KERNEL (an integrand). David Hilbert used the German word kern in Nachrichten von d. Königl. Ges. d. Wissensch. zu Göttingen (Math.-physik. Kl.) (1904) 49 (OED2)
Kernel occurs in English in 1909 in Introd. Study Integral Equations by M. Bôcher: "K is called the kernel of these equations" (OED2).
KERNEL (elements mapped into identity element) is found in English in 1946 in E. Lehmer's translation of Pontrjagin's Topological Groups (OED2).
KITE. Deltoid appears in 1879 in Dictionary of Scientific Terms: "Deltoid, a four-sided figure formed of two unequal isosceles triangles on opposite sides of a common base" (OED2).
Kite appears as a geometric term in the 1893 Funk and Wagnalls Standard Dictionary.
KLEIN BOTTLE occurs in C. Tompkins, "A flat Klein bottle isometrically embedded euclidean 4-space," Bull. Am. Math. Soc. 47, 508 (1941).
KLEIN FOUR GROUP. Vierergruppe is found in 1884 in Vorlesungen uber das Ikosaeder und die Aufloesung der Gleichungen vom funften Grade by Felix Klein:
Offenbar umfasst unsere neue Gruppe von der Identitaet abgesehen nur Operationen von der Periode 2, und es ist zufaellig, das wir eine dieser Operationen an die Hauptaxe der Figur, die beiden anderen an die Nebenaxe geknupft haben. Dementsprechend will ich die Gruppe mit einem besonderen Namen belegen, der nicht mehr and die Dieder- configuration erinnert, und sie als Vierergruppe benennen.The above citation was provided by Gunnar Berg.
The term "(Kleinsche) Vierergruppe" was used by Bartel Leendert van der Waerden (1903-1996) in 1930 in his influential textbook Moderne Algebra. It denotes the permutation group generated by (12)(34) and (13)(24), rather than the abstract product of two 2-cyclic groups. The term does not occur in the older algebra books by Weber and by Perron [Peter Flor].
The term KLEINIAN GROUP was used by Henri Poincaré.
KNOT. The first mathematical paper which mentions knots is "Remarques sur les problemes de situation" (1771) by Alexandre-Theophile Vandermonde (1735-1796).
KNOT THEORY appears in 1932 in the title Knotentheorie by Kurt Werner Friedrick Reidemeister (1893-1971).
KOLMOGOROV-SMIRNOV TEST appears in F. J. Massey Jr., "The Kolmogorov-Smirnov test of goodness of fit," J. Amer. Statist. Ass. 46 (1951).
See also W. Feller, "On the Kolmogorow-Smirnov limit theorems for empirical distributions," Ann. Math. Statist. 19 (1948) [James A. Landau].
The term KRONECKER DELTA is found in 1926 in Riemannian Geometry by Luther Pfahler Eisenhard: "These are called the Kronecker deltas and are used frequently throughout this work." [Joanne M. Despres of Merriam-Webster Inc.]
KURTOSIS was used by Karl Pearson in 1905 in "Das Fehlergesetz und seine Verallgemeinerungen durch Fechner und Pearson. A Rejoinder," Biometrika, 4, 169-212, in the phrase "the degree of kurtosis." He states therein that he has used the term previously (OED2).