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 He almost certainly realised the young man’s potential and may have appreciated his disenchantment with the outdated university curriculum.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 of number manipulation.
In its simplest form geometry deals with the shapes of things, in either two or three dimensions (although modern mathematicians also deal with multidimensional space – a study still called geometry). This area of mathematics found ready use with the architect and the builder. For the astronomer it was an invaluable tool in the search for patterns in the stars, which in turn fuelled the development of astrology.
Algebra, which was only scantily formulated before the early seventeenth century, is a language in which symbols are assigned to properties of objects. It enables mathematicians to construct equations that describe a situation or the interplay between properties (either real or imaginary) using strict rules that govern what may be done with representative symbols. A simple example would be the equation s = d/t. In words this would be ‘Speed equals distance travelled divided by time taken’. Further examples would include equations used to find the rate at which water flows through a pipe, how quickly a rocket accelerates from the launch pad, or how efficiently a muscle uses energy from glucose.
Arithmetic and geometry may be considered more everyday than algebra, in that they represent the world and the things we observe directly. Algebra is one level of abstraction away from reality, because symbols are used to represent properties, rather than being actual measurements of things. This distinction could account for the fact that arithmetic and geometry were developed into sophisticated tools and used widely very much earlier than algebra.
The Greeks viewed mathematics in a different way to the civilisations that predated them, in that they appear to have been the first to consider pure mathematics – to contemplate mathematical abstractions, rather than using mathematics solely as a tool for constructing religious structures or to develop the mystical arts. Using mathematical skills, the Greeks were able to develop elaborate theories to describe the structure of the observable universe and to postulate ways in which the planets, the Sun and the stars could be arranged in the heavens.
According to most accounts, Anaximander, who lived between 610 and 545 BC, is thought to be responsible for the first development of what became the geocentric view of the universe – the concept that the Earth lies at the centre of the universe. Before then, the Earth was believed to be a floor with a solid base of limitless depth.3
Anaximander
