The philosophy of scientific research does not always correlate with the declared philosophical views of researchers. In the light of this, we look at the activities of the interwar Lwów School of Mathematics whose leaders were Stefan Banach and Hugo Steinhaus. Non-constructive methods of proof were characteristic of the school and are closely related to the philosophical problem of the existence of mathematical objects. The problem of the relationship between formalism and intuitionism, which is tangential to the school’s activities, is (...) briefly discussed. (shrink)