Unknown Quantity: A Real and Imaginary History of Algebra (2006)

Chapter: Photos, Illustrations, and Drawings

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Suggested Citation: "Photos, Illustrations, and Drawings." John Derbyshire. 2006. Unknown Quantity: A Real and Imaginary History of Algebra. Washington, DC: Joseph Henry Press. doi: 10.17226/11540.
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—Before Universal Arithmetic—

Otto Neugebauer (1899–1990) found algebra in old Babylonian tablets.

The last moments of Hypatia (c.370–415), in the Victorian imagination.

Omar Khayyam (1048–1131) wrote poetry and tackled the cubic equation.

Girolamo Cardano (1501–1576) found a general solution for the cubic.

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Suggested Citation: "Photos, Illustrations, and Drawings." John Derbyshire. 2006. Unknown Quantity: A Real and Imaginary History of Algebra. Washington, DC: Joseph Henry Press. doi: 10.17226/11540.
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—Using Letters for Numbers—

François Viète (1540–1603) separated “things sought” from “things given.”

René Descartes (1596–1650) algebraized geometry.

Sir Isaac Newton (1642–1727) saw symmetry in solutions.

Gottfried von Leibniz (1646–1716) found relief for his imagination.

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Suggested Citation: "Photos, Illustrations, and Drawings." John Derbyshire. 2006. Unknown Quantity: A Real and Imaginary History of Algebra. Washington, DC: Joseph Henry Press. doi: 10.17226/11540.
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—From Equations to Groups—

Joseph-Louis Lagrange (1736–1813) carried symmetry forward.

Paolo Ruffini (1765–1822) believed the quintic was unsolvable.

Augustin-Louis Cauchy (1789–1857) made an “arithmetic” of permutations.

Niels Abel (1802–1829) proved Ruffini correct

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Suggested Citation: "Photos, Illustrations, and Drawings." John Derbyshire. 2006. Unknown Quantity: A Real and Imaginary History of Algebra. Washington, DC: Joseph Henry Press. doi: 10.17226/11540.
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—Discovery of the Group—

Évariste Galois (1811–1832) found permutation groups in equations.

Arthur Cayley (1821–1895) abstracted the group idea.

Ludwig Sylow (1832–1918) delved into the structure of finite groups.

Camille Jordan (1838–1922) wrote the first book on groups.

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Suggested Citation: "Photos, Illustrations, and Drawings." John Derbyshire. 2006. Unknown Quantity: A Real and Imaginary History of Algebra. Washington, DC: Joseph Henry Press. doi: 10.17226/11540.
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—Into the Fourth Dimension—

Sir William R. Hamilton (1805–1865) found a new algebra.

Hermann Grassmann (1809–1877) explored vector spaces.

Bernhard Riemann (1826–1866) launched two geometric revolutions.

Edwin A. Abbott (1838–1926) took us to Flatland.

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Suggested Citation: "Photos, Illustrations, and Drawings." John Derbyshire. 2006. Unknown Quantity: A Real and Imaginary History of Algebra. Washington, DC: Joseph Henry Press. doi: 10.17226/11540.
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—Geometers and Topologists—

Julius Plücker (1801–1868) based his geometry on lines, not points.

Sophus Lie (1842–1899) mastered continuous groups.

Felix Klein (1849–1925) urged the group-ification of geometry.

Henri Poincaré (1854–1912) algebraized topology.

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Suggested Citation: "Photos, Illustrations, and Drawings." John Derbyshire. 2006. Unknown Quantity: A Real and Imaginary History of Algebra. Washington, DC: Joseph Henry Press. doi: 10.17226/11540.
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—Lady of the Rings, and Some Lords—

Eduard Kummer (1810–1893) used algebra on Fermat’s Last Theorem.

Richard Dedekind (1831–1916) discovered ideals.

David Hilbert (1862–1943): A geometry of tables, chairs, and beer mugs.

Emmy Noether (1882–1935) pulled it all together.

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Suggested Citation: "Photos, Illustrations, and Drawings." John Derbyshire. 2006. Unknown Quantity: A Real and Imaginary History of Algebra. Washington, DC: Joseph Henry Press. doi: 10.17226/11540.
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—Modern Algebra—

Solomon Lefschetz (1884–1972) harpooned a whale.

Oscar Zariski (1899–1986) refounded algebraic geometry.

Saunders Mac Lane (1909–2005) attained a higher level of abstraction.

Alexander Grothendieck (1928–): “As if summoned from the void.”

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