Isaac Newton: The Last Sorcerer. Michael White

      In ’63 [Newton] being at Stourbridge fair brought a book of astrology to see what there was in it. Read it ‘til he came to a figure of the heavens which he could not understand for want of being acquainted with trigonometry. Bought a book of trigonometry, but was not able to understand the demonstrations. Got Euclid to fit himself for understanding the ground of trigonometry. Read only the titles of the propositions, which he found so easy to understand that he wondered how anybody would amuse themselves to write any demonstrations of them.³³

      Whether or not Newton had any official help with mathematics towards the end of his second year at Cambridge is difficult to ascertain. In March 1664 Isaac Barrow began a series of mathematical lectures as part of his duties as the first Lucasian Professor – a position he had accepted that winter. We know that Barrow and Newton were acquainted closely a few years after this, and that Barrow surrendered his chair to Newton in 1669, but it is by no means certain that Newton attended Barrow’s mathematics lectures. According to statutes laid down by the King, these lectures were for fellow-commoners only. This may have prevented Newton; however, such rules were flaunted openly and, being the sort of student he was, Newton may have worked his way in despite his lowly social position within the university.

      For the future advancement of science, his efforts at teaching himself advanced mathematics were of the utmost significance. Without an understanding of algebra, Newton could not have developed the calculus, and without that he could not have manipulated and communicated his physics – calculus provided the formal structure needed to turn his notions of gravity from concept to hard science.

      In 1664 such grand designs were some way ahead; more pressing were the demands of the university. Although he had been working consistently hard, his efforts had been exerted almost entirely outside the curriculum. Like Darwin, Einstein, Hawking and many other great scientists after him, Newton found himself ill-prepared for the various exams he needed to pass in order to continue as a student.

      Having realised that his charge was more interested in mathematics and the latest philosophical ideas from Europe than in the official curriculum, Newton’s tutor, Benjamin Pulleyn, referred him to Isaac Barrow for his scholarship appraisal. Newton was required to pass an examination in April 1664 which would make him an undergraduate scholar, allowing him to sit for his BA the following spring. Pulleyn presumed that Barrow would be the most useful fellow to access the young man’s talents. Unfortunately, Barrow decided to quiz Newton on Euclid. This could have spelled disaster, because Newton had paid little attention to simple Euclidean theorems en route to more advanced mathematics. Conduitt tells us:

      When he stood to be scholar of the house his tutor sent him to Dr Barrow then mathematical professor to be examined, the Dr examined him in Euclid which Sir I. had neglected and knew little or nothing of, never asked him about Descartes’ Geometry which he was master of. Sir I. was too modest to mention it himself & Dr Barrow could not imagine that one could have read the book without first [being] master of Euclid, so that Dr Barrow conceived then but an indifferent opinion of him but however he was made scholar of the house.³⁴

      Having been made aware of his deficiency, true to form, Newton immediately went back to the basics of mathematics and quickly absorbed Euclidean geometry and simple algebraic theorems. His dedication is evident from the fact that the most dog-eared and tatty book in Newton’s library was Euclidis Elementorum by Isaac Barrow.

      Newton may have made up for his mistakes, but, viewing the situation dispassionately, it is clear that he must have received help in convincing the fellows of his true worth. If the interview with Barrow had indeed gone as badly as Conduitt reported, it must have created a poor initial impression and Newton’s supporters must have brought their influence to bear in order to salvage the young man’s career. Humphrey Babington was rising high in the college hierarchy (becoming a senior fellow in 1667), and he enjoyed the King’s favour. The well-documented fact that Newton visited him frequently during the plague years spent in Woolsthorpe shows that the two men remained in contact throughout Newton’s early years in Cambridge. Having helped to get him into Trinity, Babington would not have wanted him to flunk his scholarship. He almost certainly realised the young man’s potential and may have appreciated his disenchantment with the outdated university curriculum.

      Even though he brushed up his Euclid, Newton clearly did little in the way of formal study for the BA examinations the following spring. As a result, he did graduate – but in an undistinguished manner. According to Stukeley, ‘when Sir Is. stood for his Bachelor of Arts degree, he was put in second posing, or lost his groats, as they call it,^* which is looked upon as disgraceful’.³⁵

      In a larger historical perspective, the fact that in the spring of 1665 Newton graduated with a mere second-class BA is laughable, but in the pantheon of scientific greats this is not so unusual. Robert Darwin had to remove his son Charles from medical studies in Edinburgh because it was clear he would make nothing of his time there; Albert Einstein scraped through his degree and then found it almost impossible to find a job; and Stephen Hawking, who was unpopular with the Oxford University authorities because he spent more time on the river than in lecture theatres, was awarded a first only to ensure that he did his PhD in Cambridge. But, for the twenty-two-year-old Newton, graduation, whatever the grade, was enough to secure his future at the university. Setting an example for his scientific heirs, he had long since decided that his vocation was to unravel the laws governing God’s universe; passing exams was merely a means to an end and was conducted with the minimum of effort. He now had official sanction to pursue his true goal, but even he, with the arrogance of youth and a single-minded determination, could not have realised just how soon would come his first successes en route to his dream.

       Chapter 4 Astronomy and Mathematics Before Newton

       In every piece there is a number – maybe several numbers, but if so there is also a base-number, and that is the true one. That is something that affects us all, and links us all together.

      ARVO PÄART (composer)¹

      Number and pattern have always held a fascination, and the true origins of mathematics and astronomy are certainly ancient. The earliest form of organised mathematics, in which numbers were meaningfully manipulated and patterns recorded, is credited to the Babylonians of around 4000 BC, who recorded star patterns and named constellations. They had also developed a surprisingly advanced set of mathematical rules, including a sophisticated method of counting – a skill employed by the record-keeper, the farmer and the architect. It is thought that the last of these professions may also have employed simple forms of algebra and geometry.

      Modern research, such as John North’s work on ancient stone circles, has demonstrated that the ancient Britons must also have possessed some knowledge of geometry in order to build such structures as Stonehenge, started about 3500 BC,² and the ancient Egyptians had highly developed mathematical and engineering skills which they employed in the building of the Great Pyramid at Giza some 1,000 years later. In these ancient civilisations, mathematics and astronomy were blended together intimately and had rich associations with mysticism and the occult. Astronomy and astrology were viewed as one and the same, and mathematics gained an almost spiritual status as a tool for the astrologer/astronomer. It was not until Greek times that mathematics and, to a lesser extent, astronomy were separated from religion and considered worthy of academic attention. While maintaining their spiritual associations, they then gradually became subjects for pure analysis and reasoning.

      All mathematics may be viewed as composed of three central subjects: arithmetic, geometry and algebra. As the most immediately useful to a wide range of crafts and professions, arithmetic was the earliest form of mathematics to be developed, and grew to include all forms