Earliest Known Uses of

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, 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. 
RECENT CHANGES: On Aug. 4, 2015, the entry functional calculus was revised to show an earlier use found by Frédéric Jaëck.
These pages attempt to show the first uses of various words used in mathematics. Research for these pages is ongoing, and a citation should not be assumed to be the earliest use unless it is indicated as such.
Mathematical Words: Origins and Sources by John Aldrich is an excellent article and companion to this web site.
Please see also Earliest Uses of Various Mathematical Symbols, Images of Mathematicians on Postage Stamps, and Ambiguously Defined Mathematical Terms at the High School Level.
These pages are maintained by Jeff Miller, a teacher at Gulf High School in New Port Richey, Florida. The principal contributors are John Aldrich, Julio González Cabillón, Carlos César de Araújo, and James A. Landau. Other contributors are Manoel de Campos Almeida, Antranig Basman, Dave Cohen, John Conway, Martin Davis, Karen Dee Michalowicz, Joanne M. Despres of MerriamWebster Inc., Bill Dubuque, Mark Dunn, John G. Fauvel, Walter Felscher, Giovanni Ferraro, Tom Foregger, Michael N. Fried, John Harper, Antreas P. Hatzipolakis, Barnabas Hughes, Samuel S. Kutler, Franz Lemmermeyer, Avinoam Mann, Peter M. Neumann, Ken Pledger, Paul Pollack, Jim Propp, Aldo I. Ramirez, Lee Rudolph, Randy K. Schwartz, Max Urchs, Tom Walsh, William C. Waterhouse, and David Wilkins.
“Perhaps I may without immodesty lay claim to the appellation of Mathematical Adam, as I believe that I have given more names (passed into general circulation) of the creatures of mathematical reason than all the other mathematicians of the age combined.” —James Joseph Sylvester, Nature 37 (1888), p. 152.