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, function, abscissa, parameter, coordinate and perhaps derivative; 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.

A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z - Sources

RECENT CHANGES: On April 16 the entry infinitely small was revised to show that Wallis used the term in Latin in 1655 and an entry was added for adequality.

A much-improved entry for factorial by John Aldrich was added on April 15.

On March 28 the cosecant entry was revised to show an earliest known use in English in 1658 by John Newton, and to show that Rheticus apparently did not use cosecans. This new information comes from Glen Van Brummelen.

On March 28 an entry pointless was added, and the entry point was revised, both by John Aldrich.

James Landau has found in a Google print search that Boole used conditional probability in 1854. The entry for that term will be updated soon.


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 Merriam-Webster 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.

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