Eduard Ott-Heinrich Keller (22 June 1906 in

Frankfurt Frankfurt, officially Frankfurt am Main (; Hessian: , "Frank ford on the Main"), is the most populous city in the German state of Hesse. Its 791,000 inhabitants as of 2022 make it the fifth-most populous city in Germany. Located on its na ...

– 5 December 1990 in Halle) was a German mathematician who worked in the fields of

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

and

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

. He formulated the celebrated problem which is now called the

Jacobian conjecture In mathematics, the Jacobian conjecture is a famous unsolved problem concerning polynomials in several variables. It states that if a polynomial function from an ''n''-dimensional space to itself has Jacobian determinant which is a non-zero co ...

in 1939. He was born in Frankfurt–am-Main, and studied at the universities of Frankfurt,

Vienna en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...

, Berlin and

Göttingen Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...

. As a student of

Max Dehn Max Wilhelm Dehn (November 13, 1878 – June 27, 1952) was a German mathematician most famous for his work in geometry, topology and geometric group theory. Born to a Jewish family in Germany, Dehn's early life and career took place in Germany. ...

he wrote a dissertation on the

tiling Tiling may refer to: *The physical act of laying tiles *Tessellations Computing *The compiler optimization of loop tiling *Tiled rendering, the process of subdividing an image by regular grid *Tiling window manager People *Heinrich Sylvester The ...

of space with

cube In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. The cube is the only r ...

s. This led to another 'Keller conjecture': the Keller cube-tiling conjecture from 1930. Subsequently he worked with

Georg Hamel Georg Karl Wilhelm Hamel (12 September 1877 – 4 October 1954) was a German mathematician with interests in mechanics, the foundations of mathematics and function theory. Biography Hamel was born in Düren, Rhenish Prussia. He studied at Aa ...

in Berlin, habilitating in 1933 with a thesis on

Cremona transformation In algebraic geometry, the Cremona group, introduced by , is the group of birational automorphisms of the n-dimensional projective space over a field It is denoted by Cr(\mathbb^n(k)) or Bir(\mathbb^n(k)) or Cr_n(k). The Cremona group is naturally ...

s. The Jacobian conjecture is quite naturally posed in that setting. The motivation for looking at rather general

polynomial transformations In mathematics, a polynomial transformation consists of computing the polynomial whose roots are a given function of the roots of a polynomial. Polynomial transformations such as Tschirnhaus transformations are often used to simplify the solutio ...

, say of the

projective plane In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect in a single point, but there are some pairs of lines (namely, parallel lines) that do ...

, came from the

singularity theory In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it ...

for

algebraic curve In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane c ...

s. During

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

he taught in a naval college in

Flensburg Flensburg (; Danish, Low Saxon: ''Flensborg''; North Frisian: ''Flansborj''; South Jutlandic: ''Flensborre'') is an independent town (''kreisfreie Stadt'') in the north of the German state of Schleswig-Holstein. Flensburg is the centre of the ...

. After the war he had several positions, and was appointed a professor at

Martin Luther University of Halle-Wittenberg Martin Luther University of Halle-Wittenberg (german: Martin-Luther-Universität Halle-Wittenberg), also referred to as MLU, is a public, research-oriented university in the cities of Halle and Wittenberg and the largest and oldest university i ...

in 1952, as successor of H. W. E. Jung.

References

*
Biography
(in German)

External links

* {{DEFAULTSORT:Keller, EOH 1906 births 1990 deaths 20th-century German mathematicians Geometers Academic staff of the University of Münster