# Hajós, György

(Budapest, February 21st, 1912 – Budapest, March 17th, 1972)

An excellent mathematician and geometrician of world renown. His most well known result is the proof of the famous Minkowski-guess.

He completed his secondary school studies at the Piarist Grammar School and, then, he graduated from the Péter Pázmány University of Sciences, faculty of mathematics and physics in 1929. As a university student, he developed the proof of a grid-geometric theorem of H. Minkowski considered to be the simplest to this very day.

He was a grammar school teacher until 1935 and, then, an assistant lecturer, a lecturer and private tutor at the Technical University of Budapest until 1949. From 1949 until his death, he was professor and headed the Department of Geometry at the Loránd Eötvös University of Sciences. He obtained his doctorate in 1938.

He achieved his most important scientific result in 1941 by means of proving the so-called Minkowski-guess (Minkowski-Hajós theorem). This guess was published in the journal "Geometrie der Zahlen".

During the previous decades, very famous mathematicians had attempted to prove the guess; nevertheless, they were able to obtain only partial results. Hajós started from the geometric form of the guess and he proved its purely algebraic equivalent formulation by using group-theory. For this reason, the Loránd Eötvös Mathematical and Physical Society awarded him the Kőnig Gyula prize in 1942.

He wrote articles on nomography, error calculation, Bolyai-Lobacsevsky geometry, the multidimensional orthocentric simplex Feuerbach sphere, discrete geometry, the arranged pattern theorem (jointly with Alfréd Rényi), and also achieved valuable results in these fields.

He participated actively in professional life. He was secretary of the Hungarian Academy of Sciences Mathematical and Physical Department and the editor-in-chief of Acta Mathematica Academiae Scientiarum Hungaricae for ten years. He was the president of the János Bolyai Mathematical Society for a long period.

*Memberships:* associate member (1948), ordinary member (1953) of the Hungarian Academy of Sciences; associate member of the Romanian Academy of Sciences (1965), member of the Deutsche Akademie der Naturforscher Leopoldina (1967); member of the Executive Committee of the International Mathematics Union, president of the Bolyai János Mathematical Society.

*Honours:* Kossuth Prize (1951, 1962); Order of the People's Republic; Beke Manó memorial prize; Order of the Finnish Lion Commander.

*Selected bibliography:*

- Hajós, Gy., Über einfache und mehrfache Bedeckung des n-dimensionalen Raumes mit einem Würfelgitter.
*Matematische Zeitschrift,* 1941

- Hajós, Gy., On a new presentation of the hyperbolic trigonometry by aid of the Poincaré model.
*Annales Univ. Sci. Budapestiensis etc., Sectio Math.,* 7. 1964

**Minkowski theorem**

Minkowski's theorem on convex bodies published in 1896 is the most important theorem in the geometry of numbers, and is the basis for its existence as a separate branch of number theory.

His other theorem on linear forms is a corollary of the general theorem. The question was the solvability of a system of inequalities with integers. Minkowski has already known, that the lesser than or equal signs in the inequalities could be replaced by the strict inequality except one.

The problem when the first inequality in Minkowski's theorem on linear forms can be replaced by strict inequality was solved with group-theoretical methods by G. Hajós.