Task: Question Answering
Input (English): Context: Mathematics (from Greek  "máthma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics., Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: "Journal for Pure and Applied Mathematics")., In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds., In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain. As a result, the graph of a differentiable function must have a (non-vertical) tangent line at each point in its domain, be relatively smooth, and cannot contain any breaks, bends, or cusps., Heinrich Wilhelm Feodor Deahna ( 8 July 1815 -- 8 January 1844 ) was a German mathematician . He is known for providing proof of what is now known as Frobenius theorem in differential topology , which he published in Crelle 's journal in 1840 . Deahna was born near Bayreuth on July 8 , 1815 , and was a student at the University of Göttingen in 1834 . In 1943 he became an assistant mathematics teacher at the Fulda Gymnasium , but he died soon afterwards in Fulda , on January 8 , 1844 ., In mathematics, a differentiable manifold is a type of manifold that is locally similar enough to a linear space to allow one to do calculus. Any manifold can be described by a collection of charts, also known as an atlas. One may then apply ideas from calculus while working within the individual charts, since each chart lies within a linear space to which the usual rules of calculus apply. If the charts are suitably compatible (namely, the transition from one chart to another is differentiable), then computations done in one chart are valid in any other differentiable chart., Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry. The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century. , Subject: feodor deahna, Relation: field_of_work, Options: (A) algebra (B) applied mathematics (C) differential geometry (D) english (E) mathematics (F) topology
Output (English): differential geometry