The Mathematics PhD in the United
Historical Notes for the Mathematics
be alarmed by discrepancies between what is written below and what is written
in some of the MGP entries. The latter are being revised and so the problem is
only a temporary one. Some links are to draft entries.)
The UK has
an unbroken tradition of 800 years of university mathematics but for nearly all of that time the
creation of doctors played no part
in the process of preparing the next generation of mathematicians. The PhD is new to the UK,
compared to Germany or even
to the United States
(see NSF US Doctorates). It
appeared at the end of the First World War and it was not until after the
Second that a PhD became part of the usual preparation of a university
mathematician. There may be a chain of teachers back to Bradwardine
(d. 1349), to Newton (d. 1727), to Cayley
(d. 1895) but there is no
chain of doctors.
entrants into academic mathematics typically have PhDs and they may have some
post-doctoral research experience as well. See the advertisements for Academic Jobs on the London Mathematical Society’s
website. (The LMS (MacTutor)
is the UK’s
national association for Mathematics.)
past was very different but, because people and practices last, not so very
was supervising PhDs until the 1980s. His own PhD, awarded in 1931, was
supervised by H.
F. Baker MGP who graduated in 1888!
A first degree was Baker’s qualification for a distinguished career in pure
mathematics. T. M. F. Smith was President of the Royal
Statistical Society in 1991-3. His qualification was also a first degree,
awarded in 1959. In 1888 the first degree was absolutely standard, in 1959 it
was unusual, but not as unusual as Coxeter’s PhD in 1931. The production of
PhDs by means of PhDs is a recent phenomenon.
looking up British mathematicians in the Mathematics Genealogy
- Do not expect to
find many PhDs before 1940.
- Do not be
surprised to find supervisors (advisors) with only a first
- Do not
expect long lines of descent. The PhDs before 1940 were almost necessarily
‘first generation’ PhDs but for decades afterwards the system contained
many supervisors without PhDs.
- Do not
expect uniformity. The percentage of people entering academic
mathematics with PhDs went from 0 in 1920 to nearly 100% today but the movement
was not uniform over time, nor uniform across branches of mathematics. The
PhD as entry requirement came sooner to pure mathematics than to
The aim of these notes is to save the user
of MGP from jumping to too many
wrong conclusions. Wrong conclusions cannot be entirely avoided for there are
wrinkles enough in the system to confuse anybody. One wrinkle—of historic
interest only now—illustrates how qualifications may not be what they seem. Sylvester
completed his studies at St. John’s College,
Cambridge in 1837.
Not being a member of the Church of England (he was a Jew) Sylvester was
disqualified from graduating from Cambridge.
However, his work at St John’s
was recognised by Trinity College Dublin and he was awarded a BA (and an MA)
from that institution in 1841. He never
studied at Trinity Dublin. There are equally surreal PhD stories. In
was awarded a PhD by Cambridge
University. He had been a
student of Russell
but left in 1913 without a degree. In 1929 Ramsey
designated his supervisor and Wittgenstein presented as his thesis a work
written 10 years before, away from Russell, away from Cambridge and while
Ramsey, 14 years his junior, was still at school.
on the History of the PhD
The image of a PhD system has been present since 1850, there has been a PhD degree since
1920 and a functioning PhD system since around 1950. These notes describe how
these changes took place and give some basic information about British degrees
and practices. Today there are more than 100 universities in the UK; see here for links to maths departments and here and here for graduate programmes. The universities
frame their own degree regulations and these, beyond a basic similarity, are quite
varied. I have not written a survey of these institutions, nor a key to how
each institution has interpreted the letter D in the course of its
history. Further, the notes treat only the UK,
although, through the British Empire and
Commonwealth, British thought and practice about universities have influenced
developments all over the world. The
historian Hank Nelson discusses the PhD in Australia;
see also Ian D. Rae (2002) False Start for the PhD in Australia, Historical Records of Australian Science, 14(2) 129-141 abstract. In Canada where the influence of the United States
was much stronger the PhD came much earlier: for references see the notes
to M. L. Friedland The University of
Toronto: A History.
- The basic
reference for the origins of the PhD is Renate Simpson How the PhD came to Britain. A Century of Struggle
for Postgraduate Education, Society for Research into Higher
- Renate Simpson has just
published The Development of the PhD
Degree in Britain,
1917-1959 and Since: An Evolutionary and Statistical History in Higher
Press. This treats the first fifty years of the PhD system in Britain.
- The mathematicians of the
transition period are very well served by two databases, June Barrow-Green's BritMath and A E L
Women in the British Isles, 1878-1940. BritMath provides
detailed information on 750 mathematicians from the period 1860-1940. Mathematical
Women gives the qualifications of all the 2500 women who
graduated in mathematics between 1878 (when women were first admitted) and
1940. Of the BritMath mathematicians about 150 have PhDs.
- To illustrate the varieties
of personal experience I have made links to the biographies in John
O’Connor & Edmund Robertson’s MacTutor History of
Mathematics Archive. For additional colour there are links to the
title pages of books where authors can be seen displaying their
- 800 years of mathematics in
Oxford (the oldest university in the British Isles) are surveyed in Oxford Figures: 800 Years of the Mathematical Sciences edited
by John Fauvel, Raymond Flood and Robin Wilson, Oxford University Press
See also I. W. Busbridge Oxford Mathematics and
- For the Scottish university scene see Stuart Wallace “National
Identity and the Idea of the University in 19th-Century Scotland” Higher
Education Perspectives, 2, 2006.
- The standard reference work on the
universities of the Commonwealth is the Commonwealth Universities Yearbook published by the
Association of Commonwealth Universities London.
1800, as in 1600, there were two universities in England,
four in Scotland (MacTutor)
and none in Wales or Northern Ireland—Trinity College Dublin was the only
university in Ireland.
The national scientific academy, the Royal
Society of London (MacTutor)
dates from 1662. Election to its fellowship, indicated by the initials FRS, was (and is) a prized distinction.
In 1800 the English universities, Oxford and Cambridge, were nothing
like modern research universities and almost moribund compared to the two main
Scottish universities, Edinburgh
and Glasgow. In
the course of the 19th century the old universities were reformed and new ones
were created. Mathematical Women gives a list
of the universities awarding degrees in mathematics in the early 20th century;
today there are many more. It also gives the numbers of students graduating
(men as well as women) from each institution, which gives some idea of the
scale of university mathematics. Information on the number of academics in each
institution can be found from BritMath.
- The two English
universities in 1800, Oxford and Cambridge, are placed in a European context in L. W.
B. Brockliss “The European University in the Age of Revolution, 1789-1850”
ch. 2 of The History of the
University of Oxford, volume VI: Nineteenth-Century Oxford (eds. M. R. Brock & M. C. Curthoys), Clarendon
Press, Oxford 1997. (Amazon.)
degrees, BA and MA
the 19th century and for many years after the introduction of the PhD in
the 20th century the standard degree qualification of the university
mathematician was a BA or MA; see e.g. this title
page from Todhunter,
MGP or this from
most of the 19th century the only mathematics degrees were first
degrees—in today’s terms. At Oxford and Cambridge
the Bachelor of Arts (BA) was awarded on the basis of the student’s examination
performance. The Master of Arts (MA) involved no further academic work and was
essentially a formal recognition that the person actually was a BA! This is
still the case in Oxbridge; see here
for the current Cambridge
practice. The MA was required for full membership of the university and so
university teachers were invariably MAs. The existence of two degrees, awarded
at different dates for the same course of study, is a source of confusion and
explains some of the discrepancies in the dates given by different authorities.
the first degree was, and is still, called the MA.
The University of Cambridge
was the centre of mathematical teaching and research in Britain in the 19th century and the first half
of the 20th: “The study of Higher Mathematics in the British Empire is now
practically concentrated at Cambridge”
wrote the Times newspaper in 1906.
More than two-thirds of those listed in BritMath were students at Cambridge and
Cambridge figures dominate the MacTutor biographies. The
Cambridge Mathematical Tripos had great prestige and success in it was widely
regarded as the best qualification for an academic career in mathematics.
Indeed until the Second World War graduates from other universities would take
the Cambridge degree (or part of it) as a form of post-graduate study: Jeffreys
MGP and Davenport
are instances. Jeffreys, for example, had two first degrees; the later ‘higher’
degree is the one given on the MGP page.
new faculties of the old universities and the new universities created in the
19th and 20th centuries used the established terms Bachelor and Master for
their degrees, although the new institutions did not follow the ancient
universities’ practice of conferring an MA upon a BA. Some universities adopted
the name Bachelor of Science (BSc) for their degree in mathematics. The
post-graduate Master’s degree is a fairly recent development. It is rare in
pure mathematics but since the 1960s it has been widely offered in statistics.
- Andrew Warwick Masters of Theory: Cambridge
and the Rise of Mathematical Physics, Chicago University
Press, 2003. (Amazon.)
This contains a very thorough study of the mathematics tripos in the 19th
century. (The British mathematical physicists of the 19th century had
degrees in mathematics.) There is a useful review by Grattan-Guinness in
the SIAM News.
doctorates existing in 1800 were in Divinity,
Law, Medicine and Music. Dr
Wallis, the Savilian
professor of geometry at Oxford 1649-1703, was a doctor of divinity,
DD, because he was a theologian before he was a mathematician. These doctorates
were not like the modern PhD for the award recognised an established reputation
in a field, not the quality of a piece of work done at the beginning of a
career. In the course of the 19th century
doctorates in other subjects were created on the same pattern.
1882 Cambridge introduced the ScD, a doctorate
open to Cambridge
graduates who had produced a significant body of scientific work; a LittD for
scholarship in the humanities was also created. Other universities established
similar degrees. The British university is not generous with titles, for only a
minority of academics have the title “professor”, and perhaps the move was a
case of keeping up with titled foreigners. The award of the ScD did not mark
the beginning of a career, it recognised a successful career. Writing in the
20th century, Jeffreys
described the Cambridge ScD as “more or less equivalent to being proposed for
the Royal Society.” Jeffreys himself submitted work for the equivalent degree
at the University
of Durham and was awarded
its DSc. Many distinguished graduates took advantage of this doctoral
possibility, but not all; the title
page of Whitehead
Principia Mathematica shows one
author with an ScD, one without. Following the creation of the PhD, the term higher
doctorate came to be used for the ScD, or its equivalent elsewhere (most
often denoted by DSc). British universities still award higher research degrees
but today almost all of those receiving them have a PhD already. See here
for what Cambridge
expects of an ScD today and here
for an application form.
Halley, Wallis’s successor at Oxford,
was made a Doctor
of Civil Law in 1710. This was not in recognition of any distinction in law
but in recognition of Halley’s scholarship in producing an edition of
Apollonius’s Conics. Samuel Johnson, the poet and dictionary maker, was
a later recipient of an honorary doctorate from Oxford: “they have sent
me a degree of Doctor of Laws, with such praise in the Diploma as perhaps ought
to make me ashamed …” In the 19th century James
Clerk Maxwell (title
page) was an honorary doctor of law from Edinburgh University. Another LLD
J. Routh; Routh, unlike Maxwell, lived to collect a Cambridge ScD as well (title
page). Honorary doctorates are still conferred by British universities;
which particular title is chosen will vary with the university but the title is
- Simpson How the PhD came to Britain chapter 3.
- The Jeffreys quote is in David Howie (2002) Interpreting Probability: Controversies
and Developments in the Early Twentieth Century, New York, Cambridge University Press.
- The UKCGE
has recently surveyed Higher
Doctorate Awards in the UK.
story of the award of Johnson’s honorary doctorate in March 1775 is told
in Boswell’s Life
research degrees, fellowship dissertations, Smith’s Prize essays
19th century British university reformers looked to Germany for a model of the modern
university and the higher degree was an element in the German system. Higher
degrees to follow on from a bachelor’s degree and serve as a preparation for an
academic career started to appear in the 1860s. The DSc introduced by London University
in 1860 was a higher degree for advanced study
rather than research and was assessed by examination but the Edinburgh DSc had
an element of research. In 1885 the London
regulations were changed and the DSc became a genuine research degree; Charlotte
Women MGP was awarded a DSc in
1885, at the end of the examination era. In 1895 all the Scottish universities
adopted a five year research degree open to graduates from other universities.
In Cambridge there was no feeling
that a research degree was necessary for its own graduates but the university
created a Bachelor of Arts by Research for graduates from other universities;
this could be completed in one year. This was not a popular degree and BritMath lists only one person
with it, appropriately the unique Ramanujan.
The BA by Research was a curiosity but there were two other research
developments that had a lasting influence on mathematical life in Cambridge.
Cambridge men had two
opportunities to impress, the tripos examinations and the Smith’s Prize,
the latter a competition open to the best students. Originally the Smith’s
Prize was based on written examinations but from 1885 it was awarded for the
best essay. The prize became
the focus for post-graduate research as students might spend a year
working on their entry. In the early days, at least, there was no system of
supervision and so no declaration of ‘parentage.’ Sometimes there was a clear
supervisor, e.g. Barnes’s
supervision of Littlewood
MGP entered the lore of
mathematics. Smith’s Prize Winner did
not appear with MA after the person’s name but it was a very significant
qualification and the list of winners given by Barrow-Green is a
who’s who of Cambridge
mathematics. In 1936, when Fred
began his research career, his objective was the prize since “gaining either a
Smith’s or a Rayleigh was considered to be almost a guarantee of a post in some
university.” The Rayleigh Prize was
an additional prize first awarded in 1911. As well as the winners, other
creditable performers would be named; in 1935 altogether 9 names appeared.
After the Second World War, as the PhD system became established, submitting an
essay became a stage in the making of a PhD.
The other innovation was the fellowship dissertation.
In 1872 Trinity College introduced the dissertation into
its fellowship competition and some other colleges followed. See, for example,
the MacTutor entries for A.
N. Whitehead MGP and H.
W. Richmond MGP. Fellowship dissertations
continued into the PhD era—see P.
still exist. Both Cambridge
developments are illustrated in the careers of Louis
Mordell MGP from the 1910s and Alan
Turing from the 1930s.
Mordell’s essay for the Smith’s Prize was successful but his fellowship
dissertation was not. For Turing one essay was successful both as a Smith’s
Prize entry and as a fellowship dissertation. Subsequently Turing went to Princeton for a PhD MGP.
H. C. Whitehead MGP
, from Oxford, Turing was attracted to Princeton
by the opportunity of working with a particular supervisor, rather than by the
PhD qualification which was not required for a career in Britain.
was possible to go abroad for a PhD but there was little incentive to do so. In
the nineteenth century it became a tradition for British chemists to go to Germany to
obtain a doctorate but in other subjects it was unusual to go abroad. BritMath has two instances of
mathematicians with foreign PhDs from the era before the First World War: Grace
Chisholm Young Math
with a PhD from Göttingen and Harry
Bateman MGP with
a PhD from Johns Hopkins. Both were unusual cases. As a woman, Miss Chisholm
had very restricted opportunities in Britain. Bateman already had 60
publications and the most likely explanation for his wanting a PhD is that in America, where
he was working, an academic was expected to have one. At Johns Hopkins, thirty
years before, Sylvester MGP had
been in at the birth of the US
doctoral system but his career as a PhD supervisor ended when he returned to England.
For Sylvester’s activity in America
see Parshall & Rowe “American Mathematics comes of Age: 1875-1900” in AMS
History of Mathematics, Volume 3.
- For the early research degrees see Simpson
chapters 2 & 3.
- The Cambridge research
degree was significant in the history of the Cavendish (physics)
laboratory. See ch. 4 of Dong-Won Kim (2002) Leadership and Creativity: A History of the Cavendish Laboratory,
1871-1919, Kluwer. See Google
Book Search for an extract.
- For the Smith’s prize see June
Barrow-Green (1999) “A Corrective to the Spirit of too Exclusively Pure
Mathematics”: Robert Smith (1689-1768) and his Prizes at Cambridge University,
Annals of Science, 56, 271-316. Appendix 1 lists the
winners from 1885 to 1940 with the ‘grades’ their essays received. There
is no information about unsuccessful entries..
- Barrow-Green describes the fellowship dissertation
system but there does not seem to be any list of who wrote what.
1917 British universities resolved to create a PhD degree. However, deciding to
create a degree is not the same as deciding that the degree should matter.
There was no resolution to create a system in which the PhD would be an essential
part of the preparation of the university academic. The system evolved without
anybody planning it.
The PhD degree
the beginning of the 20th century the case for a PhD type degree had been made
and won—at least outside Cambridge (and Oxford). In 1917 representatives of the universities
met and agreed that they would establish a PhD degree. The key resolution said
For the better promotion of
research in this country, and for the encouragement of advanced work by
“graduate” students from abroad, a degree or title of Doctor should be
instituted, attainable after a period of not less than two years whole-time
work devoted to advanced study or research …
universities acted together under strong political pressure. Imperial
considerations were important. There had long been anxiety that students from
the dominions would go to Germany
or the United States
and be weaned away from the mother country.
Oxford was the first
university to institute such a degree, although its choice of title, DPhil, was
idiosyncratic. The first Oxford DPhil in mathematics was awarded in 1921. The
first Cambridge PhD in mathematics was awarded in 1924 to an Australian Thomas Cherry MGP.
concept of supervision had to evolve. C.
R. Rao MGP
described his experience as a student in Cambridge
in the 1940s and later as a supervisor in India
and the US.
“I asked Fisher [Rao’s supervisor] to suggest a research problem for my Ph.D.
thesis. He said the problem must be mine and that he would only advise me if
and when I encountered difficulties. This was good advice. I used to say the
same to my Ph.D. students without success. There were only 2 cases (out of 50),
where the students chose their own problems.”
The practice in the UK,
until recently at least, has been for a student to have a single supervisor.
the supervised dissertation, there is another route to the PhD, the staff PhD. A member of staff at a
university may obtain a PhD by submitting published work. There is usually no supervisor and the staff PhD is more
like a baby ScD than a regular PhD. In 1935 F N
was appointed as an assistant lecturer at University College London; in
1938 she was awarded a PD. “I took it by sending in 4 papers I had already
published.” This route to a PhD still exists; see here for a
typical set of regulations.
H. E. Daniels RSS president 1974-5 MGP was
awarded an external PhD from the University of Edinburgh;
an external student does not attend the university. Daniels was ineligible for
a staff PhD because he was not working at a university and he was not old
enough for an ScD. “Aitken was nominally my supervisor but hadn’t the faintest
idea of what I was doing.” Daniels did not really need a supervisor, as he was
already a well-established researcher.
the general issue of the PhD, David recalled, “You did not need [a doctorate]
or you did not need it at that time anyway.” She also recalled that Karl
Pearson, for whom she had worked, did not think it “a good thing.”
Looking back, Daniels did not seem to think it a good thing either. “[Research]
is about having ideas. What happens with the run-of-the-mill Ph.D. student is
that you lay a trail of clues for him, which he follows, you hope, and in the
end he produces his thesis. Well, it seems to me that this is self-defeating.”
reminiscences are from statisticians but the experiences and attitudes they
describe have a wider relevance.
has been continuing debate about the character of the PhD and there has been a
movement away from the traditional pattern which involved only research to one
involving advanced courses as well. The EPSRC (the state science funding
body) and its predecessors have been important voices in these debates. The PhD
experience is much more variable than the undergraduate experience. Supervision
has ranged from “Hello, go away and come back when you are finished!” to very
close supervision on a topic worked out in detail by the supervisor. The EPSRC
(and its predecessors) have tried to codify and regulate the process. See the guidelines
for its current model of how student and supervisor should work together. This
document breathes anxiety that the student will not submit the dissertation on
time and late completion has been an issue for decades.
- The ET Interview:
Professor C.R. Rao: Interviewed
by Anil K. Bera, Econometric Theory, 19, (2) (2003),
- N. M. Laird, A Conversation
with F N David, Statistical Science 4, (3) (1989), 235-246. JSTOR
- P. Whittle, A Conversation with Henry Daniels, Statistical
(3), (1993) 342-353. JSTOR Project
The PhD system
universities have never been obliged
to recruit only PhDs as lecturers but increasingly they have come to do so. The
state played a role in this. The Department of Scientific and Industrial
Research (DSIR), the body founded during the First World War to
support scientific research, provided scholarships, though only in very small
numbers. The number of scholarships was increased after the Second World War.
The Engineering and Physical Sciences Research Council (EPSRC), the current version
of the DSIR continues to do so.
Simpson’s Development charts the first four
decades of the PhD system. She finds (p. 321) that 23,505 students were
admitted to study for the PhD in all subjects at UK universities in the period
1917-59. Of these admissions 1230 were to mathematics. The top four
universities were Cambridge with 568 (46.3% of
the total), Imperial College with 195 (15.9%), Oxford with 185 (15.0%) and University
College London with 131 (10.7%). Over the decades the numbers grew although the
Second World War stalled the growth: the admissions figures by decade for the
six largest institutions were 96 (1920s), 207 (1930s), 306 (1940s) and 611
(1950s). Simpson does not report employment destinations.
is information on the growing importance of the PhD as a qualification for an
academic job in the research conducted for the inquiry into higher education in
which resulted in the Robbins report. One of the volumes reported on Teachers in Higher Education.
- This found that, in 1961-2, 72% of university teachers in science (the category
covering mathematics) had a doctorate of some kind, including a higher
doctorate. In the humanities the figure was 29%.
- It also found that 45% of
those recruited in 1959-61 had
a doctorate. The authors comment, “the proportion of teachers with higher
degrees is lower among those who took their first degree within the last
ten years than among older staff, since many of the more recent recruits
are of course still working for a higher degree.” The comment reflects the
practice of hiring people who had not yet completed their PhD and also the
possibility of hiring on condition that the employee starts a PhD. It also
reflects the absence of higher doctorates amongst the recruits.
In 1989 the Science and Engineering Research Council
(successor to the DSIR and predecessor of EPSRC) set up a
committee to review mathematics education. By then it had become axiomatic that
the university mathematician has a PhD. The Kingman report concluded that the
current supply of mathematics PhDs is “dangerously inadequate.” The report
contains some interesting data. It gave the number of full time academic staff
in university mathematics departments as 1500 with 20 post-doctoral fellows and
120 research assistants. It estimated that in 1990 around 115 PhD students
completed their degree. It also estimated that to hold current staff levels
constant would require recruitment at the level of 80 posts per year, 30 each
in pure and applied mathematics and 20 in statistics and operational research.
There is more recent information in the 2004
review of UK
research in mathematics which was undertaken by an international team for the
almost all of its 800 years the university system was a virtually closed system
in which the academics were recruited from the ranks of local graduates. De
Moivre, the seventeenth century refugee from Catholic France, had no entry
into the universities, while refugees from Nazi Germany in the 1930s,
especially junior people such as H. O.
Neumann MGP and
Rado MGP often
entered the system by taking a second PhD; see Siegmund-Schultze
however, to meet the shortfall in locally produced PhDs universities have
increasingly recruited foreign mathematicians and university mathematics, like
the entire university system, has become very open.
References and further
- Renate Simpson The
Development of the PhD Degree in Britain, 1917-1959 and Since:
An Evolutionary and Statistical History in Higher Education, Mellen
- Higher Education:
Report of the Committee appointed by the Prime Minister under the
chairmanship of Lord Robbins, 1961-63 Committee on Higher Education:
Appendix 3, Teachers in Higher Education. Cmnd. 2154. London, Her Majesty’s Stationery Office.
- Mathematics: Strategy for the
Future, Report of the
Mathematics Strategy Review Panel chaired by John Kingman, Science and Engineering Research Council.1991.
Mathematicians Fleeing from Nazi Germany. Individual Fates and
Global Impact, Princeton
- The International Review of UK
Research in Mathematics: A Review undertaken by the EPSRC and the Council for the Mathematical
- Where will the next generation of UK
mathematicians will come from? A meeting with this theme took place on 18-19 March
2005 in Manchester.
The emphasis was on the teaching of mathematics in secondary schools but
there are links relevant to the PhD crisis.
- Some of the analysis in A.
Oswald & S. Machin “UK Economics and the Future Supply of Academic
Journal, 110, (2000),
version applies to mathematics.
- The PhD is itself the subject of research: see e.g.,
this (Australian) paper
‘It’s a PhD not a Nobel Prize’ by Mullins and Kiley on the examining of
PhD theses and the University of Exeter bibliography
for doctoral supervisors.
- For a
survey of current thinking on the PhD in Britain
see C. Park “New Variant PhD: The Changing Nature of the Doctorate in the UK,” Journal of Higher Education Policy and
Management, 27, (2005),
- The range of UK university qualifications is described
Framework for Higher Education Qualifications in England, Wales and
Northern Ireland and in The
Framework for Higher Education Institutions in Scotland.
- The Higher Education
Statistics Agency HESA
provides statistics on higher education in the UK.
UK GRAD Programme has lots of miscellaneous information on the PhD
scene in the UK
- The 2000 report on Graduate Education
Reform in Europe, Asia and the Americas has a section on the UK.
- Wikipedia has
several useful entries. The following are worth consulting, although they
contain some slips: Master
of Arts (Oxbridge and Dublin), Doctorate, Doctor of Philosophy, British
- BSHM Links to Web
Sites on the History of Mathematics.
John Aldrich, University of Southampton,
Southampton, UK. (home) February 2006. Latest
changes November 2010
I am grateful to June Barrow-Green, A E L Davis, Anthony
Edwards, Karen Parshall, Renate Simpson, Fred Smith and Brian Stewart for information,
corrections and suggestions.