Bhabha's father understood his son's predicament, and he agreed to finance his studies in mathematics provided that he obtain first class on his Mechanical Sciences Tripos exam. Bhabha took the Tripos exam in June 1930 and passed with first class. Afterwards, he excelled in his mathematical studies under Paul Dirac to complete the Mathematics Tripos. Meanwhile, he worked at the Cavendish Laboratory while working towards his doctorate in theoretical physics. At the time, the laboratory was the center of a number of scientific breakthroughs. James Chadwick had discovered the neutron, John Cockcroft and Ernest Walton transmuted lithium with high-energy protons, and Patrick Blackett and Giuseppe Occhialini used cloud chambers to demonstrate the production of electron pairs and showers by gamma radiation.