Unknown Quantity is a history of algebra for ordinary (i.e. not especially mathematical) readers.
I have tried to cover the entire history of the subject, from 1800 B.C. down to the present day, describing all the main lines of development.
From the Introduction:
This is not a textbook. I hope only to show what algebraic ideas are like, how the later ones developed from the earlier ones, and what kind of people were responsible for it all, in what kind of historical circumstances.
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Here is the table of contents. Note that the main narrative is interrupted here and there with "math primers" — brief, simple accounts of key mathematical topics that the reader will need to understand in order to get the most from the chapters that follow.
 Contents |
|
| • | Introduction |
| • | Math Primer: Numbers and Polynomials |
| Part 1: The Unknown Quantity | |
| 1 | Four Thousand Years Ago |
| 2 | The Father of Algebra |
| 3 | Completion and Reduction |
| • | Math Primer: Cubic and Quartic Equations |
| 4 | Commerce and Competition |
| 5 | Relief for the Imagination |
| Part 2: Universal Arithmetic | |
| 6 | The Lion's Claw |
| • | Math Primer: Roots of Unity |
| 7 | The Assault on the Quintic |
| • | Math Primer: Vector Spaces and Algebras |
| 8 | The Leap into the Fourth Dimension |
| 9 | An Oblong Arrangement of Terms |
| 10 | Victoria's Brumous Isles |
| Part 3: Levels of Abstraction | |
| • | Math Primer: Field Theory |
| 11 | Pistols at Dawn |
| 12 | Lady of the Rings |
| • | Math Primer: Algebraic Geometry |
| 13 | Geometry Makes a Comeback |
| 14 | Algebraic This, Algebraic That |
| 15 | From Universal Arithmetic to Universal Algebra |
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Here is a list of the persons shown in the picture "well" at the center of the book.
| Otto Neugebauer (1899-1900) | Sir William R. Hamilton (1805-1865) |
| Hypatia (c.370-415) | Hermann Grassmann (1809-1877) |
| Omar Khayyam (1048-1131) | Bernhard Riemann (1826-1866) |
| Girolamo Cardano (1501-1576) | Edwin A. Abbott (1838-1926) |
| François Viète (1540-1603) | Julius Plücker (1801-1868) |
| René Descartes (1596-1650) | Sophus Lie (1842-1899) |
| Sir Isaac Newton (1642-1727) | Felix Klein (1849-1925) |
| Gottfried von Leibniz (1646-1716) | Henri Poincaré (1854-1912) |
| Joseph-Louis Lagrange (1736-1813) | Eduard Kummer (1810-1893) |
| Paolo Ruffini (1765-1822) | Richard Dedekind (1831-1916) |
| Augustin-Louis Cauchy (1789-1857) | David Hilbert (1862-1943) |
| Niels Abel (1802-1829) | Emmy Noether (1882-1935) |
| Évariste Galois (1811-1832) | Solomon Lefschetz (1884-1972) |
| Arthur Cayley (1821-1895) | Oscar Zariski (1899-1986) |
| Ludwig Sylow (1832-1918) | Saunders Mac Lane (1909-2005) |
| Camille Jordan (1838-1922) | Alexander Grothendieck (1928–) |
Of course, many other algebraists are covered in the book. I had to make a selection for the "well."
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