Otto E. NeugebauerMay 26, 1899February 19, 1990By N. M. Swerdlow |
Courtesy of Brown University Photo Laboratory |

OTTO NEUGEBAUER WAS THE most original and productive scholar of the history of the exact sciences, perhaps of the history of science, of our age. He began as a mathematician, turned first to Egyptian and Babylonian mathematics, and then took up the history of mathematical astronomy, to which he afterward devoted the greatest part of his attention. In a career of sixty-five years, he to a great extent created our understanding of mathematical astronomy from Babylon and Egypt, through Greco-Roman antiquity, to India, Islam, and Europe of the Middle Ages and Renaissance. Through his colleagues, students, and many readers, his influence on the study of the history of the exact sciences remains profound, even definitive.

Neugebauer was born in Innsbruck, Austria, his father Rudolph Neugebauer a railroad construction engineer and a collector and scholar of Oriental carpets. His family soon moved to Graz where his parents died when he was quite young. He attended the Akademisches Gymnasium, and was far more interested in mathematics, mechanics, and technical drawing than in the required courses in Greek and Latin. Because his family was Protestant, he was exempted from mandatory instruction in religion, which also pleased him.

In 1917 he learned that he could receive his graduation certificate without passing a Greek examination if he enlisted in the Austrian Army, which he promptly did. Before long, he found himself an artillery lieutenant, principally a forward observer, on the Italian front. He later remarked mordantly that these were among the happiest days of his life. Following his discharge, in the fall of 1919 he entered the University of Graz in electrical engineering and physics, and in 1921 transferred to the University of Munich, where he attended lectures by Arnold Sommerfeld and Arthur Rosenthal. He had lost his entire inheritance, safely invested in government bonds, through the Austrian hyperinflation, and he spent a miserable winter with little food and water frozen in his room each morning.

During this year his interests
changed to mathematics, and in the fall of 1922 following Sommerfeld's
advice he moved on to the Mathematisches Institut at the University of
Göttingen. He began his studies with the new director of the
Institut, Richard Courant, who became a very close friend, also took
courses with Edmund Landau and Emmy Noether, and in 1923 became an
assistant at the Institut and special assistant to Courant in 1924.
Significantly, he was also in charge of the *Lesezimmer*, the
library. During 1924-25 he was at the University of Copenhagen with
Harald Bohr, another close friend, with whom he published in 1926 a
paper on differential equations with almost periodic functions, one of
Bohr's specialties, which turned out to be his only paper in pure
mathematics.

For again, Neugebauer's interests had
changed, this time to the history of Egyptian mathematics for which he
studied Egyptian with Hermann Kees and Kurt Sethe. His thesis *Die
Grundlagen der ägyptischen Bruchrechnung* (Springer, 1926), was
principally an analysis of the table in the Rhind Papyrus for the
expression of fractions of the form *2/n* as a sum of different
unit fractions, fractions with the numerator 1, and curiously stirred up
a good deal of controversy. In 1927 he received his *venia legendi*
for the history of mathematics, and in the fall term became Privatdozent
and began lecturing on mathematics and on the history of ancient
mathematics. At this time he married Grete Bruck, a fellow student and
very fine mathematician, who later assisted him in much of his work.
They had two children, Margo, born in 1929, and Gerry in 1932. In 1929
he founded, with O. Toeplitz and J. Stenzel as co-editors, *Quellen
und Studien zur Geschichte der Mathematik, Astronomie und Physik
(QS)*, a Springer series devoted to the history of the mathematical
sciences and divided into two parts, Abteilung A for the publication of
sources and B for studies, in which he published extended papers on
Egyptian computational techniques in arithmetic and geometry (*QS
*B 1, 1930-31). The previous year he had gone to Leningrad to assist
W. Struve in preparing for publication the Moscow Papyrus, the most
important text for geometry, which appeared in *QS* A 1 (1930).

Since 1927, however, he had been investigating a more
important and interesting subject, namely, Babylonian mathematics, for
which he had learned Akkadian and worked in Rome with Father P. A.
Deimel, S. J., of the Pontificio Istituto Biblico. His first paper on
Babylonian mathematics, in 1927, was an account of the origin of the
sexagesimal system, and by 1929 he was gathering new material at Berlin
and other collections for the publication of a substantially complete
corpus of texts. During the next few years, he published a number of
articles, mostly in *QS *B, and eventually published the corpus in
*Mathematische Keilschrift-Texte* (*MKT*) (*QS *A 3, 3
vols., 1935-37). At the beginning of the preface he quoted Anatole
France, one of his favorite authors: "L'embarras de l'historien
s'accroît avec l'abondance des documents." This was not the last
time this was to prove true. *MKT* is a colossal work, in size, in
detail, in depth, and its contents show that the riches of Babylonian
mathematics far surpass anything one could imagine from a knowledge of
Egyptian and Greek mathematics.

In l931 he became the
founding editor of the review journal *Zentralblatt für
Mathematik und ihre Grenzgebiete* (*Zbl*), his most important
contribution to modern mathematics. The following year he was promoted
to Extraordinarius, founded *Ergebnisse der Mathematik und ihrer
Grenzgebiete*, a Springer series of short monographs on current
mathematics, and in 1933, with W. Flügge, the *Zentralblatt
für Mechanik*, which was separated from *Zbl*. Then
politics intervened. On January 30, 1933, Hitler became chancellor, and
the following April 7 the Law for the Restoration of the Civil Service
authorized the removal of civil servants of non-Aryan descent or of
uncertain loyalty. On Thursday, April 26, a local newspaper carried the
notice that six professors, including Courant and Noether, were to be
placed on leave. Courant designated Neugebauer acting director of the
institut, but students were by then agitating to stop the lectures of
Landau and Paul Bernays and attacking Neugebauer as *politisch
unzuverlässig* "politically unreliable" (his political views
were always very liberal). That weekend he was asked to sign an oath of
loyalty to the new government, and when he refused was promptly
suspended as *untragbar* and denied access to the Institut
building. Why *untragbar* (intolerable)? Here is one possible
reason: A Nazi official once requested that he explain why he was in
Leningrad in 1928, since it might be thought he was secretly a
Bolshevik. His answer was to point out that in 1930 he was at the
Vatican, so perhaps they might suspect that he was secretly a Jesuit.
After several months of uncertainty about what would happen next, Harald
Bohr arranged a three-year appointment as professor at Copenhagen, which
Neugebauer took up in January 1934.

In Copenhagen he
prepared for the summer term a series of lectures on Egyptian and
Babylonian mathematics that became the first of his books directed to a
general readership, *Vorgriechische Mathematik* (Springer, 1934),
which was intended as the first volume of a set of three called
*Vorlesungen über Geschichte der antiken mathematischen
Wissenschaften*. The second was to be on Greek mathematics,
specifically Archimedes and Apollonius, and on pre-Euclidean
mathematics, showing its relation to Babylonian, and the third on
mathematical astronomy, principally on Babylonian astronomy and on
Ptolemy. So far he had written only a single paper touching on
Babylonian astronomy, a review of *The Venus Tablets of Ammizaduga
*(1928) by Langdon, Fotheringham, and Schoch, in which he demolished
the chronology of the Old Babylonian Dynasty that had been established
from heliacal risings and settings of Venus. In 1938 he did something
similar to Egyptian chronology by showing the *Bedeutungslosigkeit*
of the Sothic Cycle for dating the introduction of the Egyptian
calendar.

However, the three-volume *Vorlesungen*
were never completed, as he later told the story, for the following
reason: While working on the mathematical cuneiform texts for
*MKT,* he also considered it efficient to write the account of the
astronomical cuneiform texts, principally ephemerides in the form of
arithmetic functions for computing lunar and planetary phenomena, for
the third volume. These had originally been identified by J. N.
Strassmaier and deciphered by J. Epping in the 1880s. Since many had
been published and analyzed by F. X. Kugler in *Die babylonische
Mondrechnung* (1900) and *Sternkunde und Sterndienst in Babel
*(1907-24), it appeared reasonable to summarize Kugler's results and
extend them to the few more recently published texts, about fifty in
all. In order to restore damaged and missing sections of texts, he
developed procedures using linear diophantine equations with the number
of periods and the number of excess lines of each arithmetic function in
the ephemerides as unknowns. The result of these checks was the joining
and dating of many previously unrelated fragments, the insight that some
functions ran continuously for hundreds of years, and in general a far
deeper understanding of the mathematical structure of the texts. He
realized that what was now required was nothing less than a new edition
of all the texts with a methodologically consistent analysis, a project
going far beyond his original intention. So he put aside Greek
mathematics and went to work seriously on Babylonian astronomy, and at
first the results came rapidly, beginning with a paper in 1936 on the
method of dating and analyzing texts using diophantine equations. He
then published a series of papers, in the first of which he set out a
proposal for a complete edition of all classes of Babylonian
astronomical texts: mathematical, observational, and astrological, that
is, celestial omens, with the cooperation of additional collaborators.
In 1936-37 he had lectured on lunar and eclipse theory, the first
results of his new analyses and the basis of two papers in *QS* B 4
in which he showed the applications of his methods. But then came the
events of the fall of 1938, and it was to be many years before he, and
he alone, completed his part in this great enterprise.

Throughout this entire period, as conditions continued to
deteriorate in Germany, there was concern about *Zbl*, edited by
Neugebauer with the assistance of his wife in Copenhagen and published
by Springer in Berlin. On March 14, 1938, Wilhelm Blaschke of Hamburg, a
member of the board of editors, wrote to him that in his opinion it
appeared that the number of German contributors and the proportion of
the German language in *Zbl* had declined steadily, and if this
continued there would sooner or later be difficulties for the publisher.
Neugebauer sent a sharp reply. From its first day, he wrote, *Zbl*
had been an international journal using the most qualified reviewers. If
the proportion of English had increased, this was simply because the
production of mathematics in America had increased and the most
competent reviewers happened to be American. (In fact, at that time
about half the 300 or so reviewers were in America and England and only
about 60 in Germany, with entire fields completely unrepresented. And
many of the reviews in German were actually written by Russians.) The
changes intended by Blaschke would have destroyed *Zbl*, and in the
fall the threat became a reality. When Neugebauer received the October 8
index issue, he found that Tullio Levi-Civita had been deleted from the
editorial board. He wrote to Ferdinand Springer about this, and received
a reply that Levi-Civita's name had been removed because he had been
dismissed from his professorship in Rome due to the (anti-Semitic)
legislation in Italy. Springer went on to request that, in accordance
with the German mathematicians and the *zuständigen Stellen*
(cognizant authorities), the work of German mathematicians no longer be
reviewed by *Emigranten* and that Neugebauer make an unconditional
and binding promise to this by December 1. It is evident that Springer's
hand was forced, but it is also evident that conditions had become
impossible. Neugebauer immediately refused to accept the terms, and
wrote to members of the editorial board informing them that he intended
to resign as of December 1 and encouraging them to do the same. On
November 14 Courant, now at New York University, received a cable:
"Common immediate resignation of American editors very desirable.
Neugebauer." He also sent a printed post card to all reviewers
announcing his resignation. The effect was dramatic. Letters and
telegrams of resignation were sent to Springer by Bohr, G. H. Hardy,
Courant, J. D. Tamarkin, and O. Veblen, members of the editorial board,
and by a very large number of reviewers. English-language contributions
to *Zbl* were greatly reduced by the middle of 1939 and all but
gone by the beginning of 1940. (*Zbl* ceased publication in 1944.
Since its resumption in 1948, every issue has carried the notice
"Founded by O. Neugebauer.")

It was clear that
*Zbl* could no longer be relied on, and in the United States action
was immediately undertaken to replace it and bring in Neugebauer. Veblen
had been in correspondence about the situation with R. G. D. Richardson,
secretary of the American Mathematical Society and dean of the graduate
school at Brown University, and Richardson moved fast. There were two
principal forces working to bring Neugebauer to Brown. One was
Richardson, among the first and strongest advocates of the new journal,
who arranged for Brown to provide facilities; the other was R. C.
Archibald, a historian of mathematics who had built a splendid
mathematics collection in the Brown library. On December 20 Richardson
and H. M. Wriston, president of Brown, each wrote to Neugebauer to offer
him a professorship in the mathematics department, and Richardson also
asked him to direct the American equivalent of *Zbl*. He came to
Providence on February 16 for a stay of ten weeks. President Wriston
announced his acceptance of the professorship on February 27, and
arrangements were made for beginning work on *Mathematical Reviews*
(*MR*) that summer. In May he returned to Copenhagen, stopping in
Cambridge on the way to give the W. Rouse Ball Lectures at Trinity
College. By mid-summer he was back in Providence with his family, and
was soon joined by Olaf Schmidt, his and Bohr's student and his research
assistant in Copenhagen, who continued as his assistant while an
instructor in the mathematics department. The initial work was setting
up *MR* for which 350 reviewers and 700 subscribers were enlisted
before the first issue appeared in January 1940. It was decided to begin
with articles published after the middle of 1939, and the first issue
actually appeared on time in January 1940. Still more remarkable, at the
end of the first fiscal year, of an anticipated budget of $20,000, there
remained a surplus of more than $5,000, something that would now amaze
the American Mathematical Society and *MR*. After overseeing
*MR* for its first few years, he turned over much of the editorial
responsibility to Willy Feller, who became the executive editor in 1944.

From the moment he arrived in the United States,
Neugebauer began writing in English. He also applied for American
citizenship immediately, and he never again set foot in Germany. There
is a story concerning Neugebauer's use of English, known to some
mathematicians. In March of 1941 he received a letter from a former
colleague from Göttingen, then in Leipzig and a contributor to
*Zbl*, advising him that, as the director of two international
journals, if he valued his relations with German mathematicians, he
should take the small extra trouble to use his *Muttersprache*. Can
you not, he asked, at least show consideration for feelings you do not
share? Neugebauer's reply was directly to the point:

As to the last paragraph of your letter, I must remark that the language I use in my letters does not depend on my mother but on my secretary. It interests me very much that the so-called German mathematicians now require the editor of an international journal to use their language. During the time I was editor of the

During his first several years at Brown, Neugebauer
published a number of general papers on ancient astronomy and
mathematics, describing in outline the content of these sciences, his
methods of interpretation, and what he considered the most interesting
areas for future research. These papers, later reprinted in *Astronomy
and History* (1983), were not only the introduction of his interests
and methods in English, but were also the first extensive presentations
of his work for a general readership of historians of science and
humanists, showing the excitement of a new discovery of the sciences of
antiquity. The culmination of these writings was *The Exact Sciences
in Antiquity* (1951, 2nd ed. 1957), a survey of Egyptian and
Babylonian mathematics and astronomy, and their relation to Hellenistic
science and its descendants. But it is far more than a survey of these
sciences, for Neugebauer here allowed himself the freedom to comment on
subjects from antiquity to the Renaissance. The expert can learn
something from it, and from its notes, every time it is read, and for
the general reader it is, in my opinion, the finest book ever written on
any aspect of ancient science.

Neugebauer also turned
Brown into the leading institution for the study of the history of the
exact sciences. In his first year he taught Babylonian astronomy. A year
later he gave a series of public lectures on ancient chronology, and he
lectured frequently at other universities. Together with Archibald, he
founded a new journal of the history of the mathematical sciences called
*Eudemus*, to be published by Munksgaard with subvention by Brown.
The first issue appeared in 1941, but then the war made its continuation
impossible. In the spring of 1941 he gave a lecture at the Oriental
Institute of the University of Chicago, and there met a young
Assyriologist, Abraham Sachs, who had received his doctorate from Johns
Hopkins in 1939 and was working on the *Chicago Assyrian
Dictionary*, then as now the WPA of Assyriology. Neugebauer decided
immediately that this was the person to continue the great project of
publishing all the astronomical texts, and arranged with the Rockefeller
Foundation for Sachs to come to Brown as a Rockefeller Foundation
fellow. When the Department of the History of Mathematics was formed in
1947, Sachs joined the faculty, becoming associate professor in 1949 and
professor in 1953. For more than forty years Sachs was Neugebauer's
closest colleague and closest friend, with whom he discussed at length
nearly everything he wrote.

The next appointment was in Egyptology. Brown received a bequest to form a Department of Egyptology, for which Wriston told Neugebauer to find an Egyptologist. The choice itself was not difficult. Since 1945 he had been corresponding on Egyptian astronomy with Richard Parker, an assistant professor at the University of Chicago who then became the field director of the Oriental Institute's epigraphic survey at Luxor. It was not easy to get him, but Neugebauer and Wriston did, and in the fall of 1949 Parker became the Wilbour professor of Egyptology. In 1959 Gerald Toomer, who, to the dismay of his colleagues in classics at Oxford, had become interested in ancient mathematics, came as a special student for two years, and after returning for successive summers became an associate professor and the third member of the department in 1965. Finally, David Pingree, who began working with Neugebauer while a graduate student and then a junior fellow in Sanskrit and classics at Harvard, after eight years at Chicago, became the third "theft" from the Oriental Institute, joining the department in 1971, two years after Neugebauer's nominal retirement at seventy. With Neugebauer, Sachs, Parker, Toomer, and Pingree, there was hardly a subject in the history of the exact sciences from antiquity to the Renaissance, and hardly a classical language, that was not covered at Brown. The work of these scholars, of their students, their students' students, now extended to three generations, and of the many visitors to the department is a direct product of the school created by Neugebauer at Brown, and of course his influence extends through his writings to every serious scholar of the history of the mathematical sciences.

With an expert Assyriologist as collaborator,
one of Neugebauer's first projects was to return to Babylonian
mathematics and examine whatever might be contained in American
collections. This was mostly done by Sachs, who found substantial
additions to the texts of *MKT*. Their edition and analysis of the
new texts, published as *Mathematical Cuneiform Texts* (*MCT*)
in 1945, is not merely a supplement to *MKT*, but an independent
study that has been the standard account of Babylonian mathematics in
English ever since. Still more extensive were the astronomical cuneiform
texts, of which the original study was complete by 1945, although it
continued to grow as more texts were discovered, and the entire work was
rewritten more than once to incorporate them. Again Anatole France was
right. *Astronomical Cuneiform Texts* (*ACT*) was finally
published in three volumes in 1955 by the Institute for Advanced Study,
and immediately marked a new age in the study of ancient astronomy.
Neugebauer had assembled in all about three hundred texts, most dating
from the last three centuries B.C. Through years of assiduous
calculation, he had dated and completed damaged texts and joined
fragments, and he set out all this material with full philological and
technical analysis of the underlying theory, computational procedure,
and astronomical application. Every reading and every page of the
manuscript had been gone over repeatedly by Sachs, whose name Neugebauer
always said really belonged on the publication. The first volume
contains ephemerides of lunar theory and eclipses and the procedure
texts for their computation, the second planetary ephemerides and
procedure texts, and the third the translations of the restored
ephemerides and photographs or hand copies of all the texts. In the
preface he expressed his respect to the shades of the scribes of
Enu¯ma-Anu-Enlil. "By their untiring efforts they built the
foundations for the understanding of the laws of nature which our
generation is applying so successfully to the destruction of
civilization. Yet they also provided hours of peace for those who
attempted to decode their lines of thought two thousand years later."

Next was Egyptian astronomy. There are two sorts, from
older, purely Egyptian sources, such as tomb ceilings and coffin lids,
and from later, Hellenistic sources, monumental zodiacs and papyri,
sometimes showing Greek or Babylonian influences. None of it is very
sophisticated, and Neugebauer was always at pains to lay the ghost of
profound Egyptian astronomical wisdom. During his last year in
Copenhagen he published with A. Volten in *QS* B 4 (1938) the
demotic Papyrus Carlsberg 9, of the second century A.D., on the 25-year
lunar cycle, and in 1940 there appeared with H. O. Lange an edition of
Papyrus Carlsberg 1, also of the second century, but preserving a far
older hieratic text with demotic translation and commentary on celestial
mythology and cosmology and the decans. Two years later he published the
known Hellenistic planetary texts and demotic horoscopes, but the really
extensive work was done together with Parker, especially after he came
to Brown and they began working on an edition of all Egyptian sources.
It was a task that took more than twenty years to complete, but at last
during 1960-69 the three volumes (in four) of *Egyptian Astronomical
Texts* (*EAT*) were published by Brown. Here it was at last, all
the Egyptian wisdom: decans, constellations, and star clocks of the
Middle and New Kingdoms, Hellenistic monumental zodiacs and papyri,
including all those previously published. And what did it amount to?
With particular perversity Neugebauer began the ten-page section on
Egypt in his later *History of Ancient Mathematical Astronomy* with
the provocative sentence, "Egypt has no place in a work on the history
of mathematical astronomy." Nevertheless, EAT is a fascinating and
beautiful work of scholarship, and through it the content of Egyptian
astronomy is now known and for the most part understood.

Hellenistic sources were far more heterogeneous. In addition
to Greek treatises in standard editions and the manuscript materials in
the *Catalogus Codicum Astrologorum Graecorum *(*CCAG*), there
were an unknown number of astronomical and astrological papyri.
Neugebauer began gathering whatever he could find--eventually many
papyrologists sent him anything with numbers on it--and publishing
occasional articles, something that continued for the rest of his life.
By luck, the chief librarian at Brown, Henry Bartlett Van Hoesen, was a
classicist and papyrologist--this was before university libraries were
turned over to bureaucrats with degrees in something called "library
science"--and together they began assembling an edition of all known
Greek horoscopes, both from literary sources and papyri. Their
publication, *Greek Horoscopes *(1959), remains the standard work
on its subject, unlikely to be superseded, and is also an excellent
introduction to the techniques of Greek astrology.

But
there was a yet larger project, in fact the largest of all. Ever since
the promise of the third volume of the *Vorlesungen*, Neugebauer
intended to publish a history of mathematical astronomy. The form and
extent of the work changed over time. Originally it was to have been on
antiquity alone, but later it was to continue through the Middle Ages
and Renaissance as far as Kepler. Neugebauer was indefatigable in taking
notes on sources with detailed analyses. Already in Copenhagen he began
analyzing the *Almagest*, since it was intended for the
*Vorlesungen*, and over the years his notes extended to most
published ancient texts, later Greek texts in manuscript, Indian,
Arabic, and medieval Latin sources, and indeed on to Copernicus, Tycho,
and Kepler. When, after the publication of *ACT*, he began to write
all of this up, Anatole France's dictum proved as true as ever, so in
the end the project was again restricted to antiquity. *A History of
Ancient Mathematical Astronomy *(*HAMA*) appeared in 1975 in
three volumes as the first publication in Springer's *Sources and
Studies in the History of Mathematics and Physical Sciences*, the
relation of which to *QS* should be obvious. Like *ACT*, it
had the immediate effect of establishing the history of ancient
astronomy on a new foundation, and since the astronomy of the Middle
Ages and Renaissance is in most respects a continuation of antiquity, it
really placed the astronomy of more than two thousand years on a new
foundation. Neugebauer arranged the work to cover the most important
things first, namely, an exposition of the *Almagest* and what can
be known of Ptolemy's more or less direct antecedents, Apollonius and
Hipparchus, and a systematic exposition of Babylonian astronomy going
beyond *ACT* both in the breadth of its subject and depth of
analysis, a section he was revising until the last minute before
publication. After the notorious ten-page "Book III" on Egypt, comes
early Greek astronomy through the first century B.C., concentrating upon
whatever can seriously be reconstructed of mathematical astronomy,
including Babylonian influences, from the surviving texts, unfortunately
all elementary, supplemented by papyri, inscriptions, and later sources.
The fifth part, on Roman and late antiquity, is devoted mainly to
planetary and lunar theory in papyri, astrological sources, and, with
more secure texts, to Ptolemy's works apart from the *Almagest* and
to later sources, principally Theon's edition of Ptolemy's *Handy
Tables*. Finally, the sixth part is an appendix on the chronology,
astronomy, and mathematics, including diophantine equations, useful to
the study of ancient mathematical astronomy, in which he set out
materials and methods assembled over many years both from diverse
sources and of his own invention.

For all its 1200 pages
of text and nearly 250 pages of figures *HAMA* is an economical
work; its subject is the technical content of ancient mathematical
astronomy, and cultural matters are kept to a minimum. I have mentioned
that at one time *HAMA* was to have covered a longer period. What
happened to the rest? Over the years, Neugebauer published parts of it
separately, sometimes in collaborative projects, and its parts are
substantial. In fact, he was late to come to the Middle Ages, his first
important publications being on the astronomy of Maimonides (1949) and a
commentary on Maimonides's *Sanctification of the New Moon*
translated by Solomon Gandz (1956), in earlier years a contributor to
*QS*. It is best to consider the paralipomena to *HAMA* by
subject: Byzantine sources based on Arabic in the astronomical
terminology of Vat. gr. 1058 (1960)--later identified by Pingree as
translations by Gregory Chioniades--and the commentary on the treatise
in Paris gr. 2425 (1969), the treatise itself later published by
Alexander Jones (1987); Arabic in the translations and analyses of two
works on the motion of the eighth sphere and the length of the year
attributed (at least one falsely, it now appears) to Tha¯bit ibn
Qurra (1962), and a large commentary on al-Khwrizm's tables (1962),
examining in particular their use of Indian methods; Indian astronomy
itself in his commentary to Pingree's edition and translation of the
Pañcasiddhntik of Varhamahra (1970); Renaissance astronomy with
N. M. Swerdlow in the analysis of Copernicus's *De
revolutionibus* (1984).

The last subject Neugebauer
took up was Ethiopic astronomy, chronology, and computus, that is, the
ecclesiastical calendar. He had long been intrigued by the primitive
astronomical section of the *Book of Enoch*, originally written in
Aramaic and surviving complete only in Ethiopic (Ge'ez), which appeared
to contain simplified Babylonian elements, and he also noticed from the
catalogue of Ethiopic manuscripts in Vienna, passages that suggested a
relation with Hellenistic astronomy and calendars. The question was,
what was this material about, and was there more of it? After learning
Ge'ez--the only Semitic language that is not perverse, he called it
(since it includes the vowels)--and studying many manuscripts, he found
that the astronomical content was slight, but the calendrical and
chronological information preserved from late antiquity and the Middle
Ages was very interesting indeed. Chronology had in fact always been his
third subject besides astronomy and mathematics; earlier he had
collaborated with W. Kendrick Pritchett on *The Calendars of
Athens* (1947) and analyzed the calendar of the *Très riches
heures* for Millard Meiss (1974). Now he again took up chronology
seriously. *Ethiopic Astronomy and Computus* (1979) is the summary
of what he found, organized by subject in alphabetical order. There is
much of interest here, but to name only the most significant result, he
was able to reconstruct the Alexandrian Christian calendar and its
origin from the Alexandrian Jewish calendar as of about the fourth
century, at least two hundred years prior to any other source for either
calendar. Thus, the Jewish calendar was derived by combining the 19-year
cycle using the Alexandrian year with the seven-day week, and was then
slightly modified by the Christians to prevent Easter from ever
coinciding with Passover, which would be a very great sin. Neugebauer
was amused to point out that the ecclesiastical calendar, considered by
church historians to be highly scientific and deeply complex, was
actually primitively simple. He then published separately the
astronomical chapters of the *Book of Enoch* (1981) in his own
translation and commentary, both rather different from the literature on
Enoch by Biblical scholars.

Considerably more complex
than either of these was *Abu Shaker's "Chronography"* (1988), an
analytical summary of a chronological and calendrical treatise
originally written in Arabic by a thirteenth-century Coptic Jacobite.
The treatise probably contains more technical information on
ecclesiastical calendars than any other source, including the curious
fact that the sequence of 29- and 30-day months is identical in the
Jewish and Islamic calendars, showing that the Islamic calendar was in
fact derived from the Jewish by suppressing intercalation, in accordance
with Muhammad's prohibition. Thus far, I know of no reaction to this
discovery. Finally, in *Chronography in Ethiopic Sources* (1989),
he assembled a great deal of chronographical information, that is,
intervals between epochs and dates of events, mostly in tabular form.

A few years after he came to this country, Neugebauer began to spend part of his time at the Institute for Advanced Study in Princeton, and from 1950 for the remainder of his life was a long-term member, a continuous association of forty years. Robert Oppenheimer, then director, had told him he would be welcome permanently any time he wished, but he preferred to remain at Brown and visit the Institute periodically. He always found the faculty and visitors at the Institute stimulating; following his retirement from Brown in 1969 and the death of his wife in 1970, he regularly spent several weeks there each fall and spring, and in the fall of 1984 he left Providence and moved permanently to the Institute.

Through these years, his
late eighties, Neugebauer's research continued to flourish at the
Institute. He completed and published his books on Ethiopic chronology,
wrote articles, and returned to an analysis of Kepler's *Astronomia
nova*. Then in the summer of 1988 he received a photograph of a scrap
of papyrus with numbers on it--hardly the first time--and immediately
went to work deciphering its content. What he found was truly wonderful:
a part of a column concerned with the length of the month from a
Babylonian lunar ephemeris, known principally from tablets of the second
century B.C., but here found in a Greek papyrus of the second or third
century A.D. Since a single column is of no use by itself, the papyrus
must once have contained several columns, if not a complete ephemeris
for computing either the first visibility of the moon or the possibility
of eclipses each month. This was the most important single piece of
evidence yet discovered for the *extensive* transmission of
Babylonian astronomy to the Greeks, and just as remarkable, for the
continuing use of sophisticated Babylonian methods for four hundred
years, even after Ptolemy wrote the *Almagest*, which, without the
papyrus, would have seemed unbelievable. As he so often remarked, we
know very little. The account of the papyrus was published in a memorial
volume for Abe Sachs (1988).

If there is a single,
central concern that runs through Neugebauer's work, it is an interest
in mathematical science itself, apart from any particular application in
any particular civilization, as an expression of sheer ingenuity in
abstract thinking, an ingenuity apparent among mathematicians and
astronomers whether their language was Akkadian, Greek, Sanskrit,
Arabic, or Latin, and whatever forms the mathematical sciences took in
their day. From this concern was born the detailed and technical
cross-cultural approach, in no way described adequately as the study of
"transmission," that he applied to the history of the exact sciences
from the ancient Near East to the European Renaissance. This can be
seen, is perhaps summarized, in his last paper, "From Assyriology to
Renaissance Art," published in the *Proceedings of the American
Philosophical Society* in 1989, which is on the history of a single
astronomical parameter, the mean length of the synodic month, from
cuneiform tablets, to the papyrus fragment just mentioned, to the Jewish
calendar, to an early fifteenth-century book of hours. And for this
concern with mathematical science itself, we must be grateful, for only
a true mathematician, which Neugebauer always remained, would recognize
and expend the effort necessary to reveal the extraordinary ingenuity,
creativity, and also continuity of Babylonian scribes, of Hipparchus and
Ptolemy, of Varhamahra and al-Khwrizm, of their descendants as far as
the Renaissance, and really up to the present day.

Neugebauer was the recipient of many honors. He received his
first honorary degree, the one he valued most, in 1938 from St. Andrews,
where he had a splendid time and played the only round of golf of his
life on the Old Course. Given the choice of degrees, he chose a doctor
of (both) laws since he had studied neither. Doctors of science followed
from Princeton in 1957 and Brown in 1971. He was a member of the Royal
Danish Academy, Royal Belgian Academy, Austrian Academy, British
Academy, Irish Academy, American Philosophical Society, American Academy
of Arts and Sciences (resigned 1959), National Academy of Sciences
(elected 1977), Académie des Inscriptions et Belles-lettres, and
other learned and professional societies. He received the American
Council of Learned Societies' Award for Outstanding American University
Professors in 1961, the Award for Distinguished Service to Mathematics
of the Mathematical Association of America for his founding and editing
of *Zbl* and *MR* in 1979, the American Philosophical
Society's highest award, the Franklin Medal, in 1987, and in the same
year Brown University's highest award, the Susan Culver Rosenberger
Medal of Honor. For various publications he received the John F. Lewis
Prize of the American Philosophical Society in 1952 for "The Babylonian
Method for the Computations of the Last Visibilities of Mercury," the
Heineman Prize in 1953 for *The Exact Sciences*, the Pfizer Prize
of the History of Science Society in 1975 for *HAMA*, and a second
Pfizer Prize in 1985. In 1986 he received the Balzan Prize of 250,000
Swiss francs, which he donated to the Institute for Advanced Study.

A bibliography of Neugebauer's nearly 300 publications
through his eightieth year by J. Sachs and G. J. Toomer, with his
assistance, was published in *Centaurus* (22[1979]:257-80). The
number of additions since then is not small. A more extended memoir of
his life and work, upon which this memoir is based, may be found in
the* Proceedings of the American Philosophical Society
*(137[1993]:139-65), and a shorter version similar to this one in the
*Journal for the History of Astronomy* (24[1993]:289-99). I am very
grateful to Asger Aaboe, Edward Kennedy, Edith Kirsch, David Pingree,
Janet Sachs, and Gerald Toomer for information and many helpful
comments.

RETORNO