After he was released from the prison camp, Neugebauer moved around. First he studied electrical engineering and physics at the University of Graz from 1919 to 1921, then he studied mathematics and physics at the University of Munich with Sommerfeld. He settled in Göttingen in 1922 where he began a serious study of mathematics having become friends with Courant, Harald Bohr, and Aleksandrov. His friendship with Bohr developed into a mathematical collaboration and they wrote a joint paper on almost periodic functions. It was to be Neugebauer's first and last paper on mathematics as such for his work at this point took a definite turn.
Neugebauer was an expert in languages and he had studied Egyptian. It was natural, therefore, for Bohr to ask his friend to review a publication on the Rhind papyrus. Once he had begun to study the work, Neugebauer realised that the subject which he wanted to work in was the history of mathematics. He approached Courant and Hilbert to see if he could work for his doctorate on the history of Egyptian unit fractions. They agreed to supervise such a project and Neugebauer received his doctorate for a dissertation on this topic in 1926.
In 1927 Neugebauer was appointed to the staff at Göttingen and he began to lecture on the history of ancient mathematics. One student who attended this first lecture course was Bartel van der Waerden and, as a result, he also developed an interest in ancient mathematics and was to publish works of major importance throughout his life.
However, in 1927 Neugebauer decided that he wanted to research into Babylonian mathematics and, to enable him to do so, he learnt Akkadian which is the language in which the Babylonians wrote their tablets. The Babylonians wrote on tablets of unbaked clay, using cuneiform writing. The symbols were pressed into soft clay tablets with the slanted edge of a stylus and so had a wedge-shaped appearance (and hence the name cuneiform). Many tablets, the earliest dating from around 1700 BC, had survived and Neugebauer knew that they were held by various museums but at that time little work had been undertaken to study them and to evaluate the Babylonian contribution. Gray writes in :-
Neugebauer was to publish his 3-volume collection on mathematical tablets in the mid-1930s. They established the great richness of Babylonian mathematics, far exceeding anything one could have guessed from Greek or Egyptian sources.Another project which Neugebauer became involved in was the building of a new Mathematical Institute at Göttingen. This was completed in 1929, with support from the Rockefeller Foundation, and Courant and Neugebauer jointly directed the Institute until 1932. However, Neugebauer had before this started the first of two projects which would be among the most important contributions anyone has made to mathematics. He persuaded Springer-Verlag to publish a journal reviewing all mathematical publications, which would complement their reviewing journals in other topics. In 1931 the first issue of Zentralblatt für Matematik appeared, edited by Neugebauer.
Zentralblatt für Matematik rapidly became an indispensable tool for all mathematicians. However, the political situation in Germany as the Nazis came to power was to bring about changes which completely changed the course of Neugebauer's career. As Boas writes in :-
He opposed the National Socialists in Germany from the beginning and was forced out of his academic position as a consequence.Davis  recalls Neugebauer saying:-
If you never heard the sound of Nazi boots below you in the street, you cannot understand the history of the period.I'm sure that Neugebauer is right, yet his very quote may aid us a little in our understanding of the situation. Fortunately Neugebauer had a good friend in Harald Bohr, and he invited Neugebauer to move to the University of Copenhagen in January 1934. Neugebauer took the editorial office of Zentralblatt für Matematik to Copenhagen with him and from 1934 until 1938 Zentralblatt continued to flourish from its headquarters there. The struggle to produce the reviewing journal became more difficult throughout this period, however, for the Nazis tried more and more to influence the editorial policy of the journal. Sadly some fine mathematicians were seduced by the Nazi ideas and mathematicians such as Blaschke attacked the journal.
Matters came to a head in 1938 when Springer-Verlag insisted that Zentralblatt für Matematik be produced in accordance with Nazi principles. Levi-Civita, who was on the editorial board, was dismissed and Neugebauer, together with almost the whole of the editorial board, resigned. Neugebauer destroyed all the records of the journal except for the cumulative index.
Neugebauer was a highly respected historian of mathematics, and the world of mathematics could not afford to lose the reviewing journal that it had come to depend on in only a few years. Veblen arranged for Brown University to offer Neugebauer a chair and the American Mathematical Society saw the chance to support Neugebauer in founding a new reviewing journal. Neugebauer sailed to the United States and :-
... the index to the Zentralblatt came with Neugebauer, although the U.S. customs almost confiscated it as potentially subversive, and it survives to this day.In a remarkably short time Neugebauer had Mathematical Reviews up and running. The journal started reviewing articles which appeared from July 1939 and the first issue appeared in January 1940. Neugebauer continued as editor of Mathematical Reviews until 1945 when a full-time executive editor was appointed. Neugebauer policy regarding reviews was an interesting one. He :-
... always insisted that the length of the review was not intended to be directly proportional to the importance of the paper; indeed, a bad paper needed to have a review sufficiently detailed so that nobody needed to look at the paper itself, whereas a really important paper needed only to be called to the world's attention.In 1947 Neugebauer was appointed Professor of the History of Mathematics at Brown University. His contributions to the history of ancient mathematics and astronomy continued to astound. Gray writes in  that:-
... his greatest pleasure was in entirely reshaping and extending our knowledge of the history of science. Indeed, the message that Babylonians knew more (and, he impishly insisted, the Egyptians knew less) than most people believe still needs amplification today. The high levels of scholarship that now prevails in the subject gives every prospect that received opinion will change, and that high level is largely due to the standards he set himself, his organisational skills, and the support he was able to attract.Among his classic texts we should mention The Exact Sciences in Antiquity (1951) and the three volume History of Ancient Mathematical Astronomy (1975). Pyenson writes :-
Neugebauer belongs to a tradition of intensive scholarly publishing more at home in Europe than in America. His writings are technically demanding, assuming the reader is familiar with ancient and modern languages as well as the secondary literature. Neugebauer, an independent thinker who in his youth was a partisan of left-wing politics, flew no ideological flag in his scholarly work. He strove mightily to avoid the signal affliction of scholarship - tedium. His work sparkles with original insight and energetic prose.Neugebauer received many awards, prizes, and honorary degrees. He was elected to membership of the leading academies around the world including the Royal Danish Academy of Sciences, the Royal Belgium Academy of Science, the Austrian Academy of Sciences, the British Academy, the Irish Academy and National Academy of Sciences (United States). The American Philosophical Society awarded him their Franklin Medal. He received the Balzan Prize in 1986. Boas writes in  that his greatest pleasure was in the award he received in 1979 from the Mathematical Association of America when they gave him their Award for Distinguished service to Mathematics. The article  gives Neugebauer's main contributions which led to the award and, although his distinguished work on the history of science is praised, the main reason for the honour was his contribution to reviewing journals. It:-
... is that he founded, and for many years edited, first the "Zentralblatt für Matematik" ..., and later, "Mathematical Reviews", and so gave mathematics the essential tool of a working abstracting service.From the 1940s onwards, although still on the faculty at Brown University, Neugebauer spent considerable time at the Institute for Advanced Study at Princeton. After he retired from Brown University in 1969 he spent more time at Princeton where he was made a permanent member of the Institute for Advanced Study in 1980.
Article by: J J O'Connor and E F Robertson