“Fasting nights have a shadow of religion without any substance. ’Tis only supping more pleasantly out of the public hall. And this does great mischief by sending young students to find suppers abroad, where they get into company and grow debauched. Whether would it not be better to license undergraduates to sup together in such places as the Dean shall appoint, with a Monitor to note the names of the absent?
[251]
]“All these lectures to consist in extemporary explications of books in such an easy, short, and clear manner as may be most profitable to the auditors. And if any Lecturer or other person shall compose any treatise which shall be preferred and used by the major part of the Mathematic or Philosophic Lecturers, the University shall give the author either £20, or if those Lecturers request it, £30, £40 or £50, out of their Common Chest.
“Commissioners to be appointed for some years to set on foot, inspect, and amend the institution.
“No oaths of office to be imposed on the Lecturers. I do not know a greater abuse of religion than that sort of oaths: they being harder to be kept than the Jewish Law, so that yearly absolutions have been instituted. The papists, who believe such absolutions, might be excused for instituting such oaths, but we have no such doctrine, and yet continue their practices. Admonitions and pecuniary mulcts for neglect of duty are less cruel punishments than the consequence of perjury, and may be as effectual.”
[33] Camb. Univ. Library, Newton MSS. section viii, No. 5. Add. 4005/6, A.
[252]
]CHAPTER XV.
THE HISTORY OF THE MATHEMATICAL TRIPOS.
The Mathematical Tripos has played so prominent a part in the history of education at Cambridge and of mathematics in England, that a sketch of its development[34] may be interesting to general readers.
So far as mathematics is concerned the history of the University before Newton may be summed up very briefly. The University was founded towards the end of the twelfth century. Throughout the middle ages, the instruction given to students was organized on lines similar to those current at Paris and Oxford, and to qualify for a degree it was necessary to perform various exercises, and especially to keep a number of acts or to oppose acts kept by other students. An act consisted in effect of a [253] ]debate in Latin, thrown, at any rate in later times, into syllogistic form. It was commenced by one student, the respondent, stating some proposition, often propounded in the form of a thesis, which was attacked by an opponent or opponents, the discussion being controlled by a senior graduate. The teaching was largely in the hands of young graduates—every master of arts being compelled to reside and teach for at least one year—though no doubt colleges and private hostels supplemented this instruction in the case of their own students.
The reformation in England was largely the work of Cambridge divines, and in the University the renaissance was warmly welcomed. In spite of the disorder and confusion of the Tudor period, new studies and a system of professional instruction were introduced. The earliest lectureships created by the University seem to have been one in Latin established in or before 1492 and one in mathematics established in or before 1501: they mark the beginning of the system of teaching by experts which has superseded the medieval system of compulsory teaching by all regent masters. The fact that one of these lectureships was in mathematics shows that as early as 1500 the subject was regarded as important. Tunstall, subsequently the most eminent English arithmetician of his time, migrated in 1496 from Oxford to Cambridge, and [254] ]most of the subsequent English mathematicians of the Tudor period were at Cambridge; of these I may mention Record (who migrated, probably about 1535, from Oxford), Dee, Digges, Blundeville, Buckley, Billingsley, Hill, Bedwell, Hood, Richard and John Harvey, Edward Wright, Briggs, and Oughtred. Under the Elizabethan statutes of 1570, notwithstanding many disadvantages, the mathematical school continued to grow. Horrox, Seth Ward, Foster, Rooke, Gilbert Clerke, Pell, Wallis, Barrow, Dacres, and Morland may be cited as prominent Cambridge mathematicians of the succeeding century.
Newton’s mathematical career dates from 1665; his reputation, abilities, and influence attracted general attention to the subject. He created a school of mathematics and mathematical physics, among the earliest members of which I note the names of Laughton, Samuel Clarke, Craig, Flamsteed, Whiston, Saunderson, Jurin, Taylor, Cotes, and Robert Smith. Since then Cambridge has been regarded as, in a special sense, the home of English mathematicians, and from 1706 onwards we have fairly complete accounts of the course of reading and work of mathematical students.