algebra: Quick Facts

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Oct. 26, 2026

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Map of the Greco-Roman world highlighting the birthplaces of notable ancient mathematicians, marked with the pi symbol and labeled with their names. Cities such as Athens, Alexandria, Syracuse, and Miletus are shown around the Mediterranean, with modern country boundaries outlined. An inset provides detail for the region of Greece and western Anatolia.

Map showing the birthplaces of prominent mathematicians from the Islamic world, marked with city names and mathematician names across the Middle East and Central Asia. Cities such as Baghdad, Basra, Harran, and others are labeled, each associated with a historical mathematician. Modern country boundaries and a locator inset of the region are included.

The French mathematician René Descartes (1596–1650) demonstrated that the square root of any line segment could be constructed by the simple, but ingenious, addition of a line segment with unit length.

Figure 5: Diagrams of lattices and one non-lattice (see text).

Figure 6: The partition lattice π4 (see text).

Figure 7: Lattices with special properties (see text).

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Topics

algebraic structure theory of equations Sturm’s theorem principle of homogeneity elementary algebra modern algebra linear algebra rational root theorem binomial theorem Descartes’s rule of signs analysis probability theory cryptology computer science combinatorics statistics geometry automata theory set theory information theory

Key People

John von Neumann

American mathematician

Diophantus

Greek mathematician

Sir William Rowan Hamilton

Irish mathematician and astronomer

Emmy Noether

German mathematician

Thomas Harriot

English mathematician and astronomer

Aryabhata

Indian astronomer and mathematician

Bhāskara II

Indian mathematician

Soviet postage stamp featuring a portrait of Al-Khwarizmi in a turban, with Russian text and decorative border, issued to commemorate the 1200th anniversary of his birth.

al-Khwārizmī

Muslim mathematician

James Joseph Sylvester

English mathematician

James H. Wilkinson

English mathematician

Sir Michael Francis Atiyah

British mathematician

Zhu Shijie

Chinese mathematician

Andrei Okounkov

Russian mathematician

Saunders Mac Lane

American mathematician

al-Karajī

Persian mathematician and engineer

Lev Semyonovich Pontryagin

Russian mathematician

Charles Hermite

French mathematician

Richard Dagobert Brauer

American mathematician

Gerd Faltings

German mathematician

Henri Cartan

French mathematician

Italian-born physicist Dr. Enrico Fermi draws a diagram at a blackboard with mathematical equations. circa 1950.

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algebra: Quick Facts

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