The terms UMBRAL CALCULUS and UMBRAL NOTATION were coined by James Joseph Sylvester (1814-1897).
UNDECAGON. The earlier term for an 11-sided polygon, hendecagon (or endecagon), is 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 G鐰el (1906-1978) in 1931 in the title Uber formal unentscheidbare S酹ze der Principia Mathematica und verwandter Systeme (On Formally Undecidable Propositions in Principia Mathematica and Related Systems).
UNIFORM DISTRIBUTION. Uspensky (1937) 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].
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].
The term UNIVERSAL ALGEBRA was first used by James Joseph Sylvester (1814-1897) 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].
UNKNOWN. In Miscellanea Berolinensia (1710) Leibniz used the phrase "incognita, x," which is translated "the unknown x."
Unknown is found in English in 1817 in the sentence "The demonstration is by resolution of a quadratic equation involving several unknown" in Algebra of the Hindoos, with arithmetic and mensuration by Henry T. Colebrooke (OED2).