# Earliest Known Uses of Some of the Words of Mathematics

LEFT TO RIGHT: James Joseph Sylvester, who introduced the words matrix, discriminant, invariant, totient, and Jacobian; Gottfried Wilhelm Leibniz, who introduced the words variable, constant, derivative, function, abscissa, parameter, and coordinate; René Descartes, who introduced the terms real number and imaginary number; Sir William Rowan Hamilton, who introduced the terms vector, scalar, tensor, associative, and quaternion; and John Wallis, who introduced the terms induction, interpolation, continued fraction, mantissa, and hypergeometric series.

These pages attempt to show the first uses of various words used in mathematics. Research for these pages is ongoing, and the uses cited should not be assumed to be the first uses that occurred unless it is stated that the term was introduced or coined by the mathematician named. If you are able antedate any of the entries herein, please contact Jeff Miller, a teacher at Gulf High School in New Port Richey, Florida, who maintains these pages. See also Earliest Uses of Various Mathematical Symbols.

The principal contributor for these pages is Julio González Cabillón. Others who have assisted are Dave Cohen, Aldo I. Ramirez, Michael N. Fried, Franz Lemmermeyer, William C. Waterhouse, John Conway, John Harper, Randy K. Schwartz, Ken Pledger, Jim Propp, Avinoam Mann, David Wilkins, John G. Fauvel, Lee Rudolpoh, Bill Dubuque, Manoel de Campos Almeida, Antreas P. Hatzipolakis, Tom Walsh, Mark Dunn, Samuel S. Kutler, Paul Pollack, James A. Landau, Martin Davis, Karen Dee Michalowicz, Peter M. Neumann, Giovanni Ferraro, and Joanne M. Despres of Merriam-Webster Inc.

Abbreviations: OED2 refers to the Oxford English Dictionary, Second Edition; MWCD10 is Merriam-Webster's Collegiate Dictionary, Tenth Edition; RHUD2 refers to the Random House Dictionary of the English Language, Second Edition Unabridged. If the earliest use of a word known to Webster is its appearance in a dictionary, the date is preceded by "ca."; in those cases, it can be assumed earlier uses of those words exist.

Oxford English Dictionary Note: Mark Dunn, Senior Assistant Science Editor for the New OED, writes, "One thing we are now paying more attention to than the original editors is the issue of foreign coinages. We are as often as possible trying to trace the coinage of a term (where applicable), even where this was in a foreign language. This happens more often in mathematics than in most subjects, but the OED has far fewer such coinages, partly I think because many concepts are interpreted in different ways as the subject develops, so the original work becomes less relevant and is gradually forgotten, making it difficult to trace." Dunn would appreciate any assistance by readers of this page regarding coinages of mathematical terms. Any such information provided to this page will be available to him also.