analysis • Differential calculus • Differential geometry • Differential topology • Ergodic theory • Foundations of mathematics • Functional analysis • Game theory • Geometry • Global analysis • Graph theory • Group theory • Harmonic analysis • Homological algebra • Invariant theory • Logic • Non-Euclidean geometry • Nonstandard analysis • Number theory • Numerical analysis • Operations research • Representation theory • Ring theory • Set theory • Sheaf theory • Statistics • Symplectic geometry • Topology

Applied math

Computational fluid dynamics • Econometrics • Fluid mechanics • Mathematical physics • Science

History of math

Algorism • Ancient Greek mathematics • Euclid's Elements • Hindu–Arabic numeral system • History of algebra • History of calculus • History of logarithms • Indian mathematics • Principia Mathematica

Other

Mathematics and mysticism • Mathematical Platonism • Mathematics education • Mathematics, from the points of view of the Mathematician and of the Physicist • Philosophy of mathematics • Unification in science and mathematics


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