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A history of the study of mathematics at Cambridge online

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was made in 1854 to assist candidates in judging of the relative
difficulty of the questions asked, by informing them of the
marks assigned to each question. The marks for the book-work
and rider of each question were printed on a little slip of
paper which was given to the candidates at the same time as
the examination paper 1 .

It is not unusual to hear the remark that the scheme of
the tripos from 1839 to 1873 was framed so as to discourage
those who wished to apply mathematics to physical questions ;
but that opinion is, I think, framed on a misunderstanding.
The university insisted that her mathematical graduates should
have a thorough knowledge of all the elementary subjects, and
left to them the particular sciences to which they might (if
they felt inclined) apply it. It only needs a glance at the
tripos lists to see that this course was in no way prejudicial to
any branch of mathematical science. Indeed I believe that if
the senate had not been so anxious to define exactly what
might and what might not be asked, but had allowed the
subjects of the examination to grow by the gradual introduction
of questions from the more recent applications of mathematics,
there is no reason why the regulations of 1841 or of 1848
should not meet all the requirements of the present time.
Under those regulations the Cambridge graduate who devoted
himself to mathematical research possessed a great advantage

1 I mention the fact rather because these things are rapidly forgotten
than because it is of any intrinsic value. I possess a complete set of
slips which came to me from Dr Todhunter.


over his continental colleagues in the wider range of his
general mathematical knowledge. That advantage has recently
been abandoned, but on the other hand a man on taking his
degree is now a specialist in some small part of one branch of
the subject. Time alone can shew which is the better system.
I myself have no doubt that it is in general wiser to defer
specialization until after a man has taken his first degree, but
the drift of recent legislation has been in the other direction.

The curious origin of the term tripos has been repeatedly
told, and an account of it may fitly close this chapter. There
were three principal occasions on which questionists were
admitted to the degree of bachelor. The first of these was the
comitia prior a held on Ash -Wednesday for the best men in
the year. The next was the comitia posteriora which was held
a few weeks later, and at which any student who had dis-
tinguished himself in the quadragesimal exercises subsequent
to Ash- Wednesday had his seniority reserved to him. Lastly,
there was the comitia minora, or the general bachelor's com-
mencement, for students who had in no special way dis-
tinguished themselves. In the fifteenth century an important
part in the ceremony on each of these occasions was taken by
a certain "ould bachilour," who as the representative of the
university had to sit upon a three-legged stool or tripos "before
Mr Proctours" and test the abilities of the would-be graduates
by arguing some question with the "eldest son," who was the
senior and representative of them. To assist the latter in
what was generally an unequal contest, his "father," that is,
the officer of his college who was to present him for his degree,
was allowed to come to his assistance.

The ceremony was a serious one, and had a certain religious
character. It took place in Great St Mary's Church, and
marked the admission of the student to a position with new
responsibilities, while the season of Lent 1 was chosen with a
view to bring this into prominence. The puritan party ob-

1 Grave scandal was caused at Oxford by a custom of giving suppers
after the quadragesimal exercises for the day were over, and this even in


jected to the observance of such ecclesiastical ceremonies, and
in the course of the sixteenth century they converted the
proceedings into a sort of licensed buffoonery. The part
played by the questionist became purely formal. A serious
debate still sometimes took place between the father of the
senior questionist and a regent master, who represented the
university; but the discussion always began with an intro-
ductory speech by the bachelor, who came to be called Mr
Tripos just as we speak of a judge as the bench or of a rower
as an oar. Ultimately the tripos was allowed to say pretty
much what he pleased, so long as it was not dull and was
scandalous. The speeches he delivered or the verses he
recited were generally preserved by the registrary, and were
known as the tripos verses : originally they referred to the
subjects of the disputations then propounded. The earliest
copies now extant are those for 1575.

The university officials, to whom the personal criticisms
in which the tripos indulged were by no means pleasing,
repeatedly exhorted him to remember "while exercising his
privilege of humour, to be modest withal." In 1740, says Mr
Mullinger 1 , u the authorities after condemning the excessive
license of the tripos announced that the comitia at Lent would
in future be conducted in the senate-house ; and all members
of the university, of whatever order or degree, were forbidden
to assail or mock the disputants with scurrilous jokes or un-
seemly witticisms. About the year 1747-8, the moderators
initiated the practice of printing the honour lists on the back
of the sheets containing the tripos-verses, and after the year
1755 this became the invariable practice. By virtue of this

" the holy season of Lent." Bachelors detected in so acting were liable
to immediate expulsion: but as a concession to juvenile weakness the
sophister was allowed to give an entertainment in the previous term
provided the expenditure did not exceed sixteen-pence. See vol. n.
p. 453 of Munimenta academica, by Henry Anstey, in the Kolls Series,
London, 1868.

1 Mullinger's Cambridge, pp. 175, 176.


purely arbitrary connection these lists themselves became
known as the tripos; and eventually the examination itself,
of which they represented the results, also became known by
the same designation."

A somewhat similar position at the comitia majora (or
congregation held on Commencement-day) to that of the tripos
on Ash- Wednesday was filled by the prevaricator or varier,
who was the junior M.A. regent of the previous year, or his
proxy. But he never indulged in as much license as the " ould
bachilor," and no determined effort to turn that ceremony into
a farce was ever made.

The tripos and prevaricator ceased to recite their speeches
about 1750, but the issue of the verses by the former has never
been discontinued. At present these verses are published on
the last day of the Michaelmas term, and consist of four odes,
usually in Latin but occasionally in Greek, in which current
events or topics of conversation in the university are treated
satirically or seriously. They are written for the two proctors
and two moderators by undergraduates or commencing bachelors,
who are supposed each to receive a pair of white kid gloves in
recognition of their labours. Since 1859 the two sets, corre-
sponding to the two days of admission, have been printed
together on the first three pages of a sheet of foolscap paper.
On the fourth page the order of seniority of the honour men
of the year is printed crosswise in columns, the sheet being
folded into four parts, so that all the names can be read with-
out opening the page to more than half its extent.

Thus gradually the word tripos changed its meaning "from
a thing of wood to a man, from a man to a speech, from a
speech to two sets of verses, from verses to a sheet of coarse
foolscap paper, from a paper to a list of names, and from a list
of names to a system of examination 1 ."

1 Wordsworth, p. 21.



SECTION 1. The mediaeval university.
SECTION 2. The university from 1525 to 1858.

MY object in writing the foregoing pages was to trace the
development of the study of mathematics at Cambridge from
the foundation of the university to the year 1858. Some
knowledge of the history, constitution, and organization of the
university is however (in my opinion) essential to any who
would understand the manner in which mathematics was intro-
duced into the university curriculum and the way in which it
developed. To a sketch of these subjects this chapter is accord-
ingly devoted. I have made it somewhat fuller than is abso-
lutely essential for my purpose, in the hope that I may enable
the reader to realize the life of a student in former times.

1 The materials for this chapter are mainly taken from the University
of Cambridge by J. Bass Mullinger, Cambridge, (vol. i. to 1535), 1873,
(vol. n. to 1625), 1884; the Annals of Cambridge by C. H. Cooper, 5
vols., Cambridge, 1842 1852; Observations on the statutes by George
Peacock, London, 1841 ; the collection of Documents relating to the uni-
versity and colleges of Cambridge, issued by the Eoyal Commissioners
in 1852; and lastly the Scholae academicae by C. Wordsworth, Cambridge,
1877. For the corresponding references to Oxford I am mainly indebted
to the Munimenta academica, by H. Anstey, Kolls Series, London, 1868,
and to a History of Oxford to 1530, by H. C. M. Lyte, London, 1886.
The works of Peacock, Mullinger and Lyte contain references to all the
more important facts.


The history of the university is divisible into three toler-
ably distinct periods. The first commences with its founda-
tion towards the close of the twelfth century, and terminates
with the royal injunctions of 1535. This was followed by some
thirty or forty years of confusion, but about the end of the
sixteenth century the university assumed that form and
character which continued with but few material changes to-
the middle of this century. Most of its members would, I
think agree that a fresh departure in its development then
began, the outcome of which cannot yet be predicted.

The mediaeval university.

Cambridge, like all the early mediaeval universities, arose
from a voluntary association of teachers who were exercising
their profession in the same place. Of the exact details of its
early history we know nothing ; but the general outlines are
as follows.

A university of the twelfth or thirteenth century usually
began in connection with some monastic or cathedral school in
the vicinity of which lecturers had settled. As soon as a few
teachers and scholars had thus taken up their permanent
residence in the neighbourhood they organized themselves (but
in all cases quite distinct from the monastic schools) as a sort
of trades union or guild, partly to protect themselves from the
extortionate charges of tradesmen and landlords, partly be-
cause all men with a common pursuit were then accustomed to
form such unions. Such an association was known as a uni-
versitas magistrorum et scholarium. A universitas scholarium,
if successful in attracting students and acquiring permanency,
always sought special legal privileges, such as the right of
fixing the price of provisions and the power of trying legal
actions in which their members were concerned. These pri-
vileges generally led to a recognition, explicit or implicit, of
the guild by the crown as a studium generate, i.e. a body with
power to grant degrees which conferred a right of teaching


anywhere within the kingdom. The university was frequently
incorporated at or about the same time. It was still only a
local corporation, but it entered on its third and final stage of
development when it obtained recognition, explicit or implicit,
from the pope (or emperor). This gave its degrees currency
throughout Christendom, and it thenceforward became a re-
cognized member of a body of closely connected corporations.
Such is the general outline of the history of a mediaeval
university. In later times the title of university was confined
to degree-granting bodies, and any other place of higher
education was termed a studium generale.

The records and charters of the university of Cambridge
were burnt in 1261, in 1322, and again in 1381. We must
therefore refer to the analogy of other universities, and parti-
cularly of Paris (which was the typical mediaeval university,
and was taken as a model by those who first organized Oxford
and Cambridge), to obtain an idea of its early history, filling in
the dates of the various steps in its development by means of
allusions thereto in trustworthy authorities.

It seems almost certain that there was no university at
Cambridge in 1112, when the canons of St Giles's moved from
the church of that name to their new priory at Barnwell. It is
also known that the university existed in its first stage, (i.e.
as a self -constituted and self-governing community), in the year
1209, since several students from Oxford migrated in that year
to the university of Cambridge. At some time before the
latter date, and probably subsequent to 1112, one or more
grammar-schools were opened in Cambridge, either under the
care of the monks at Barnwell priory, or of the conventual
church at Ely, or possibly of both authorities. The connection
between these schools and the beginning of the university has
always appeared to me to be a singularly interesting historical
problem, though it has hitherto attracted but little attention.

Most critics consider that the university of Paris arose from
the audiences that came together to hear William of Cham-
peaux lecture on logic in 1109, or his pupil Abelard on


theology some thirty years later; and that these lectures were
delivered with the sanction of the chapter of Ste. Genevieve.
It is generally believed that the university of Oxford arose in
a similar way from the students who were attracted there to
hear the lectures of Robert Pullen on theology in 1133, and of
Vacarius on civil law in 1149; and that as the monks of
St Friedeswyde's were probably French, the lectures were given
in their house and by their invitation. Paris and Oxford were
important towns, and not unnaturally became universities.
Cambridge, however, was a small village. In 1086 it only con-
tained 373 hovels grouped round St Peter's church, while
about half a mile off were a few cottages clustered round
St Benet's Church; and in 1174, after being burnt to the
ground, it was only partially rebuilt. It is thus at first sight
difficult to see why lecturers should have settled there, and
the analogies of other universities throw but little light on it.
I suspect the explanation is that students were attracted in
the first instance by the great fair held once every year at
Stourbridge, which is an open common lying within the boun-
daries of the borough.

The village of Cambridge was situated at the end of a pro-
montory which projected into the fens, and commanded the
northernmost ford by which the eastern counties could commu-
nicate with the midlands. Away to the Wash stretched a vast
succession of watery fens, across which a stranger could scarcely
hope to pass in safety save at the end of a dry summer or after
a long frost. The position was thus an important one, both
strategically and commercially ; and the annual fair at Stour-
bridge became one of the two great centres of trade for northern
and central Europe 1 . Thither the merchants from Germany and
the Low countries came by boat from Bishop's Lynn up the Ouse
and Cam to exchange their goods for the wool and horses from
the western counties and midland shires; and miles of tents

1 The other great mediaeval fairs were Leipzig and Nijnii Novgorod.
Stourbridge, though now a mere shadow of its former self and yearly
diminishing in importance, is still one of the largest fairs in England.


and booths were put up in streets according to elaborate rules,
which at a later time were regulated by act of parliament.

Thus for a month in the year many thousands of travellers
were brought to Cambridge, and led, I conjecture, to the estab-
lishment of a uriiversitas scholarium, for which the monks and
more advanced students of the grammar-schools supplied part
of the audiences. It is noticeable that until a few years ago
doctors were required to wear scarlet when the fair 1 was
proclaimed thus putting that ceremony on a level for univer-
sity purposes with the five or six great feasts of the church.
Even as late as Newton's time it was apparently an important
mart for scientific books and instruments (see pp. 52, 53).

Whatever was the cause of its location at Cambridge the
university existed in 1209; and from an allusion 2 in some
legal proceedings in 1225 to the chancellor of the university,
and from the fact that when in 1229 Henry III. invited
French students to leave Paris and settle in England the
majority preferred to come to Cambridge, it is clear that it was
then an organized and well-known university.

In 1231 Henry III. gave to the university jurisdiction over
certain classes of townsmen; in 1251 he extended it so as to
give exclusive legal jurisdiction in all matters concerning
scholars, and finally confirmed all its rights in 1260. These
powers were granted by letters and enactments, and the
first charter of which we now know anything was that given
by Edward I. in 1291. It was, however, the custom at
both universities to solicit a renewal of their privileges at the
beginning of each reign (an opportunity of which they often
took advantage to get them extended), and it is possible that the
dates here given may be those of the renewals of the original
charters which, as stated above, were burnt in the fourteenth

1 A collection of references to the fair will be found in pp. 153 165
of the Life of Ambrose Bomvicke edited by J. E. B. Mayor, Cambridge,

2 Record office, Coram Eege Rolls, Hen. III. nos. 20 and 21.


The university was recognized by letters from the pope in
1233, but in 1318 John xxn. gave it all the rights which were
or could be enjoyed by any university in Christendom. Under
these sweeping terms it obtained, as settled in the Barn well
process 1430, exemption from the jurisdiction both of the
bishop of Ely and the archbishop of Canterbury. A survival
of this papal recognition, which involved a right of migration,
still exists in the customary admission of a graduate of Oxford
or Cambridge to an ad eundem degree at the other university.
The singular privilege of conferring degrees possessed by the
archbishop of Canterbury is also derived from the position of
the pope as the head of every university in Christendom.

It may be interesting if I add the corresponding dates for
Paris and Oxford, since the mediaeval histories of the three
universities are closely connected. The university of Paris
was formed at some time between 1100 and 1169; legal
privileges were conferred by the state in 1200; and its degrees
were recognized as conferring a right to teach throughout
Christendom in 1283. The university of Oxford was formed
at some time between 1149 and 1180; legal privileges were
conferred by the state in 1214; and its degrees were recognized
by the pope in 1296. The university of Cambridge, as I
have just explained, was formed at some time between 1112 and
1209; legal privileges were conferred by the state in 1231;
and its degrees were recognized by the pope in 1318. Two
other mediaeval universities rival Paris in antiquity: these
were the legal school at Bologna and the medical school at
Salerno, but at these the education was technical rather than

The characteristic feature of these five mediaeval univer-
sities Paris, Bologna, Salerno, Oxford, and Cambridge 1 is
that they thus grew into the form they ultimately took. They
were recognized by the state and church, but they were not,
like the later universities, created by a definite act or charter.

A mediaeval university was at first formed of a collection

1 They are probably the five oldest universities in Europe.
B. 15


of teachers and pupils with hardly any pretence of organization.
So loose was the connection of its members with one another
that there was a constant series of secessions. These secessions
play a much smaller part in the history of Oxford and Cam-
bridge than in that of the continental universities, as after
1334 the English universities imposed an oath on their
graduates never to teach as in a university anywhere in
England except at Cambridge and Oxford, "nor to acknow-
ledge as legitimate regents those who had commenced in any
other town in England 1 ." It must be remembered that the two
universities were very closely connected, and that till 1535 a
certain proportion of the students divided their time between
the two.

It is probable that at the beginning of the thirteenth
century there was no code of rules at Cambridge for the
guidance of its members. The ancient statutes are undated,
but there is every reason to believe that the constitution of the
university in the fourteenth century, which is described in the
following pages, only differed in details from that which was
in practical force during most of the preceding century.

The governing body of the university was termed the
regent-house, and it was at first strictly confined to those
graduates who were actively engaged in teaching. In the
twelfth and thirteenth centuries the final degree of master
was merely a license to teach : no one sought it who did not
intend to use it for that purpose and to reside 2 , and only those
who had a natural aptitude for such work were likely to enter

1 Peacock, Appendix A, xxviii; Munimenta academica, 375. At Oxford
until 1827 every newly-created master had also to swear that he would
never consent to the "reconciliation of Henry Symeon." Henry Symeon
is said to have been a master of arts who obtained an office in the reign
of King John (1199 1216) by representing that he was only a bachelor.
For this offence the implacable university held him up for over 600 years
to the obloquy of every successive generation. Peacock, A., xxiii ;
Munimenta academica, 432, 473 ; Lyte, 214.

2 A survival of this idea exists in the technical description of a doctor
of divinity at Oxford and Cambridge as sacrae theologiae professor.


so ill-paid a profession. It was thus obtainable by any student
who had gone through the recognized course of study and
shewn he was of good moral character. Outsiders were also
admitted, but not as a matter of course. By the beginning of
the fourteenth century students began to seek for degrees
without any intention of teaching; and in 1426 the university
of Paris took on itself to refuse a degree to a student a
Slavonian, one Paul Nicolas who had performed the necessary
exercises in a very indifferent manner. He took legal pro-
ceedings against the university to compel them to grant the
degree, but their right to withhold it was established 1 , and
other universities then assumed a similar power. He was, I
believe, the first student who was " plucked."

The degree gave the right to teach, but after about 1400
the university only granted it on condition that the new
master should lecture in the schools of the university for at
least one year. Many of those who had ceased to do so were
however still resident and engaged in the work of the univer-
sity; and in course of time heads of hostels, various executive
officers, and finally all graduates who had ceased to teach,
formed a second assembly called the non-regent house, whose
consent was necessary to the more important graces. The two
houses taken together formed the senate of the university.

The constitution was thus rendered singularly complex.
Some matters were decided by the regents alone, others by the
concurrence of both houses voting separately, others by both
houses sitting and voting together, and lastly, others by both
houses sitting together but with the right of voting confined
to the regents 2 . Finally, every measure had to be approved
by the chancellor.

The executive of the non-regent house was vested in the
two scrutators 3 . But the proctors (sometimes also called
rectors) were the two great officers of the university : they

1 See Bulajus, vol. v. p. 377.

2 Statuta antiqua, 2, 21, 50, 71, 163.

3 Peacock, 21 et seq.


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