Karol Borsuk (8 May 1905 – 24 January 1982) was a Polishmathematician. His main area of interest wastopology. He made significant contributions toshape theory, a term which he coined. He also obtained important results infunctional analysis. He was a professor of mathematics at theUniversity of Warsaw, a member of thePolish Academy of Sciences, thePolish Mathematical Society and a leading representative of theWarsaw School of Mathematics.

Karol Borsuk
Born	(1905-05-08)8 May 1905 Warsaw,Congress Poland,Russian Empire
Died	24 January 1982(1982-01-24) (aged 76) Warsaw,Poland
Nationality	Polish
Alma mater	Warsaw University
Known for	Borsuk's conjecture Borsuk–Ulam theorem Bing–Borsuk conjecture Absolute retract Absolute neighborhood retract Shape theory
Scientific career
Fields	Mathematics
Doctoral advisor	Stefan Mazurkiewicz
Notable students	Samuel Eilenberg Jan Jaworowski Krystyna Kuperberg Włodzimierz Kuperberg Andrzej Trybulec Krzysztof Edward Haman

Borsuk was born in 1905 inWarsaw to father Marian, a surgeon, and mother Zofia (née Maciejewska). In 1923, he graduated from theStanisław Staszic State Gymnasium in Warsaw.^[1] Between 1923–1927, he studied mathematics at the Faculty of Philosophy of theUniversity of Warsaw.

He received hismaster's degree anddoctorate from Warsaw University in 1927 and 1930, respectively. HisPhD thesis title wasOn the Subject of Topological Characterization of Euclidean Spheres and his advisor wasStefan Mazurkiewicz. From 1929 to 1934, he worked at the Faculty of Mathematics at the University of Warsaw. He became a professor in 1938. In the interwar period, Borsuk visitedLwów, which was a thriving center of mathematics of theSecond Polish Republic, and began his collaboration withStanisław Ulam, especially in the field of topology. Borsuk joined the mathematicians in theScottish Café and contributed to the open problems which they wrote down in thefamous book.^[2]

DuringWorld War II, he run a stationary store and provided a secret meeting place for theHome Army. He designed and published a number ofboard games includingAnimal Husbandry, which enjoyed great popularity and was re-released in 1997 asSuperfarmer.^[3] In the years 1939–1944, he gavesecret lectures at the University of Warsaw. In 1943, he was arrested for his participation in the resistance movement and spent a couple of months at thePawiak Prison.^[4] During theWarsaw Uprising in 1944, he was transported alongside his family to theDulag 121 Camp inPruszków. He managed to escape from the camp and remained in hiding until the end of the war.^[5]

In 1945, he completed a project in collaboration withBronisław Knaster andKazimierz Kuratowski concerning the establishment of theInstitute of Mathematics of the Polish Academy of Sciences.^[6] In 1946, he returned to the University of Warsaw where he served as the Head of the Institute of Mathematics from 1952 to 1964. In 1952, he became a member of thePolish Academy of Sciences, and in 1953, a corresponding member of theBulgarian Academy of Sciences. He was also a member of thePolish Mathematical Society. He worked as an editor-in-chief ofDissertationes Mathematicae and deputy editor-in-chief ofFundamenta Mathematicae. In 1946–47, he lectured at the Institute for Advanced Study atPrinceton University, in 1959–60 at theUniversity of California at Berkeley, in 1963–64 at theUniversity of Wisconsin at Madison, and in 1967–68 atRutgers University–New Brunswick.^[5] In 1954, he received theOfficer's Cross of theOrder of Polonia Restituta for his "outstanding contributions to science".^[7] In 1976, he was awarded anhonorary doctorate by theUniversity of Zagreb.^[8]

Borsuk's students include:Samuel Eilenberg, Andrzej Kirkor,Jan Jaworowski, Andrzej Granas, Antoni Kosiński, Karol Sieklucki, Włodzimierz Holsztyński, Rafał Molski, Hanna Patkowska, Andrzej Jankowski,Włodzimierz Kuperberg, Stanisław Spież,Krystyna Kuperberg, Jerzy Dydak,Andrzej Trybulec, Marian Orłowski, Alfred Surzycki.^[9]

Borsuk introduced the theory ofabsolute retracts (ARs) andabsolute neighborhood retracts (ANRs), and thecohomotopy groups, later called Borsuk–Spanier cohomotopy groups. He also foundedshape theory. He has constructed various beautiful examples oftopological spaces, e.g. an acyclic, 3-dimensionalcontinuum which admits a fixed point freehomeomorphism onto itself; also 2-dimensional, contractible polyhedra which have no free edge.

His topological and geometric conjectures and themes stimulated research for more than half a century; in particular, his open problems stimulated the infinite-dimensional topology. Some of the notable mathematical concepts that bear Borsuk's name includeBorsuk's conjecture,Borsuk–Ulam theorem andBing–Borsuk conjecture.

In 1936, he married Zofia Paczkowska.^[2] One of his two daughters, Magdalena, who was a Professor of Paleontology, was married to Polish mathematicianAndrzej Białynicki-Birula.^[10] He died in Warsaw in 1982 and was buried at thePowązki Cemetery.^[11] In 2008, a commemorative plaque in honour of Borsuk was unveiled at the entrance to the tenement house in Warsaw at Filtrowa 63 Street where the mathematician used to live.^[12]

• Geometria analityczna w n wymiarach (1950) (translated to English asMultidimensional Analytic Geometry,Polish Scientific Publishers, 1969)
• Podstawy geometrii (1955)
• Foundations of Geometry (1960) withWanda Szmielew, North Holland publisher^[13]
• Theory of Retracts (1967), PWN, Warszawa.
• Theory of Shape (1975)
• Collected papers vol. I, (1983), PWN, Warszawa.

• Zygmunt Janiszewski
• Stanislaw Ulam
• Scottish Café
• Ham sandwich theorem

• O'Connor, John J.;Robertson, Edmund F.,"Karol Borsuk",MacTutor History of Mathematics Archive,University of St Andrews
• Karol Borsuk at theMathematics Genealogy Project