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Algebraic geometry

branch of mathematics dealing with algebraic varieties and their generalizations (schemes, etc.) From Wikiquote, the free quote compendium

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Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.

Quotes

  • While the move from dimension 2 to dimension 3 appears to be the obvious step there is a sense in which one should move from 2 to 4. This comes from the consideration of complex algebraic geometry. For complex dimension 1 this theory was started by Abel and continued by Riemann. For algebraic varieties of complex dimension n the real dimension is 2n, so the case n = 2 leads to 4-dimensional real manifolds. The key figures in the topology of higher-dimensional algebraic varieties were Lefschetz, Hodge, Cartan and Serre. While general algebraic geometry was one of the major developments of the second half of the 20th century, the topology of real 4-manifolds had a great surprise in store when Simon Donaldson made spectacular discoveries opening up an entirely new area.
  • Should you just be an algebraist or a geometer? is like saying Would you rather be deaf or blind? If you are blind, you do not see space: if you are deaf, you do not hear, and hearing takes place in time. On the whole, we prefer to have both faculties.
    • Michael Atiyah (2000). Mathematics in the 20th Century: geometry versus algebra, Mathematics Today, 37(2), 46- 53.
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See also

Wikipedia has an article about:

Mathematics
Mathematicians
(by country)

Abel Anaxagoras Archimedes Aristarchus of Samos Averroes Arnold Banach 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 Riemann Russell Schwartz Serre Tao Tarski Thales Turing Weil Weyl Wiles Witten

Numbers

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

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

Ancient Greek mathematics Euclid's Elements History of algebra History of calculus History of logarithms Indian mathematics Principia Mathematica

Other

Mathematics and mysticism 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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