[6] The stated reason for his first name was "…the never-to-be-forgotten increase, of every sort, wherewith God favoured the country about the time of his nativity.

After graduation, Mather worked as a chaplain attached to a garrison in the Channel Islands from 1659 to 1661 with a short stint at a church in Gloucester in 1660.

[13] After Cromwell's death in 1658, Mather felt less secure in his post in the Channel Islands due to Charles II's return to the throne.

[5] In 1661, with the advent of the English Restoration and resurgence of Anglicanism, Increase returned to Massachusetts Bay Colony, where he married Maria Cotton.

[4] On November 27, 1676, Mather's home, the meeting house, and a total of 45 buildings in Boston's North End were destroyed by a fire.

Despite his absences he did make some changes: re-implementation of Greek and Hebrew instruction, replacement of classical Roman authors with Biblical and Christian authors in ethics classes, enactment of requirements that students attend classes regularly, live and eat on campus, and that seniors not haze other students.

While engaged in petitioning he published pieces to build popular support for his positions, such as A Narrative of the Miseries of New-England, By Reason of an Arbitrary Government Erected there Under Sir Edmund Andros (1688) and A Brief Relation for the Confirmation of Charter Privileges (1691).

[22] Increase Mather's book Remarkable Providences was published in 1684 and forwards a doctrinal belief in the real power of witchcraft.

In November 1692, he published Cases of Conscience Concerning Evil Spirits which defended the judges and trials, but also expressed words of caution, perhaps due to public pressure.

In the postscript, included with the initial first edition of the book, he mentions his own attendance at the trial of George Burroughs and his agreement with the capital judgment against him.

[30] Throughout his life Mather was a staunch Puritan, opposing anything openly contradictory to, mutually exclusive with, or potentially "distracting" from, his religious beliefs.

He firmly believed in the direct appearance of God's disfavor in everyday life, e.g. the weather, political situations, attacks by Native Americans, fires and floods, etc.

During his tenure at Harvard he regularly stamped out any relaxation of Puritan strictness, such as latitudinarianism, which had flourished during his overseas absence.

[5] Following his acceptance of the Covenant, Solomon Stoddard and others attempted to further liberalize Puritanism by baptism of children who had nonmember parents[5] and admittance of all but the openly immoral to services.

[7] In John Neal's 1828 novel Rachel Dyer, Increase Mather appears at the end of Martha Corey's witchcraft trial to announce the guilty verdict and give a speech.