# Earliest Known Uses of Some of the Words of Mathematics (J)

**J-SHAPED**is found in 1911 in

*An Introduction to the Theory of Statistics*by G. U. Yule (David, 1995).

**JACKKNIFE**in Statistics. David (1995) gives Rupert G. Miller's "A Trustworthy Jackknife,"

*Annals of Mathematical Statistics,*

**35**(1964), 1594-1605 as the first published use of the term. Miller explains that John W. Tukey had adopted the term because "a boy-scout's jackknife is symbolic of a rough-and-ready instrument capable of being utilized in all contingencies and emergencies." M. H. Quenouille, in "Notes on Bias in Estimation"

*Biometrika,*

**43**, (1956), 353-360, had written colourlessly of a procedure for supplying "an approximate correction for bias" [John Aldrich].

The term

**JACOBIAN**was coined by James J. Sylvester (1814-1897), who used the term in 1852 in

*The Cambridge & Dublin Mathematical Journal.*

Sylvester also used the word in 1853 "On a Theory of the Syzygetic Relations of Two Rational Integral Functions, Comprising an Application to the Theory of Sturm's Functions, and That of the Greatest Algebraical Common Measure,"

*Philosophical Transactions of the Royal Society of London,*CXLIII, Part III, pp. 407-548: "In Arts. 65, 66, I consider the relation of the Bezoutiant to the differential determinant, so called by Jacobi, but which for greater brevity I call the Jacobian." C. G. J. Jacobi's (1804-1851) paper was

*De determinantibus functionalibus*(1841).

**JEFFREYS PRIOR.**In 1946 Harold Jeffreys published "An Invariant Form for the Prior Probability in Estimation Problems,"

*Proceedings of the Royal Society, A*,

**186**, 453-461. He incorporated the material in the second edition of his

*Theory of Probability*(1948). The expression "Jeffreys prior" (or variants of it) became established in the 1960s; see e.g. Bruce M. Hill "The Three-Parameter Lognormal Distribution and Bayesian Analysis of a Point-Source Epidemic,"

*Journal of the American Statistical Association*,

**58**, (1963), 72-84 or J. Hartigan "Invariant Prior Distributions,

*Annals of Mathematical Statistics*,

**35**, (1964), 836-845.

See NONINFORMATIVE PRIOR

**JENSEN'S INEQUALITY**was given in J. L. W. V. Jensen's "Sur les fonctions convexes et les inégalités entre les valeurs moyennes,"

*Acta Math*.,

**30**, (1906), 175-193. This paper is based on his earlier 'Om konvexe funktioner og uligheder mellem midelvaerdier,'

*Nyt Tidsskr. Math. B*

**16**(1905), pp. 49-69. The inequality is discussed in

*Inequalities*by G. H. Hardy, J. E. Littlewood and G. Polya (1934).

See CONVEX FUNCTION.

**JERK**was used by J. S. Beggs in 1955 in

*Mechanism*iv. 122: "Since the forces to produce accelerations must arise from strains in the materials of the system, the rate of change of acceleration, or jerk, is important" [OED].

The word has found its way into at least one calculus textbook.

**JORDAN CANONICAL FORM**refers to a result given by Camille Jordan in the section "Réduction d'une substitution linéaire à sa forme canonique" (p. 114) of his

*Traité des substitutions et des équations algébriques*(1870).

In English the term is found in 1889 in

*A Treatise on Linear Differential Equations Volume I*by Thomas Craig. The table of contents has "Jordan's Canonical Form of the Substitution corresponding to any Critical Point." [Google print search by James A. Landau]

**JORDAN CURVE**appears in W. F. Osgood, "On the Existence of the Green's Function for the Most General Simply Connected Plane Region,"

*Transactions of the American Mathematical Society,*Vol. 1, No. 3. (July 1900): "By a

*Jordan curve*is meant a curve of the general class of continuous curves without multiple points, considered by Jordan,

*Cours d'Analyse,*vol. I, 2d edition, 1893..." [OED].

**JORDAN CURVE THEOREM**is dated 1915-20 in RHUD2.

*Jordan curve-theorem*is found in D. W. Woodard, "On two-dimensional analysis situs with special reference to the Jordan curve-theorem,"

*Fundamenta*(1929).

*Jordan curve theorem*is also found in L. Zippin, "Continuous curves and the Jordan curve theorem,"

*Bulletin A. M. S.*(1929).

**JULIA SET**is named for Gaston Julia and a construction in his "Mémoire sur l'iteration des fonctions rationnelles,"

*Journal de mathématiques pures et appliquées,*

**8**(1918) pp. 47–245. MathWorld

*Julia set*is found in English in 1976 in the

*Canadian Journal of Mathematics*28/1211: "We consider now those Julia sets which are sets of non-uniqueness and hence are very far from being Weierstrass sets." [OED]