Detailed Instructions: In this task you will be given a text passage from a trivia quiz. You should choose the category this question belongs to from these categories: History, Science, Social Science, Fine Arts, Literature. You can only choose one category, so if in doubt, please choose the closest match.
Problem:Sophie Kowalevski completed a theorem involving local existence and uniqueness of analytical partial differential equations initially proven in a special case by this man, whose name, along with that of Binet, is also appended to a formula generalizing the multiplicativity of the determinants of two matrices. If the partial sums of an infinite series become arbitrarily close to each other, said infinite series converges under a test named after this man, who is also the namesake of a set of differential equations for finding holomorphic functions in the complex plane with Riemann, as well as a theorem stating that the closed line integral of holomorphic functions in simply connected subsets of the complex plane is equal to zero. A theorem stating that the product of the length of two vectors is greater than their inner product is named after, FTP, which German mathematician, along with Hermann Schwarz
Solution:
Science