In the first half of the 20th century, Poland was a flourishing centre of mathematics. Outstanding Polish mathematicians formed the Lwów School of Mathematics (with Stefan Banach, Stanisław Mazur, Hugo Steinhaus, Stanisław Ulam) and Warsaw School of Mathematics (with Alfred Tarski, Kazimierz Kuratowski, Wacław Sierpiński and Antoni Zygmund). Numerous mathematicians, scientists, chemists or economists emigrated due to historic vicissitudes, among them Benoit Mandelbrot, Leonid Hurwicz, Alfred Tarski, Joseph Rotblat and Nobel Prize laureates Roald Hoffmann, Georges Charpak and Tadeusz Reichstein. In the 1930s, mathematician and cryptologist Marian Rejewski invented the Cryptographic Bomb which formed the basis of the effort that allowed the Allies to crack the Enigma code.