Boštík studied at the Czech Technical University in Prague (1933–1937) and at the Prague Academy of Fine Arts (1945), where his teacher was Willy Nowak. He was a member of Umělecká beseda (1942) and UB 12 (1960). His early works were influenced by Camille Corot and Paul Cézanne, but by the 1950s he set his sights on abstraction. His humanist outlook found expression in the monument to the Holocaust victims in the Pinkas Synagogue in Prague (1959), where he and Jiří John created a work of art unique for its time out of the 77 297 names of the Czech Jewish victims of Nazism.