Master of Trinity College, Cambridge [1] [2] .

John was the son of the famous admiral, Edward Montague, killed at Solebay. In effect, John was provided a sinecure, the mastership of Trinity College, Cambridge, as a reward for his fathers service (1683-1700). Although considered a weak master, his politics may have been important in Cambridge's evolution.

Entered Cambridge, 1672; made master of Sherburn Hospital by his relative Bishop Crewe, 1683; made Doctor by Royal mandate, 1686; made master of Trinity College, Cambridge, directly by the Crown, 1683; Vice-chancellor, 1687; resigned mastership of Trinity and became Dean of Durham, either in 1699 or 1700; remained Dean of Durham until 1728.

Blamed for a decline in Trinity's reputation, but served during difficult times.

"But perhaps the most serious, as well as consequential, event connected with the 1674 elections was the appointment of John Montague as fellow. He was the fourth son of Admiral Edward Montague, first earl of Sandwich, who died in battle three months after his son entered Trinity College on 12 April 1672. The following year John was created M.A., jure natalium, and now in September 1674 he wished to be elected fellow. Thomas Ross, Montague's former tutor and presently the king's librarian and groom of the private chamber, mobilized both Samuel Pepys and the duke of Monmouth to act on Montague's behalf. On 26 September the king sent a letter to Barrow instructing the master and seniors of Trinity to elect the young nobleman, notwithstanding Montague's "not being a scholar" and grant him all necessary dispensations so that he could sit for examination. Montague was elected. He was also created doctor of divinity in 1682 (at age of 27!) by royal mandate and the following year appointed master of Trinity, a post he held for seventeen years. Small wonder that it was under the mastership of Montague - as congenial a person as he may have been - that the college entered a state of rapid deterioration, for the master kindled neither discipline nor learning." Feingold

"... Trinity, as a royal foundation, was a particularly vulnerable target for ... royal pressure. ... Part of the reason for the decline of Trinity after Barrow's death was that his successors, John North (1677-83) and John Montagu (1683-1699), were more inclined to buckle under such royal pressure so that royal favor rather than academic merit became the path to advancement within the college. ...

... North's problems were compounded by the crisis in the college's finances caused by the building of the Wren Library, which was begun by Barrow in 1676. With unaccustomed humor North left instructions that at his death he should be buried in the antechapel so that "the fellows might trample upon him dead as they had done living." Trinity continued to drift under the mastership of the aristocratic Montagu, who, in 1700, was replaced by Richard Bentley, whose determined efforts to make the college the academic center of the university and himself the college's autocrat led to one of the longest and most tangled quarrels in the long annals of academic dispute.

Barrow's death in 1677, then, marked the beginning of a period of decline... It also came at a time when the college's enrollments began to drop markedly... under Montagu (1683-99) enrollment fell still further to twenty-nine - figures that mirror the more general decline in ... both Oxford and Cambridge during this period." Gascoigne

`Tenison (archbishop and primate, ed.) was ... closely involved in choosing candidates for appointments to royal benefices... Tenison appears to have used his influence to advance the career of John Montagu (master of Trinity, 1683-1700 and Dean of Durham, 1700-28) who, though undistinguished as master of Trinity, none the less had loyally supported the Revolutionary Settlement and, as the fourth son of Edward Montagu, first earl of Sandwich, came from an influential family with whig connections. According to Conduitt, after Montagu had resigned the mastership in 1700, Tenison offered the post to Newton if he would take orders; when Newton declined the offer, writes Conduitt, `Tennison pestered him to take any preferment in the Church saying to him "Why will you not? You know more divinity than all of us together." "Why then", said Sir Issac, "I shall be able to do you more service then if I was in orders"...' Gascoigne, Cambridge in the age of Enlightenment

Gascoigne quotes what was apparently a common anonymous ditty written at Oxford and quoted by Toynbee, which apparently describes affairs around 1715 at the universities:

The King observing with judicious eyes,
The state of both his Universities,
To Oxford sent a troop of horse; and why?
That learned body wanted loyalty:
To Cambridge books he sent, as well discerning
How much that loyal body wanted learning.

Sources:
[DNB].
Before Newton.
Cambridge in the age of Enlightenment.

http://www.montaguemillennium.com/familyresearch/h_1728_john.htm