Johann Karl August Radon (; 16 December 1887 – 25 May 1956) was an

Austria Austria, formally the Republic of Austria, is a landlocked country in Central Europe, lying in the Eastern Alps. It is a federation of nine Federal states of Austria, states, of which the capital Vienna is the List of largest cities in Aust ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. His doctoral dissertation was on the

calculus of variations The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of f ...

(in 1910, at the

University of Vienna The University of Vienna (, ) is a public university, public research university in Vienna, Austria. Founded by Rudolf IV, Duke of Austria, Duke Rudolph IV in 1365, it is the oldest university in the German-speaking world and among the largest ...

Life

RadonBrigitte Bukovics: ''Biography of Johann Radon'', in: 75 Years of Radon Transform, S. Gindikin and P. Michor, eds., International Press Incorporated (1994), pp. 13–18, was born in Tetschen,

Bohemia Bohemia ( ; ; ) is the westernmost and largest historical region of the Czech Republic. In a narrow, geographic sense, it roughly encompasses the territories of present-day Czechia that fall within the Elbe River's drainage basin, but historic ...

Austria-Hungary Austria-Hungary, also referred to as the Austro-Hungarian Empire, the Dual Monarchy or the Habsburg Monarchy, was a multi-national constitutional monarchy in Central Europe#Before World War I, Central Europe between 1867 and 1918. A military ...

, now Děčín,

Czech Republic The Czech Republic, also known as Czechia, and historically known as Bohemia, is a landlocked country in Central Europe. The country is bordered by Austria to the south, Germany to the west, Poland to the northeast, and Slovakia to the south ...

. He received his doctoral degree at the

in 1910. He spent the winter semester 1910/11 at the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...

, then he was an assistant at the German Technical University in Brno, and from 1912 to 1919 at the Technical University of Vienna. In 1913/14, he passed his

habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...

at the University of Vienna. Due to his near-sightedness, he was exempt from the draft during wartime. In 1919, he was called to become Professor extraordinarius at the newly founded

University of Hamburg The University of Hamburg (, also referred to as UHH) is a public university, public research university in Hamburg, Germany. It was founded on 28 March 1919 by combining the previous General Lecture System ('':de:Allgemeines Vorlesungswesen, ...

; in 1922, he became '' Professor ordinarius'' at the University of Greifswald, and in 1925 at the University of Erlangen. Then he was '' Ordinarius'' at the University of Breslau from 1928 to 1945. After a short stay at the

University of Innsbruck The University of Innsbruck (; ) is a public research university in Innsbruck, the capital of the Austrian federal state of Tyrol (state), Tyrol, founded on October 15, 1669. It is the largest education facility in the Austrian States of Austria, ...

he became ''Ordinarius'' at the Institute of Mathematics of the

on 1 October 1946. In 1954/55, he was rector of the University of Vienna. In 1939, Radon became corresponding member of the Austrian Academy of Sciences, and in 1947, he became a member. From 1952 to 1956, he was Secretary of the Class of Mathematics and Science of this Academy. From 1948 to 1950, he was president of the Austrian Mathematical Society. Johann Radon married Maria Rigele, a secondary school teacher, in 1916. They had three sons who died young or very young. Their daughter Brigitte (1924–2020) obtained a Ph.D. in mathematics at the

and married the Austrian mathematician Erich Bukovics in 1950. Radon, as Curt C. Christian described him in 1987 at the occasion of the unveiling of his brass bust at the

, was a friendly, good-natured man, highly esteemed by students and colleagues alike, a noble personality. He did make the impression of a quiet scholar, but he was also sociable and willing to celebrate. He loved music, and he played music with friends at home, being an excellent violinist himself, and a good singer. His love for classical literature lasted through all his life. In 2003, the Austrian Academy of Sciences founded an Institute for Computational and Applied Mathematics and named it after Johann Radon (see the external link below).

Achievements

Radon is known for a number of lasting contributions, including: * his part in the Radon–Nikodym theorem; * the

Radon measure In mathematics (specifically in measure theory), a Radon measure, named after Johann Radon, is a measure on the -algebra of Borel sets of a Hausdorff topological space that is finite on all compact sets, outer regular on all Borel sets, and ...

concept of measure as

linear functional In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear mapIn some texts the roles are reversed and vectors are defined as linear maps from covectors to scalars from a vector space to its field of ...

; * the Radon transform, in integral geometry, based on integration over

hyperplane In geometry, a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension. Like a plane in space, a hyperplane is a flat hypersurface, a subspace whose dimension is ...

s—with application to

tomography Tomography is imaging by sections or sectioning that uses any kind of penetrating wave. The method is used in radiology, archaeology, biology, atmospheric science, geophysics, oceanography, plasma physics, materials science, cosmochemistry, ast ...

for scanners (see tomographic reconstruction); * Radon's theorem, that ''d'' + 2 points in ''d'' dimensions may always be partitioned into two subsets with intersecting

convex hull In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, ...

s; * the Radon–Hurwitz numbers. * He is possibly the first to make use of the so-called Radon–Riesz property.

References

External links

* *
Johann Radon Institute for Computational and Applied Mathematics (RICAM)
{{DEFAULTSORT:Radon, Johann 1887 births 1956 deaths People from Děčín 20th-century Austrian mathematicians Academic staff of the University of Greifswald University of Vienna alumni Academic staff of TU Wien Academic staff of the University of Hamburg Academic staff of the University of Erlangen-Nuremberg Academic staff of the University of Breslau Academic staff of the University of Innsbruck Academic staff of the University of Vienna Rectors of universities in Austria Variational analysts Functional analysts Mathematicians from Austria-Hungary Burials at Döbling Cemetery

Life

Achievements

See also

References

External links