At the age of eighteen he was enrolled as a sizar at St John's College, Cambridge, whence he graduated in 1830 as fourth wrangler.
Lovering is first mentioned as master in 1619, so that Taylor probably spent seven years at the school before he was entered at Gonville and Caius College as a sizar in 1626, 1 eighteen months after Milton had entered Christ's, and while George Herbert was public orator and Edmund Waller and Thomas Fuller were undergraduates of the university.
In 1705 he entered as a sizar at Emmanuel College, Cambridge; in 1711 he was elected fellow of his college and was ordained.
On the 12th of January 1754 he was admitted as sizar at St John's College, Cambridge, and took his degree of B.A.
Lightfoot, both of whom preceded him to Trinity College, Cambridge, where he was elected a sub-sizar in 1848, becoming subsequently sizar and scholar.
He went to Cambridge as a sizar of Magdalene College in 1616, migrated to Peterhouse in 1618, was bachelor in 1619 and master of arts in 1623.
His family was poor, and the register of Emmanuel College, Cambridge, testifies to his entry as sizar on the r8th of May 1632.
There he remained a year, more or less, and "seems afterwards to have gone to Sedlescombe school in Sussex, from whence he passed to Caius College, Cambridge, on the 29th of June 1667, and was admitted a sizar of St John's, on the 2nd of February 1668-1669, aged 18."
His promise as a mathematician induced his parents to send him to the university of Cambridge, and in October 1839 he entered as a sizar at St John's College.
In 1819 he entered Trinity College, Cambridge, as a sizar.