# Asger Hartvig Aaboe

### Born: 26 April 1922 in Copenhagen, Denmark

Died: 19 January 2007 in North Haven, Connecticut, USA

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**Asger Aaboe**'s father was an officer in the Danish Army whose family came from Egaa, a small village which lies on the banks of Aarhus bay to the north of Aarhus city centre. The 'aa' in both Aaboe and in Egaa means 'brook' [2]:-

He attended the Ostre Borgerdyd Skole in Copenhagen, a famous school where J L Heiberg, who produced masterly editions of Greek mathematical and astronomical classics, had been headmaster from 1884 to 1896. Aaboe graduated in 1940 and entered the University of Copenhagen.... as Asger once explained, his family name means 'one who lives by(boe)the brook(aa)'.

Earlier in the same year, on 9 April, Germany had invaded Denmark. Danish institutions continued to function relatively normally, however, as a result of the cooperative attitude of the Danish authorities. By the summer of 1943 there was increasing hostility towards Germany and the Danish government was dissolved. However Aaboe was able to study mathematics, astronomy, physics, and chemistry at the University, being particularly influenced by his mathematics lecturer Harald Bohr. He graduated from Copenhagen with a Candidatus Magisterii in 1947 after presenting a thesis

*The Determination of Areas and Volumes in Antiquity, Especially in the Works of Archimedes*. In 1948 he went to the United States where he had been appointed to a visiting lectureship at Washington University in St Louis. There he met Joan Armstrong; they were married in 1950 and had four children, Kirsten, Anne, Erik, and Niels.

Later in 1948 Aaboe returned to Denmark to take up a position at Birkerod Statsskole where he was appointed Adjunkt in Mathematics. He remained there until 1952 when he emigrated to the United States on being offered a position as Instructor in Mathematics at Tufts University near Boston. In fact when Aaboe was appointed the institution was known as Tufts College, changing its name to Tufts University in 1954.

Aaboe continued with his interest in the history of mathematics and published the paper

*Al-Kashi's iteration method for the determination of sin*1° in 1954. In addition to holding the Instructorship at Tufts, he enrolled as a Ph.D. student at Brown University in Providence, Rhode Island, in 1955. There was good reason for Aaboe to register for a Ph.D. at Brown University for although he became the only graduate student in the History of Mathematics Department, he became a student of the eminent historian of mathematics Otto Neugebauer who had been Professor of the History of Mathematics at Brown University since 1947. Steele writes [3]:-

Given Neugebauer's interests it will not be a surprise to learn that the title of Aaboe's doctoral thesis, submitted in 1957, wasFew combinations of student and supervisor can have been as profitable as that between Neugebauer and Aaboe. When Aaboe first came to Brown, Neugebauer was in the final stages of preparing his groundbreaking study of Babylonian mathematical astronomy, Astronomical Cuneiform Texts(1955). This work would put research into Babylonian astronomy on a firm foundation through the publication and systematic analysis of more than three hundred texts found on cuneiform tablets held in the British Museum, the Oriental Institute at Chicago, the Louvre in Paris, the Staatliche Museen in Berlin, the Arkeoloji Müzeleri in Instanbul, and several smaller collections in Europe and the United States. It was natural, therefore, that Aaboe would work on Babylonian astronomy for his PhD.

*On BabyIonian Planetary Theories*.

Now Neugebauer was not the only influence of Aaboe from his time at Brown University. The Assyriologist Abraham Sachs was also at Brown and had worked with Neugebauer on Babylonian mathematical texts. Sachs had become interested in Babylonian astronomy and had gained access to hundreds of astronomical cuneiform tablets kept in the British Museum in London [3]:-

Aaboe was promoted to Associate Professor at Tufts in 1959, then two years later accepted an invitation to join the newly created Department of the History of Science and Medicine at Yale. In 1962 he became an Associate Professor in both this department and also in the Mathematics Department at Yale. He was promoted to full Professor in both departments in 1967, and ten years later became a professor in a third Yale department, namely the Department of Near Eastern Languages and Literatures. He remained in these professorial positions until he retired in 1992.Sachs passed on to Aaboe a list of tablets that were clearly related to the mathematical astronomical texts published by Neugebauer but did not appear to be part of the known systems of planetary or lunar theory. This list of tablets would provide the stimulus for much of Aaboe's research for the rest of his career.

Let us now look at some of Aaboe's publications. In 1963 he published

*On a Greek qualitative planetary model of the epicyclic variety*. O Schmidt writes in a review:-

In 1964 he wrote the bookIn a Greek papyrus of the second century A.D. there is evidence of a planetary model of epicyclic type in which the planet travels on the epicycle in the opposite direction to that correctly adopted by Ptolemy. In the paper under review it is shown that assuming the angular velocities of the centre of the epicycle and the angular velocities of the planet on the epicycle to be the same as those in AlmagestⓉ(and this is a very reasonable assumption), a model of the above mentioned type can make neither Venus nor Mars retrograde.

*Episodes from the early history of mathematics*. Steele writes [3]:-

It is a beautifully written book which the authors of this biography have read several times during their writing of articles for this archive.Aaboe took this opportunity to write a history of mathematics text that was accessible to school-children and yet still dealt with the technical details of ancient mathematics. In carrying off this challenge Aaboe displayed his gift for explaining complicated matters in clear, charming, and witty prose. His success can be seen by the fact that the book has been translated into Swedish, Danish, Spanish, Turkish, Polish and Japanese.

In

*Some Seleucid mathematical tables (Extended reciprocals and squares of regular numbers)*(1965) Aaboe looks at eight mathematical cuneiform tablets, three of which had not previously been published. In the same year he published

*On period relations in Babylonian astronomy*which made new conjectures based on texts that Abraham Sachs had found. In the following year he published the paper

*Some dateless computed lists of longitudes of characteristic planetary phenomena from the late-Babylonian period*based on fourteen texts kept in the British Museum. This source of texts also led to

*Some lunar auxiliary tables and related texts from the late Babylonian period*(1968) while the paper

*Two atypical multiplication tables from Uruk*published in the following year examined one previously unpublished paper and one which had been misidentified by Neugebauer. In

*A computed list of new moons for 319 B.C. to 316 B.C. from Babylon: B.M. 40094*(1969) he gave photographs with a translation of a cuneiform tablet in the British Museum which gives the moment of conjunction of sun and moon each month over a three year period. Its interest lies mainly in its early date. He continued to publish papers on these topics throughout his life.

In 2001 Aaboe published

*Episodes from the early history of astronomy*, a companion volume to his 1964

*Episodes from the early history of mathematics*. J P Britton writes in a review :-

Aaboe's wife Joan died in 1990 and he retired two years later. Steele writes [3]:-This slim, elegantly written volume by Asger Aaboe might have been more accurate titled 'Highlights of Planetary Theory from Babylon to Kepler' since that is in fact its subject. ...[it]provides a clear, authoritative, and frequently original introduction to the principal elements of planetary theory before Newton, which experts will find rewarding and novices accessible.

He remarried in 2006 to Izabela Zbikowska and died at his home in January of the following year after a brief illness.Despite his retirement in1992, Aaboe maintained his interest in Babylonian astronomy, continuing to publish important studies, and encouraging younger scholars in their work. I was fortunate to be one of the beneficiaries of Asger's encouragement, and spent several happy days staying with him in North Haven, discussing Babylonian astronomy, eating his fine home made bread, sailing on his boat, and listening to his stories of Sachs, Neugebauer and the other great scholars of Babylonian astronomy.

**Article by:** *J J O'Connor* and *E F Robertson*

**List of References** (3 books/articles)

**Mathematicians born in the same country**

**Other Web sites**