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.

**Words beginning with A - C****Words beginning with D - F****Words beginning with G - L****Words beginning with M - R****Words beginning with S - Z****Sources**

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.