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

Last revision: July 7, 2017

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.


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).


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). H. W. Turnbull and A. C. Aitken An Introduction to the Theory of Canonical Matrices (1932, p. 81) give this reference and comment "the matrices given there of positive integers modulo p, the determinants involved being "non-singular", that is, prime to p."

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]

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