Entering the Jagiellonian University in Kraków in 1920, Golab studied mathematics in the Faculty of Mathematics and Physics. However, although only two years into an undergraduate degree, in 1922 Golab was given a position as a teaching assistant in the Mining Academy in Kraków. He was awarded a Master's degree in mathematics from the Jagiellonian University in 1924 and in the following year published his first mathematics paper Quelques propiétés des corbes régulières . In 1926 he obtained the necessary certificate to allow him to teach mathematics at High Schools. However Golab continued teach at the Mining Academy and to undertake research in mathematics. He travelled to Delft in Holland in 1928 where he studied under Jan A Schouten. In Delft he undertook the necessary research for his doctoral dissertation with Schouten as his advisor. However he was registered as a doctoral student at the Jagiellonian University with Stanisław Zaremba as his formal thesis supervisor. Before submitting his thesis, Golab studied in Italy with Tullio Levi-Civita and E Bompiani, in Czechoslovakia with Ludwig Berwald, and also in Göttingen. His doctoral thesis Über verallgemeinerte projektive Geometrie was submitted to the Jagiellonian University in 1930 but it was only in 1931 that he defended his doctoral dissertation in Kraków. Before this, however, he had already begun to give mathematics lectures to chemists and natural scientists at the Jagiellonian University.
Since he wanted to become a university professor of mathematics, Golab worked on his habilitation. He was awarded the degree based on his paper Quelques problèmes métrique de la géometrie de Minkowski in 1932. Following this, although he continued to teach mathematics for scientists courses at the university, he also began his teaching career to mathematicians at the university. Golab also continued to lecture at the Mining Academy and in 1939 he was promoted to associate professor there. He was now 37 years old and had established himself as a top quality researcher with a remarkable record to the quantity and quality of his publications. After the 1925 paper we mentioned above, Golab published 3 papers in 1928, 3 papers in 1929, 4 papers in 1930, 1 paper in 1931, 6 papers in 1932, 9 papers in 1933, 4 papers in 1934, 5 papers in 1935, 2 papers in 1936, 5 papers in 1937, and 11 papers in 1938. However his career came to disastrous halt following the outbreak of World War II in 1939.
Poland was invaded by German troops on 1 September 1939 and by 5 September they had crossed the Vistula. The Fourteenth Army was aiming at Kraków but, although the city was not destroyed, it had to surrender to the German forces on 6 September. The general expectation was that the Germans would allow the Jagiellonian University to open and teach the 1930-40 courses. SS officer Bruno Müller ordered the rector of the University to assemble the professors and assistants of the University on 6 November to hear a lecture on the Nazi Party policy toward science and universities. Believing that this was a meeting where conditions would be laid out for the university to reopen, 105 professors and assistant professors, 33 teaching staff and 2 students assembled in room 66 of the Collegium Novum building at noon. In addition 21 professors and assistantd from the Mining Academy were attending a meeting in a different room of the Collegium Novum. Golab was one of those at the meeting in the Collegium Novum on that day.
What the Kraków university teachers did not know as they entered the Collegium Novum was that the Nazis had been working out a plan codenamed Sonderaktion Krakau as part of a wider plan to eradicate the Polish intellectuals. All were arrested including a number of visiting professors, university employees and students not included in the above totals who happened to be in the Collegium Novum at the time. Golab, of course, was one of those arrested. He was taken first to a prison in Wrocław, then to the concentration camps of Sachsenhausen and Dachau. In all 183 arrested in the Collegium Novum that day ended up in these concentration camps. Many Jews sent to these concentration camps went straight to the gas chambers but the academics were spared that fate. However conditions in the camps were extremely poor with disease, lack of proper food and sanitation, and little escape from the winter cold. Around twenty of the older professors died in the camps, or within days of being released. However on 8 February 1940, following strong international protests, around one hundred of the older professors were released. Golab, being one of the younger professors, was not released at that time and he suffered in the camps until December 1940 when, after a year of imprisonment, he was released.
Golab worked as a bookkeeper for a forestry organisation from the time of his release until the end of World War II. However, in 1942, the released academics began to operate an underground university in Kraków, despite the Nazi edicts forbidding such an organisation. Golab was one of those who, despite the knowledge that were they caught they would almost certainly have been murdered, taught at both the Mining Academy and at the Jagiellonian University. He resumed his pre-war duties at both the Mining Academy and the Jagiellonian University after the war ended. He was made an extraordinary professor at the Mining Academy in 1946 and a full professor two years later. In 1949 he was appointed as Head of the Department of Differential Geometry at the Mathematics Institute of the Polish Academy of Sciences. In 1955 he became a full professor at the Jagiellonian University where he was Head of Geometry. He continued to teach at the Mining Academy until 1962, but even after that he continued to collaborate with colleagues there.
Kucharzewski, a doctoral student of Golab at the Jagiellonian University who obtained his doctorate in 1959, writes in :-
Professor Golab dealt with different fields of mathematics such as geometry, topology, algebra, analysis, logic, functional and differential equations, the theory of numerical methods and various applications of mathematics. He wrote several didactic papers (13), popular science papers (3), historical essays (8) and biographical notes (8). However, the most important results he obtained were in the field of geometry. More than half of the total number of his publications belong to that domain (130). One can divide them into three almost equal parts; papers on the theory of geometric objects (40), papers on classical differential geometry under weak regularity assumptions (43) and papers belonging to various other domains in geometry (50) mainly connected with some special spaces such as spaces with linear or projective connection, Riemann, Minkowski and Finsler spaces, general metric spaces, etc.In  Kuczma, a doctoral student of Golab at the Jagiellonian University who obtained his doctorate in 1961, writes that Golab:-
... may be considered as the father figure of the Polish school of functional equations. All Polish mathematicians working in the theory of functional equations are - directly or indirectly - pupils of Professor Golab.Bodziony writes in :-
... at least a few dozen, perhaps even hundreds, of engineers not only had the opportunity of discussing their projects or results with Professor Golab, but also as a result of this discussion could enrich and improve their research work.In 1956 Golab published the book Tensor calculus (Polish). Z A Melzak begins a review of the text by writing:-
This is a careful book, in the classical style and the usual best traditions of the Polish school, on the Tensor Calculus, written from a geometrical point of view, and intended for students of Physics and Engineering as well as those of Mathematics. By an explicitly stated preference, the author follows the methods of Schouten ...A second Polish edition was published in 1966. It was considerably enlarged. This edition was translated into English and published in 1974. Let us also mention the book Funktionalgleichungen der Theorie der geometrischen Objekte which Golab wrote jointly with J Aczél and published in 1960.
Kucharzewski, himself a pupil of Golab, writes:-
He will always be remembered by his pupils as a conscientious researcher, great teacher and invariably helpful man.
Article by: J J O'Connor and E F Robertson