Abstract
The term “algebra” dates back to the ninth century AD, but the subject, referring to the solution of polynomial equations, is roughly four thousand years old. It originated in about 1800 BC, with the Babylonians, who solved linear and quadratic equations much as we do today. They had no symbolic notation, so their equations had numerical coefficients, with their number system consisting of positive integers and rationals. Their solutions were prescriptive: do such and such and you will arrive at the answer. But the numerous repetitions of the same type of solution suggest that the procedure functioned as a standard algorithm.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Cooke, R.: Classical Algebra: Its Nature, Origins, and Uses. Wiley, Hoboken (2008)
Crowe, M.J.: A History of Vector Analysis. University of Notre Dame Press, Notre Dame (1967)
Ebbinghaus, H.-D.: Numbers. Springer-Verlag, New York (1990)
Hankins, T.L.: Sir William Rowan Hamilton. The Johns Hopkins University Press, Baltimore (1980)
Herstein, I.N.: Topics in Algebra. Blaisdell Publishing Co., New York (1964)
Kantor, I.L., Solodovnikov, A.S.: Hypercomplex Numbers: An Elementary Introduction to Algebras. Springer-Verlag, New York (1989) (Translated from the Russian by A. Shenitzer.)
Massey, W.: Cross products of vectors in higher dimensional euclidean spaces. Am. Math. Mon. 90, 697–701 (1983)
Niven, I.: Equations in quaternions. Am. Math. Mon. 48, 654–661 (1941)
Niven, I.: The roots of a quaternion. Am. Math. Mon. 49, 386–388 (1942)
Poincaré, H.: Poincaré’s review of Hilbert’s foundations of geometry. Bull. Am. Math. Soc. 37, 77–78 (1999) (Reprinted)
van der Waerden B.L.: Hamilton’s discovery of quaternions. Math. Mag. 49, 227–234 (1976)
Wussing, H.: The Genesis of the Abstract Group Concept. MIT Press, Cambridge (1984) (Translated from the German by A. Shenitzer.)
Further Reading
Bashmakova, I.G., Smirnova, G.S.: The Beginnings and Evolution of Algebra. The Mathematical Association of America, Washington, D.C. (2000) (Translated from the Russian by A. Shenitzer.)
Berlinghoff, W.P., Gouvêa, F.Q.: Math Through the Ages: A Gentle History for Teachers and Others, Expanded Edition. The Mathematical Association of America: Oxton House Publishing, Washington, D.C. (2004)
Dobbs, D.E., Hanks, R.: A Modern Course on the Theory of Equations. Polygonal Publishing House, Passaic (1980)
Katz, V.: A History of Mathematics: An Introduction, 3rd edn. Addison-Wesley, Boston (2009)
Mazur, B.: Imagining Numbers. Farrar, Straus, and Giroux, New York (2003)
Turnbull, W.: Theory of Equations. Oliver & Boyd, New York (1957)
van der Waerden B.L.: A History of Algebra. Springer-Verlag, Berlin (1985)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Grant, H., Kleiner, I. (2015). Hypercomplex Numbers: From Algebra to Algebras. In: Turning Points in the History of Mathematics. Compact Textbooks in Mathematics. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-3264-1_8
Download citation
DOI: https://doi.org/10.1007/978-1-4939-3264-1_8
Published:
Publisher Name: Birkhäuser, New York, NY
Print ISBN: 978-1-4939-3263-4
Online ISBN: 978-1-4939-3264-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)