In the early modern era, England was significantly lagging behind the rest of Europe regarding advancements in the natural sciences and mathematics. Nevertheless, the emergence of individuals such as Isaac Newton (1642–1726 OS) signified a turning point as England began to align with, and ultimately spearhead, progress in mathematics, optics, physics, and astronomy. Newton symbolizes a culmination in this progression, albeit not its conclusion. As previously mentioned, Newton’s contributions were profoundly shaped by European intellectuals. For example, his essential trio of motion laws in “Principia” drew the principle of inertia from Isaac Beeckman (1588–1637) through René Descartes (1596–1650), and were influenced by the principles elaborated in Christiaan Huygens’ “Horologium Oscillatorium” (1673). Before exploring Newton’s achievements, it’s vital to recognize two English intellectuals, Isaac Barrow (1630–1677) and John Wallis (1616–1703), who considerably shaped Newton’s mathematical perspective on physics, presenting a distinction from the mechanical methods of European scholars. Contrary to common belief, Barrow never officially instructed Newton but did endorse him as his successor in the role of Lucasian Professor of Mathematics. Noteworthy is that Newton’s Cambridge primarily remained a medieval Aristotelian institution where mathematics held limited significance, making his shift towards a mathematical perspective in physics remarkably innovative.
Isaac Barrow was born into a lineage of distinguished scholars and theologians. After being moved from Charterhouse School due to behavioral challenges, he enrolled at Felsted School in Essex, and subsequently at Trinity College, Cambridge in 1646, where he earned a BA in 1649 and an MA in 1652. In the 1650s, Barrow committed himself to studying mathematics and the natural sciences, joining a circle of young scholars that included John Ray (1627–1705) and Ray’s eventual benefactor Francis Willughby (1625–1672). Barrow adopted Descartes’ mathematical sciences but dismissed his metaphysical ideas, which he felt led to atheism. During this period, Barrow created summaries of Euclid’s “Elements” and “Data,” along with works from Archimedes, Apollonius’ “Conics,” and Theodosius’ “The Sphaerics,” applying William Oughtred’s symbolism.
Due to the rise of puritanical beliefs, Barrow departed from England in 1655, journeying across Europe and Asia Minor before returning to Cambridge in 1659. With the support of John Wilkins, he was appointed Regius Professor of Greek at Cambridge and later became a professor of geometry at Gresham College. Following the establishment of the Lucasian Chair for Mathematics in 1663, Barrow, upon Wilkins’ recommendation, became its inaugural occupant. As Lucasian professor, he taught geometry and optics, and while he was versed in the new analytical techniques, he favored a geometrical rather than an algebraic methodology. His mathematical contributions were modern in substance yet traditional in style. Barrow devised an advanced calculus system, which featured a generalized formulation of the fundamental theorem of calculus. Newton recognized Barrow’s impact, and although Leibniz claimed no influence from Barrow, he is documented to have acquired Barrow’s “Lectiones geometricae.”
Barrow readied his optics lectures for printing with Newton’s help, who edited the manuscript while conducting his optics lectures. Building upon predecessors like Kepler, Scheiner, and Descartes, Barrow’s “Optics Lectures” was the first to address mathematically the image position in geometrical optics. He advocated for a mathematical approach to physical science, which likely influenced Newton’s “Philosophiæ Naturalis Principia Mathematica.”
Turning to John Wallis, he was an essential English mathematician of the 17th century, largely self-educated in the field. Born as the third offspring of John Wallis, a church minister, he did not pursue mathematics within grammar schools, which primarily emphasized classical languages. Notably, his engagement with mathematics began when his brother exposed him to arithmetic during holiday preparations for trade. Wallis approached mathematics more as a pastime than formal education. He attended Emmanuel College, Cambridge, graduating in 1637 and 1640, without a focus on mathematics. Ordained, he served as a chaplain while discovering cryptography and employing it for the parliamentary side during the English Civil War.
In 1649, appointed by Cromwell, Wallis secured the role of Savilian Professor of Geometry at Oxford despite lacking formal training in mathematics or previous experience as a mathematician. He held this position for over fifty years with considerable esteem. He vigorously engaged with mathematical literature, lecturing on classical works like Euclid and Archimedes, with an emphasis on new analytical techniques like those espoused by Descartes. Wallis introduced continental mathematics to England through his publications starting with “De sectionibus conicis” (1655),