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and nurtured. 3 By the age of thirteen, he was being fast-tracked not just by the teachers at the school—advanced mathematicians who carried out research alongside their teaching—but also by Joseph Kürschák, a professor at the University of Budapest. At seventeen he published an original paper (co-authored with one of his teachers), and on leaving school that year, 1921, he wanted to become a mathematician. Max von Neumann was horrified, pointing out that there was no money to be made in mathematics. But father and son agreed a compromise—the kind of compromise which made perfect sense to Johnny. He enrolled to study a “sensible” subject (chemical engineering) at the University of Berlin, later transferring to the Eidgenössische Technische Hochschule (ETH: the Swiss Technical High School) in Zürich, and simultaneously as a mathematics student at the University of Budapest, where he was already well known. Over the four years up to 1925 he duly attended lectures in Berlin and Zürich, and, by arrangement with his professor, popped in to the University of Budapest at the end of each term solely to take examinations. He also prepared athesis, on set theory, to be offered to the University of Budapest for a doctorate. His final examinations at both institutions were taken in 1925 (he passed, of course, with the highest possible grades) and his doctorate was awarded in 1926. No more was heard of chemical engineering as a career, and von Neumann started his career in mathematics as a Privatdozent (the most junior kind of lecturer) at the University of Berlin the same year, while working for a qualification known as the Habilitation , a kind of higher doctorate required in the German system before becoming a professor.
    One of von Neumann's examiners for his doctorate was the great David Hilbert, the most influential mathematician of his generation (he had been born in 1862), whose work would, as we have seen, soon be the inspiration for Turing's investigations into (in)computable problems. Hilbert was based at the University of Göttingen, and alongside his post in Berlin von Neumann was awarded a Rockefeller Fellowship, which enabled him to carry out research in Göttingen with Hilbert during the academic year 1926/7. Between 1926 and 1929 he published twenty-five scientific papers and established a reputation as a quantum theorist—his book Mathematical Foundations of Quantum Mechanics , which was published in 1932, was highly influential, coming to be regarded as a standard text—although, as we shall see, it contained one major flaw. Still in his twenties, he was a glittering star in the mathematical firmament, and his fame had spread worldwide. He had scarcely moved on from Berlin to a more senior post in Hamburg when in 1929 he was invited to visit Princeton to lecture on quantum theory. Replying that he had some personal matters to attend to first,von Neumann made a flying visit to Budapest to get married, to Marietta Kovesi, before becoming a visiting lecturer at Princeton University in February 1930.
    Although von Neumann was actually a rather poor lecturer—he had a habit of writing complicated equations in a small corner of the blackboard and erasing them before the students could copy them down—the visit led to his appointment as a professor at Princeton the following year. He loved America, America seemed to love him, and although at first he still held scientific posts in Germany and visited there in the summers, the developing political situation made this a less and less attractive arrangement. Things came to a head in 1933. In January, von Neumann was offered the opportunity to become one of the founding professors at the new Institute for Advanced Study at Princeton (with a starting salary of $10,000), and a few days later Adolf Hitler was appointed Chancellor of Germany. Within months, the new regime began a purge of Jewish academics, and von Neumann