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Otakar Borůvka (10 May 1899 – 22 July 1995) was a
Czech Czech may refer to: * Anything from or related to the Czech Republic, a country in Europe ** Czech language ** Czechs, the people of the area ** Czech culture ** Czech cuisine * One of three mythical brothers, Lech, Czech, and Rus *Czech (surnam ...
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 ...
. He is best known for his work in
graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...
..


Education and career

Borůvka was born in Uherský Ostroh, a town in
Moravia Moravia ( ; ) is a historical region in the eastern Czech Republic, roughly encompassing its territory within the Danube River's drainage basin. It is one of three historical Czech lands, with Bohemia and Czech Silesia. The medieval and early ...
,
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 ...
(today in the
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 ...
), the son of a school headmaster. He attended the grammar school in
Uherské Hradiště Uherské Hradiště (; ) is a town in the Zlín Region of the Czech Republic. It has about 25,000 inhabitants. The agglomeration with the two neighbouring towns of Staré Město (Uherské Hradiště District), Staré Město and Kunovice has over ...
beginning in 1910. In 1916, influenced by the ongoing
World War I World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...
, he moved to the military school (Realschule) in Hranice, and later he enrolled into the Imperial and Royal Technical Military Academy in
Mödling Mödling () is the capital of the Austrian Mödling (district), district of the same name located approximately 15 km south of Vienna. Mödling lies in Lower Austria's industrial zone (Industrieviertel). The Mödlingbach, a brook which rises ...
near
Vienna Vienna ( ; ; ) is the capital city, capital, List of largest cities in Austria, most populous city, and one of Federal states of Austria, nine federal states of Austria. It is Austria's primate city, with just over two million inhabitants. ...
. When the war ended, Borůvka returned to Uherské Hradiště, finished his studies in 1918 at the Gymnasium there, and became a student at the Imperial Czech Technical University of Franz Joseph, in
Brno Brno ( , ; ) is a Statutory city (Czech Republic), city in the South Moravian Region of the Czech Republic. Located at the confluence of the Svitava (river), Svitava and Svratka (river), Svratka rivers, Brno has about 403,000 inhabitants, making ...
, initially studying
civil engineering Civil engineering is a regulation and licensure in engineering, professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads ...
. In 1920,
Masaryk University Masaryk University (MU) (; ) is the second largest university in the Czech Republic, a member of the Compostela Group and the Utrecht Network. Founded in 1919 in Brno, it now consists of ten faculties and 35,115 students. It is named after To ...
opened in Brno, and Borůvka also began taking courses there. He became an assistant to Mathias Lerch at Masaryk in 1921, but Lerch died in 1922; his position at Masaryk was taken by Eduard Čech, whom Borůvka also assisted, earning his doctorate in 1923. At Čech's suggestion, Borůvka visited
Élie Cartan Élie Joseph Cartan (; 9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups, differential systems (coordinate-free geometric formulation of PDEs), and differential geometry. He ...
in
Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...
from 1926 to 1927. He earned 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 ...
from Masaryk University in 1927, and (turning down an offer from the
University of Zagreb The University of Zagreb (, ) is a public university, public research university in Zagreb, Croatia. It is the largest Croatian university and one of the oldest continuously operating universities in Europe. The University of Zagreb and the Unive ...
) he became a docent there in 1928. He continued to travel abroad through the late 1920s and early 1930s, to Cartan in Paris again as well as to
Wilhelm Blaschke Wilhelm Johann Eugen Blaschke (13 September 1885 – 17 March 1962) was an Austrian mathematician working in the fields of differential and integral geometry. Education and career Blaschke was the son of mathematician Josef Blaschke, who taugh ...
in
Hamburg Hamburg (, ; ), officially the Free and Hanseatic City of Hamburg,. is the List of cities in Germany by population, second-largest city in Germany after Berlin and List of cities in the European Union by population within city limits, 7th-lar ...
. He was promoted to assistant professor at Masaryk in 1934, given a chair in 1940, and made an ordinary professor in 1946. In 1965, he founded the new journal '' Archivum Mathematicum'', and in 1969, he became a founding member of the of the Czechoslovak Academy of Sciences, splitting his time between the Institute and his professorship at Masaryk.


Contributions

The problem of designing efficient electric distribution networks had been suggested to Borůvka by his friend Jindřich Saxel, an employee of the West Moravian Power Company, during World War I. In his 1926 paper ''O jistém problému minimálním'' (English ''On a certain minimal problem''), Borůvka solved this problem by modeling it mathematically as a
minimum spanning tree A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. ...
problem, and described the first known
algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...
for finding the
minimum spanning tree A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. ...
of a
metric space In mathematics, a metric space is a Set (mathematics), set together with a notion of ''distance'' between its Element (mathematics), elements, usually called point (geometry), points. The distance is measured by a function (mathematics), functi ...
(the set of cities to be connected by the network, together with their distances). Now called Borůvka's algorithm, his method works by repeatedly adding a connections between each subtree of the minimum spanning tree found so far and its nearest neighboring subtree. The same algorithm has been rediscovered repeatedly. It is more suitable for distributed and parallel computation than many other minimum spanning tree algorithms, can achieve
linear time In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations ...
complexity on
planar graph In graph theory, a planar graph is a graph (discrete mathematics), graph that can be graph embedding, embedded in the plane (geometry), plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. ...
s and more generally in minor-closed graph families, and plays a central role in the randomized
linear time In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations ...
algorithm of . From 1924 to 1935, Borůvka's primary interest was in
differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...
. His work in this area concerned analytic correspondences between
projective plane In mathematics, a projective plane is a geometric structure that extends the concept of a plane (geometry), plane. In the ordinary Euclidean plane, two lines typically intersect at a single point, but there are some pairs of lines (namely, paral ...
s, normal curvature of high-dimensional surfaces, and Frenet formula for curves in high-dimensional spaces. Beginning in the 1930s, Borůvka's interests shifted to
abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...
, and in particular the theory of groups. He was also one of the first to study a generalization of groups, called by him "groupoids" but now more commonly referred to as magmas. A textbook by him on groups and groupoids, originally published in Czech in 1944, went through several expansions, and translations, including an English edition in 1976. Following the war, Borůvka shifted gears again, from algebra to the theory of differential equations. He published several research papers on this subject, as well as a monograph on second-order differential equations which he published in 1971.


Awards and honors

Borůvka became a corresponding member of the Czechoslovak Academy of Sciences at its creation in 1953, and an ordinary member in 1965. In 1969, Comenius University in Bratislava gave him an honorary doctorate, and in 1994 he received a second honorary doctorate from Masaryk University in Brno. He has also been given medals by the Free University of Brussels, the
University of Liège The University of Liège (), or ULiège, is a major public university of the French Community of Belgium founded in 1817 and based in Liège, Wallonia, Belgium. Its official language is French (language), French. History The university was foun ...
,
Jagiellonian University The Jagiellonian University (, UJ) is a public research university in Kraków, Poland. Founded in 1364 by Casimir III the Great, King Casimir III the Great, it is the oldest university in Poland and one of the List of oldest universities in con ...
, Comenius University, Palacký University of Olomouc, Jan Evangelista Purkyně University in Ústí nad Labem, the
German Academy of Sciences at Berlin The German Academy of Sciences at Berlin, , in 1972 renamed the Academy of Sciences of the GDR (''Akademie der Wissenschaften der DDR (AdW)''), was the most eminent Research institute, research institution of East Germany (German Democratic Repub ...
, the Russian Academy of Sciences#Academy of Sciences of the USSR, and the Czechoslovak Academy of Sciences..


References


External links


Borůvka, Otakar
Czech Digital Mathematics Library {{DEFAULTSORT:Boruvka, Otakar 1899 births 1995 deaths People from Uherský Ostroh Czech mathematicians Masaryk University alumni Czechoslovak mathematicians