The terms UMBRAL CALCULUS and UMBRAL NOTATION were coined by James Joseph Sylvester (1814-1897).
UNBIASED. See biased and estimation.
The term UNCONDITIONAL CONVERGENCE (of a continued fraction) was coined by Alfred Pringsheim (1850-1941).
UNDECAGON. Earlier terms for an 11-sided polygon, hendecagon and endecagon, are found in English in 1704 in Lexicon technicum, or an universal English dictionary of arts and sciences, by John Harris (OED2).
Undecagon is found in English in 1728 in Chambers' Cyclopedia.
UNDECIDABLE was used by Kurt Gödel (1906-1978) in 1931 in the title Uber formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme (On Formally Undecidable Propositions in Principia Mathematica and Related Systems).
UNGULA appears in 1710 in Lexicon technicum, or an universal English dictionary of arts and sciences, by John Harris: "Ungula, in Geometry, is the Section of a Cylinder cut off by a Plane, which passes obliquely thro' the Plane of the Basse, and part of the Cylindric Surface" (OED2).
UNIFORMLY DISTRIBUTED. Uniform distribution appears in 1937 in Introduction to Mathematical Probability by J. V. Uspensky. Page 237 reads, "A stochastic variable is said to have uniform distribution of probability if probabilities attached to two equal intervals are equal." This is a slight variant of the modern terminology, which would be "a variable is said to be uniformly distributed" or "a variable from the uniform distribution" [James A. Landau].
Uniformly distributed is found in H. Sakamoto, "On the distributions of the product and the quotient of the independent and uniformly distributed random variables," Tohoku Math. J. 49 (1943).
The phrase UNIFORMLY MOST POWERFUL occurs in R. A. Fisher, "Two New Properties of Mathematical Likelihood," Proceedings of the Royal Society, Series A, vol. 144 (1934) [James A. Landau].
UNIMODAL is found in 1904 in F. de Helguero, "Sui massimi delle curve dimorfiche," Biometrika, 3, 84-98 (David, 1995).
UNIT CIRCLE is found in 1895 in Plane and spherical trigonometry, surveying and tables by George Albert Wentworth: "The circle with radius equal to 1 is called a unit circle, AA' the horizontal, and BB' the vertical diameter" [University of Michigan Historic Math Collection].
UNIVARIATE is found in 1928 in Biometrika XXa. 32: "Various writers struggled with the problems that arise when samples are taken from uni-variate and bi-variate populations" (OED2).
The term UNIVERSAL ALGEBRA was first used by James Joseph Sylvester (1814-1897) for the theory of matrix algebras in a paper, "Lectures on the Principles of Universal Algebra," published in the American Journal of Mathematics, vol. 6, 1884, according to Whitehead [Encyclopaedia Britannica, article: Algebraic Structures].
Charles S. Peirce had objected to the term in a letter to Sylvester of Jan. 5, 1882: "I confess I cannot see why the system should be called 'universal.' It is a favorite epithet among inventors of all kinds in this country; but it seems to me best to restrict it to a very exact signification. A dual 'relative' is a collection of pairs, and this is an algebra of collections of pairs."
UNKNOWN. See root.