*Last revision: Oct. 28, 2018*

**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]