Alfréd Haar ( hu, Haar Alfréd; 11 October 1885,

Budapest Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population ...

– 16 March 1933,

Szeged Szeged ( , ; see also other alternative names) is the third largest city of Hungary, the largest city and regional centre of the Southern Great Plain and the county seat of Csongrád-Csanád county. The University of Szeged is one of the m ...

) was a Hungarian

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 On ...

. In 1904 he began to study 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 ...

. His doctorate was supervised by David Hilbert. The Haar measure,

Haar wavelet In mathematics, the Haar wavelet is a sequence of rescaled "square-shaped" functions which together form a wavelet family or basis. Wavelet analysis is similar to Fourier analysis in that it allows a target function over an interval to be repres ...

, and Haar transform are named in his honor. Between 1912 and 1919 he taught at

Franz Joseph University Royal Hungarian Franz Joseph University ( hu, Magyar Királyi Ferenc József Tudományegyetem) was the second modern university in the Hungarian realm of the Austro-Hungarian Empire. Founded in 1872, its seat was initially in Kolozsvár (Clu ...

Kolozsvár ; hu, kincses város) , official_name=Cluj-Napoca , native_name= , image_skyline= , subdivision_type1 = County , subdivision_name1 = Cluj County , subdivision_type2 = Status , subdivision_name2 = County seat , settlement_type = City , l ...

. Together with

Frigyes Riesz Frigyes Riesz ( hu, Riesz Frigyes, , sometimes spelled as Frederic; 22 January 1880 – 28 February 1956) was a HungarianEberhard Zeidler: Nonlinear Functional Analysis and Its Applications: Linear monotone operators. Springer, 199/ref> mathema ...

, he made the

University of Szeged , mottoeng = Truth. Bravery. Freedom. , established = , type = Public research university , founder = Emperor Franz Joseph I , affiliation = European University Association, Science Without Borders, Confucius Institute , budget = US$220 m ...

a centre of mathematics. He also founded the ''

Acta Scientiarum Mathematicarum ''Acta Scientiarum Mathematicarum'' is a Hungarian mathematical journal published by the János Bolyai Mathematical Institute (University of Szeged). It was established by Alfréd Haar and Frigyes Riesz in 1922. The current editor-in-chief is Lajo ...

'' journal together with Riesz.

Biography

Haar was born to a

Hungarian-Jewish The history of the Jews in Hungary dates back to at least the Kingdom of Hungary, with some records even predating the Hungarian conquest of the Carpathian Basin in 895 CE by over 600 years. Written sources prove that Jewish communities lived i ...

''Transcending Tradition: Jewish Mathematicians in German Speaking Academic Culture'', Birgit Bergmann, (Springer 2012), page 63 family in Budapest on 11 October 1885 to parents Ignác Haar and Emma Fuchs. He graduated in 1903 from the secondary school Fasori Evangélikus Gimnázium where he was a student of

László Rátz László Rátz (9 April 1863 in Sopron – 30 September 1930 in Budapest) was a Hungarian mathematics high school teacher best known for educating such people as John von Neumann and Nobel laureate Eugene Wigner. He was a legendary te ...

. He started his university studies in Budapest, later moving on to

Göttingen Göttingen (, , ; nds, Chöttingen) is a university city in Lower Saxony, central Germany, the capital of the eponymous district. The River Leine runs through it. At the end of 2019, the population was 118,911. General information The ori ...

reading mathematics and sciences. Among the many famous professors he was taught by, he could count

Loránd Eötvös Baron Loránd Eötvös de Vásárosnamény (or Loránd Eötvös, , '' hu, vásárosnaményi báró Eötvös Loránd Ágoston''; 27 July 1848 – 8 April 1919), also called Baron Roland von Eötvös in English literature, was a Hungarian physicist ...

, József Kürschák,

Constantin Carathéodory Constantin Carathéodory ( el, Κωνσταντίνος Καραθεοδωρή, Konstantinos Karatheodori; 13 September 1873 – 2 February 1950) was a Greek mathematician who spent most of his professional career in Germany. He made significant ...

, David Hilbert, Felix Christian Klein and

Ernst Zermelo Ernst Friedrich Ferdinand Zermelo (, ; 27 July 187121 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics. He is known for his role in developing Zermelo–Fraenkel axiomatic se ...

. During years of the secondary school, he collaborated with the mathematical journal for secondary school students Középiskolai Matematikai Lapok, and won the national Eötvös Loránd Mathematical Competition. He enrolled to the

Technical University of Budapest Technical may refer to: * Technical (vehicle), an improvised fighting vehicle * Technical analysis, a discipline for forecasting the future direction of prices through the study of past market data * Technical drawing, showing how something is co ...

as a student of chemical engineering, but in the same year he moved on to the

University of Budapest 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, th ...

, and after a year to the

. His doctoral research was supervised by Hilbert graduating in June 1909. His 49-page thesis studies systems of Sturm–Liouville functions and spherical functions, introducing the now widely used Haar orthogonal systems. In the same year he habilitated to become a private professor of the university. In 1912, the

in Kolozsvár,

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 ...

(now Cluj-Napoca in

Romania Romania ( ; ro, România ) is a country located at the crossroads of Central, Eastern, and Southeastern Europe. It borders Bulgaria to the south, Ukraine to the north, Hungary to the west, Serbia to the southwest, Moldova to the east, and ...

) invited him along with Gyula Farkas and

to join as faculty, and he became the professor of 'Quatitics'. A number of his lecture notes from the time became established books later. After the

Treaty of Trianon The Treaty of Trianon (french: Traité de Trianon, hu, Trianoni békeszerződés, it, Trattato del Trianon) was prepared at the Paris Peace Conference and was signed in the Grand Trianon château in Versailles on 4 June 1920. It forma ...

, which ceded

Transylvania Transylvania ( ro, Ardeal or ; hu, Erdély; german: Siebenbürgen) is a historical and cultural region in Central Europe, encompassing central Romania. To the east and south its natural border is the Carpathian Mountains, and to the west the Ap ...

to Romania, the university had to move to

, the closest city within the new boundaries, where he with Riesz established the Centre of Mathematics, and the first internationally recognised Hungarian mathematical journal, the ''Acta Scientiarum Mathematicarum''. One of his doctoral students at the

was

Béla Szőkefalvi-Nagy Béla Szőkefalvi-Nagy (29 July 1913, Kolozsvár – 21 December 1998, Szeged) was a Hungarian mathematician. His father, Gyula Szőkefalvi-Nagy was also a famed mathematician. Szőkefalvi-Nagy collaborated with Alfréd Haar and Frigyes Riesz, ...

. Haar died of stomach cancer on 16 March 1933.

Fields of research

His results are from the fields of

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

and

topological group In mathematics, topological groups are logically the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time, such that the continuity condition for the group operations connects these two st ...

s, in particular he researched orthogonal systems of functions,

singular integral In mathematics, singular integrals are central to harmonic analysis and are intimately connected with the study of partial differential equations. Broadly speaking a singular integral is an integral operator : T(f)(x) = \int K(x,y)f(y) \, dy, who ...

analytic functions In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex ...

, differential equations,

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...

function approximation In general, a function approximation problem asks us to select a function among a that closely matches ("approximates") a in a task-specific way. The need for function approximations arises in many branches of applied mathematics, and comput ...

and calculus of variations.

Publications

* Haar, A.,
Zur Theorie der orthogonalen Funktionensysteme
', (''Erste Mitteilung''), Math. Ann. 69 (1910), 331–371 (at GDZ). (This is Haar's thesis, written under the supervision of David Hilbert.) * Haar, A.,
Die Minkowskische Geometrie und die Annäherung an stetige Funktionen
', Math. Ann. 78 (1918), 294–311 (at GDZ).

References

External links

* * . * . {{DEFAULTSORT:Haar, Alfred 1885 births 1933 deaths 20th-century Hungarian mathematicians University of Szeged faculty Hungarian Jews Hungarian expatriates in Germany Writers from Budapest Franz Joseph University faculty Austro-Hungarian mathematicians Deaths from cancer in Hungary Deaths from stomach cancer Fasori Gimnázium alumni Measure theorists