query: field_of_work oskar bolza
supports: Geometry (from the ; "geo-" "earth", "-metron" "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. In mathematics, a real number is a value that represents a quantity along a line. The adjective "real" in this context was introduced in the 17th century by René Descartes, who distinguished between real and imaginary roots of polynomials. In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises when either the metric requirement is relaxed, or the parallel postulate is replaced with an alternative one. In the latter case one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed, then there are affine planes associated with the planar algebras which give rise to kinematic geometries that have also been called non-Euclidean geometry. France, officially the French Republic, is a country with territory in western Europe and several overseas regions and territories. The European, or metropolitan, area of France extends from the Mediterranean Sea to the English Channel and the North Sea, and from the Rhine to the Atlantic Ocean. Overseas France include French Guiana on the South American continent and several island territories in the Atlantic, Pacific and Indian oceans. France spans and had a total population of almost 67 million people as of January 2017. It is a unitary semi-presidential republic with the capital in Paris, the country's largest city and main cultural and commercial centre. Other major urban centres include Marseille, Lyon, Lille, Nice, Toulouse and Bordeaux. Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including hydrodynamics and thermodynamics and also in engineering fields such as nuclear, aerospace, mechanical and electrical engineering. A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems. Calculus of variations is a field of mathematical analysis that deals with maximizing or minimizing functionals, which are mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. The interest is in "extremal" functions that make the functional attain a maximum or minimum value  or "stationary" functions  those where the rate of change of the functional is zero. Mathematical analysis is the branch of mathematics dealing with limits
  and related theories, such as differentiation, integration, measure, infinite series, and analytic functions. 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. The Palatinate Forest, sometimes also called the Palatine Forest, is a low-mountain region in southwestern Germany, located in the Palatinate in the state of Rhineland-Palatinate. The forest is a designated nature park covering 1,771 km and its highest elevation is the Kalmit (673 m). Oskar Bolza ( 12 May 1857 -- 5 July 1942 ) was a German mathematician , and student of Felix Klein . He was born in Bad Bergzabern , Rhenish Palatinate , known for his research in the calculus of variations , particularly influenced by Karl Weierstrass ' 1879 lectures on the subject . Südliche Weinstraße is a district ("Kreis") in the south of Rhineland-Palatinate, Germany. Neighboring districts are (from west clockwise) Südwestpfalz, Bad Dürkheim, the district-free city Neustadt (Weinstraße), Rhein-Pfalz-Kreis, Germersheim, and the French "département" Bas-Rhin. The district-free city Landau is surrounded by the district. In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. 
  The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems.<br>
  It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox. Christian Felix Klein (25 April 1849  22 June 1925) was a German mathematician and mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and on the connections between geometry and group theory. His 1872 Erlangen Program, classifying geometries by their underlying symmetry groups, was a hugely influential synthesis of much of the mathematics of the day. Bad Bergzabern is a municipality in the Südliche Weinstraße district, on the German Wine Route in Rhineland-Palatinate, Germany. It is situated near the border with France, on the south-eastern edge of the Palatinate forest, approximately southwest of Landau. Karl Theodor Wilhelm Weierstrass (31 October 1815  19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics and trained as a teacher, eventually teaching mathematics, physics, botany and gymnastics. Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the "Elements". Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. The "Elements" begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the "Elements" states results of what are now called algebra and number theory, explained in geometrical language.
candidates: abstract algebra aerospace algebra botany calculus of variations complex analysis computing english french geometry group theory language mathematical analysis mathematician mathematics nature number theory teaching
answer: geometry