In the early modern era, England fell notably behind the European mainland in the advancement of the natural sciences and mathematics. Nevertheless, this situation was destined to alter with the emergence of one of history’s most esteemed scholars, Sir Isaac Newton (1642–1726 os). Newton’s remarkable contributions were set to not only enable England to catch up but also lead in domains such as mathematics, optics, physics, and astronomy.
Newton is frequently regarded as a crucial figure in these fields, but it is vital to acknowledge that his work was profoundly shaped by European scholars. For example, his seminal three laws of motion in the “Principia Mathematica” were influenced by the principle of inertia from Isaac Beeckman (1588–1637) through René Descartes (1596–1650) and were inspired by the three laws of motion in the “Horologium Oscillatorium” (1673) by Christiaan Huygens (1629–1695).
Before exploring Newton’s groundbreaking contributions, it is important to examine two English scholars, Isaac Barrow (1630–1677) and John Wallis (1616–1703), who significantly impacted Newton’s mathematical perspective on physics, in contrast to the dominant mechanical viewpoint of European academics. Contrary to common belief, Barrow never instructed Newton but notably recommended him as his successor for the Lucasian Professorship of Mathematics at Cambridge. During Newton’s era, Cambridge was primarily a medieval Aristotelian institution with little focus on mathematics, making his embrace of a mathematical approach to physics quite revolutionary.
Isaac Barrow emerged from a scholarly lineage but began as a challenging student. He attended Felsted School and subsequently enrolled at Trinity College, Cambridge, graduating in 1649 and becoming a fellow in 1652. In the 1650s, Barrow dedicated himself to mathematics and natural sciences, adopting the mathematical elements of Descartes’ work while dismissing his metaphysics as atheistic. He produced summaries of Euclid’s “Elements” and “Data,” along with works from Archimedes, Apollonius’ “Conics,” and Theodosius’ “The Sphaerics,” utilizing the concise notation of William Oughtred.
Due to puritan pressures, Barrow left England in 1655, but he returned to Cambridge and, with the aid of John Wilkins, secured the position of Regius Professor of Greek, later becoming the professor of geometry at Gresham College. Barrow was the inaugural appointee of the Lucasian Chair of Mathematics in 1663, courtesy of Wilkins. He lectured on geometry and optics, and although he eschewed algebra, he was knowledgeable about the analytical mathematics of his time. His geometric approach led to developments similar to calculus, influencing not just Newton but also later mathematicians like Gottfried Leibniz.
Barrow prepared his optics lectures for publication, aided by Newton, who was also teaching optics. Barrow’s lectures were the first to mathematically address image positioning in geometric optics. He advocated for a mathematical framework for all physical sciences, reflecting the method evident in Newton’s “Principia Mathematica.”
Turning to John Wallis, he was a major figure in seventeenth-century English mathematics, particularly due to his self-educated background. Born to a minister, Wallis initially did not study mathematics at grammar school. He first encountered arithmetic during a Christmas break in 1631 and found it aligned with his temperament, which led him to further pursue it as a hobby while at Emmanuel College, Cambridge. Ordained, Wallis demonstrated skills especially in cryptography, contributing to the parliamentary side during the English Civil War.
Wallis’ mathematical journey gained momentum when he came across William Oughtred’s “Clavis Mathematicae” in 1647, which he absorbed quickly. Cromwell appointed him Savilian Professor of Geometry at Oxford in 1649 despite his lack of formal mathematical training, and Wallis thrived in the role for over fifty years.
Wallis introduced continental mathematical techniques to England. His “De sectionibus conicis” (1655) presented conic sections algebraically and built upon Descartes’ presentations. In 1656, he published “Arithmetica Infinitorum,” which systematized and expanded analytic methods, clearing the way for calculus. Wallis’ work had a profound influence on Newton, especially his “Arithmetica Infinitorum,” which Newton studied meticulously, recognizing its significance in a correspondence with Leibniz. Wallis also played a role in rectifying Descartes’ collision laws, introducing the concept of momentum conservation.
Both Barrow and Wallis were instrumental in molding Newton’s intellect, propelling him from the philosophical sciences of Descartes towards a mathematical approach that would ultimately lead to his groundbreaking contributions to science.