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

Austria Austria, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous c ...

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, structure, space, models, and change. History O ...

. 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 functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

(in 1910, at the

University of Vienna The University of Vienna (german: Universität Wien) is a public research university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world. With its long and rich histo ...

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 ( ; cs, Čechy ; ; hsb, Čěska; szl, Czechy) is the westernmost and largest historical region of the Czech Republic. Bohemia can also refer to a wider area consisting of the historical Lands of the Bohemian Crown ruled by the Bohe ...

Austria-Hungary Austria-Hungary, often referred to as the Austro-Hungarian Empire,, the Dual Monarchy, or Austria, was a constitutional monarchy and great power in Central Europe between 1867 and 1918. It was formed with the Austro-Hungarian Compromise of 1 ...

, now

Děčín Děčín (; german: Tetschen, 1942–1945: ''Tetschen–Bodenbach'') is a city in the Ústí nad Labem Region of the Czech Republic. It has about 47,000 inhabitants. It is the 7th largest municipality in the country by area. Administrative parts D ...

, Czech Republic. 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, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded i ...

, then he was an assistant at the

German Technical University in Brno German Technical University in Brno (German: ''Deutsche Technische Hochschule Brünn'') was a technical university in Brno. It existed from 1849 to 1945 and instruction was in German. At the time, Brno was a multicultural city with both Czech an ...

, and from 1912 to 1919 at the

Technical University of Vienna TU Wien (TUW; german: Technische Universität Wien; still known in English as the Vienna University of Technology from 1975–2014) is one of the major universities in Vienna, Austria. The university finds high international and domestic recogn ...

. In 1913/14, he passed his

habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...

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; in 1922, he became ''

Professor ordinarius Academic ranks in Germany are the titles, relative importance and power of professors, researchers, and administrative personnel held in academia. Overview Appointment grades * (Pay grade: ''W3'' or ''W2'') * (''W3'') * (''W2'') * (''W2'', ...

'' at the

University of Greifswald The University of Greifswald (; german: Universität Greifswald), formerly also known as “Ernst-Moritz-Arndt University of Greifswald“, is a public research university located in Greifswald, Germany, in the state of Mecklenburg-Western Po ...

, and in 1925 at the

University of Erlangen A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, ...

. Then he was '' Ordinarius'' at the

University of Breslau A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, ...

from 1928 to 1945. After a short stay at the

University of Innsbruck The University of Innsbruck (german: Leopold-Franzens-Universität Innsbruck; la, Universitas Leopoldino Franciscea) is a public research university in Innsbruck, the capital of the Austrian federal state of Tyrol, founded on October 15, 1669. I ...

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, born in 1924, obtained a Ph.D. in mathematics at the

and married the Austrian mathematician Erich Bukovics in 1950. Brigitte lives in Vienna. 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 In mathematics, the Radon–Nikodym theorem is a result in measure theory that expresses the relationship between two measures defined on the same measurable space. A ''measure'' is a set function that assigns a consistent magnitude to the measura ...

; * the

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

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 map from a vector space to its field of scalars (often, the real numbers or the complex numbers). If is a vector space over a field , the s ...

; * the

Radon transform In mathematics, the Radon transform is the integral transform which takes a function ''f'' defined on the plane to a function ''Rf'' defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the l ...

, in

integral geometry In mathematics, integral geometry is the theory of measures on a geometrical space invariant under the symmetry group of that space. In more recent times, the meaning has been broadened to include a view of invariant (or equivariant) transformatio ...

, based on integration over

hyperplane In geometry, a hyperplane is a subspace whose dimension is one less than that of its ''ambient space''. For example, if a space is 3-dimensional then its hyperplanes are the 2-dimensional planes, while if the space is 2-dimensional, its hyperp ...

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, astrophysics, quantu ...

for scanners (see

tomographic reconstruction Tomographic reconstruction is a type of multidimensional inverse problem where the challenge is to yield an estimate of a specific system from a finite number of projections. The mathematical basis for tomographic imaging was laid down by Johann ...

); *

Radon's theorem In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that any set of ''d'' + 2 points in R''d'' can be partitioned into two sets whose convex hulls intersect. A point in the intersection of these convex ...

, that ''d'' + 2 points in ''d'' dimensions may always be partitioned into two subsets with intersecting

convex hull In geometry, the convex hull or 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 spac ...

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 University of Greifswald faculty University of Vienna alumni Academics of TU Wien University of Hamburg faculty University of Erlangen-Nuremberg faculty University of Breslau faculty Academics of the University of Innsbruck Academics of the University of Vienna Rectors of universities in Austria Variational analysts Functional analysts Austro-Hungarian mathematicians Burials at Döbling Cemetery

Life

Achievements

See also

References

External links