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In this study, we present profiles of some distinguished graduates inmathematics of the Jagiellonian University from the years 1918-1939. We discusstheir professional paths and scholarly achievements, instances of scientificcollaboration, connections with other academic centers in Poland and worldwide,involvement in mathematical education and teacher training, as well as theirlater roles in Polish scientific and academic life. We also try to understandin what way they were shaped by their studies and how much of Krak\'owscientific traditions they continued. We find strong support for the claim thatthere was a distinct, diverse and deep mathematical stream in Krak\'ow betweenthe wars, rooted in classical disciplines like differential equations andgeometry, but also open to new trends in mathematics. Part I concerns thegraduates before the university reform, in 1918-1926.

Distinguished graduates in mathematics of the Jagiellonian University in the interwar period. Part I: 1918-1926