It is almost impossible to imagine a modern university without a large mathematics department and a whole host of professors for an ever-increasing array of mathematical subdisciplines. Mathematics and its offshoots lie at the centre of modern society. Because popular history of science has a strong emphasis on the prominent mathematicians, starting with Euclid and Archimedes, it is common for people to think that mathematics has always enjoyed a central position in the intellectual life of Europe, but they are very much mistaken if they do so. As I have repeated on several occasions, mathematics had a very low status at the medieval European university and led a starved existences in the shadows. Some people like to point out that the basic undergraduate degree at the medieval university formally consisted of the seven liberal arts, the trivium and quadrivium, with the latter consisting of the four mathematical disciplines–arithmetic, geometry, music, and astronomy. If fact, what was largely taught was the trivium–grammar, logic, rhetoric–and large doses of, mostly Aristotelian, philosophy. A scant lip service was paid to the quadrivium at most universities, with only a very low-level introductory courses being offered in them. There were no professors for any of the mathematical disciplines.
Things only began to change during the Renaissance, when the first universities, in Northern Italy, began to establish chairs for mathematics, which were actually chairs for astrology, because of the demand for astrology for medical students. The concept of general chairs for mathematics for all educational institutions began with Philip Melanchthon (1497–1560), when he set up the school and university system for Lutheran Protestantism, to replace the previously existing Catholic education system, in the second quarter of the sixteenth century.
Melanchthon did so because he was a passionate advocate of astrology and to do astrology you need astronomy and to do astronomy you need arithmetic, geometry, and trigonometry, so he installed the full package in all Lutheran schools and universities. He also ensured that the universities provided enough young academic mathematicians to fill the created positions.
Catholic educational institutions had to wait till the end of the sixteenth century before Christopher Clavius (1538–1612) succeeded in getting mathematics integrated into the Jesuit educational programme and installed a maths curriculum into Catholic schools, colleges, and universities throughout Europe over several decades. He also set up a teacher training programme and wrote the necessary textbooks, incorporating the latest mathematical developments.
England lagged behind in the introduction of mathematics formally into its education system. Even as late as the early eighteenth century, John Arbuthnot (1667–1735) could write that there was not a single grammar school in England that taught mathematics.
This is not strictly true because The Royal Mathematical School was set up in Christ’s Hospital, a charitable institution for poor children, in 1763, to teach selected boys’ mathematics, so that they could become navigators. At the tertiary level the situation changed somewhat earlier.
Gresham College was founded in London under the will of Sir Thomas Gresham (c. 1519–1579) in 1595 to host public lectures.
Amongst other topics, professors were appointed to hold lectures in both geometry and astronomy. As with the Royal Mathematical School a century later these lectures were largely conceived to help train mariners. The instructions for the geometry and astronomy professors were as follows:
The geometrician is to read as followeth, every Trinity term arithmetique, in Michaelmas and Hilary terms theoretical geometry, in Easter term practical geometry. The astronomy reader is to read in his solemn lectures, first the principles of the sphere, and the theory of the planets, and the use of the astrolabe and the staff, and other common instruments for the capacity of mariners.
The first university professorships for mathematics were set up at Oxford University in 1619 financed by a bequest from Sir Henry Savile (1549–1622), the Savilian chairs for astronomy and geometry.
Over the years it was not unusual for a Gresham professor to be appointed Savilian professor, as for example Henry Biggs (1561–1630), who was both the first Gresham professor and the first Savilian professor of geometry.
Henry Savile was motivated in taking this step by the wretched state of mathematical studies in England. Potential mathematicians at Cambridge University had to wait until a bequest from Henry Lucas (c. 1610–1663), in 1663, established the Lucasian Chair of Mathematics, whose first incumbent was Isaac Barrow (1630–1677), succeeded famously by Isaac Newton (1642–1726 os). This was followed in 1704 with a bequest by Thomas Plume to “erect an Observatory and to maintain a studious and learned Professor of Astronomy and Experimental Philosophy, and to buy him and his successors utensils and instruments quadrants telescopes etc.” The Plumian Chair of Astronomy and Experimental Philosophy, whose first incumbent was Roger Cotes (1682–1716).
Before the, compared to continental Europe, late founding of these university chairs for the mathematical sciences, English scholars wishing to acquire instruction in advanced mathematics either travelled to the continent as Henry Savile had done in his youth or find a private mathematics tutor either inside or outside the universities. In the seventeenth century William Oughtred (1574–1660), the inventor of the slide rule, fulfilled this function, outside of the universities, for some notable future English mathematicians.
One man, who fulfilled this function as a fellow of Oxford University was Thomas Allen (1542–1632), who we met recently as Kenhelm Digby’s mathematics tutor.