# Earliest Uses of Some 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,*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;*

**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

Sources

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.

James Joseph Sylvester,

*Nature*

**37**(1888), p. 152

Perhaps I may without immodesty lay claim to the appellation ofMathematical 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.

These pages were created by Jeff Miller, recently retired as a math 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.