Alfréd Haar (; 11 October 1885,

Budapest Budapest is the Capital city, capital and List of cities and towns of Hungary, most populous city of Hungary. It is the List of cities in the European Union by population within city limits, tenth-largest city in the European Union by popul ...

– 16 March 1933,

Szeged Szeged ( , ; see also #Etymology, other alternative names) is List of cities and towns of Hungary#Largest cities in Hungary, the third largest city of Hungary, the largest city and regional centre of the Southern Great Plain and the county seat ...

) 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, mathematical structure, structure, space, Mathematica ...

. In 1904 he began to study 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 ...

. His doctorate was supervised by

David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental idea ...

. The

Haar measure In mathematical analysis, the Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral for functions on those groups. This Measure (mathematics), measure was introduced by Alfr� ...

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 repr ...

, and Haar transform are named in his honor. Between 1912 and 1919 he taught at Franz Joseph University in Kolozsvár. Together with Frigyes Riesz, he made the

University of Szeged The University of Szeged () is a Public university, public research university in Szeged, Hungary. Established as the Jesuit Academy of Kolozsvár in present-day Cluj-Napoca in 1581, the institution was re-established as a university in 1872 by ...

a centre of mathematics. He also founded the '' Acta Scientiarum Mathematicarum'' 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. He started his university studies in Budapest, later moving on to

Göttingen Göttingen (, ; ; ) 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. According to the 2022 German census, t ...

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

Constantin Carathéodory Constantin Carathéodory (; 13 September 1873 – 2 February 1950) was a Greeks, Greek mathematician who spent most of his professional career in Germany. He made significant contributions to real and complex analysis, the calculus of variations, ...

, 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 set theory, Z ...

. 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 as a student of chemical engineering, but in the same year he moved on to the University of Budapest, 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 Franz Joseph University in Kolozsvár,

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

Cluj-Napoca Cluj-Napoca ( ; ), or simply Cluj ( , ), is a city in northwestern Romania. It is the second-most populous city in the country and the seat of Cluj County. Geographically, it is roughly equidistant from Bucharest (), Budapest () and Belgrade ( ...

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

) invited him along with Gyula Farkas and Frigyes Riesz 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 (; ; ; ), often referred to in Hungary as the Peace Dictate of Trianon or Dictate of Trianon, was prepared at the Paris Peace Conference (1919–1920), Paris Peace Conference. It was signed on the one side by Hungary ...

, which ceded

Transylvania Transylvania ( or ; ; or ; Transylvanian Saxon dialect, Transylvanian Saxon: ''Siweberjen'') is a List of historical regions of Central Europe, historical and cultural region in Central Europe, encompassing central Romania. To the east and ...

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 ( ...

and

topological group In mathematics, topological groups are 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 structures ...

s, in particular he researched orthogonal systems of functions, singular integrals,

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 Set (mathematics), 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 mathema ...

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

and

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 ...

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 Academic staff of the University of Szeged Hungarian Jews Hungarian expatriates in Germany Writers from Budapest Academic staff of Franz Joseph University Mathematicians from Austria-Hungary Deaths from cancer in Hungary Deaths from stomach cancer Fasori Gimnázium alumni Measure theorists