Scientists of Wales: Robert Recorde and William Jones

(March 01, 2013)

Scientists of Wales: Robert Recorde and William Jones

Some history of two mathematical symbols

Mathematics is distinguishable from other sciences in that its arguments, postulates, proofs and so on are mostly conveyed by symbols and separated letters rather than words. Perhaps this high dependence on largely unfamiliar symbols is one factor that makes many people readily, but not necessarily contentedly, admit to being ‘no good at maths’. Perhaps in mathematics education the extensive and almost exclusive use of symbols and digits is an impediment to progress for many pupils, especially the very young at the very time that they are struggling to master another language that is composed of joined letters, not symbols and numbers.

Gradually over time, most people reach an acceptable degree of competence with numbers, although many argue that today’s youngsters are not as ‘quick with numbers’ as were their grandparents. What such comments usually refer to are the four rules of number, namely: addition; subtraction; multiplication; and division. Most people would recognize the symbols of +, -, x, ÷ and also the symbol which signifies the outcome of simple operations, namely, = meaning ‘equals’, ‘is equal to’, or ‘makes’.

The history of the development of mathematical notation is fascinating; often illuminating why it became necessary. Can you imagine mathematics with only words? Would it, could it exist? We can thank a Welshman for introducing the equals sign to the world and for promoting its use in all the sciences.

Robert Recorde (c1510 – 1558)

Uncertainty surrounds the year of his birth, but 1510 is generally accepted as near the mark. More secure is the knowledge of his place of birth, Tenby in Pembrokeshire, and of his parentage: father Thomas; grandfather, also Thomas, from Kent; mother Rose, from Machynlleth.

Little is known of his boyhood, but at 15 years of age he went to Oxford University. He graduated in 1531 and was elected a Fellow of All Souls College. His story over the next twenty years is murky, but some clarity emerges in 1545, by which time he had moved to Cambridge University and graduated in medicine. There are grounds for believing that he practised medicine for a while in London, perhaps to the royals in the persons of Henry VIII, Edward VI and Mary. His medical prowess was sufficient to enable him to write a book, Urinal of Physik, which, in the opinion of some scholars, points the way to modern homeopathic medicine.

It is clear that Recorde was a significant intellect in his day and, above all, a distinguished teacher of both his specialisms of mathematics and medicine. He also had a flair for being in the right place, usually in high society, at the right time. By 1549 he was the Comptroller of the Royal Mint in Bristol and two years later he became the Royal Surveyor of Mines and Monies in Ireland.

His last years were very troubled, culminating in his death in Southwark prison in 1558. He had been committed as a debtor, so it is thought, after a bitter legal confrontation involving the Earl of Pembroke and Baron Herbert of Cardiff. Perhaps Recorde was out of his depth in the swirling waters of London politics at this time.

Whatever the truth about his political life and sad death, his mathematical legacy is rich. He wrote several books spanning a number of topics, including arithmetic, algebra and geometry. It is in one of these books –The Whetstone of Witte – that the equals sign is used for the first time, “a pair of paralleles….because no 2 things can be more equal …”. The original two lines were distinctly longer than the two which we use today. As far as I am aware, there is no statutory definition of the lengths of the two lines we use; it’s a matter of judgement at about 3 millimetres. He deserves to be remembered as a very effective communicator of mathematics to the masses. Come back RR! Visit the museum in his honour in Tenby.

Copy taken from The Whetstone of Witte, Robert Recorde, 1557

The text reads: "Howbeit, for easie alteratiõ of equations. I will propounde a fewe exãples, bicause the extraction of their rootes, maie the more aptly bee wroughte. And to auoide the tediouse repetition of these woordes : is equalle to : I will sette as I doe often in woorke vse, a paire of paralleles, or Gemowe lines of one lengthe, thus: =====, bicause noe .2. thynges, can be moare equalle. And now marke these nombers."

William Jones (1675 – 1749)

William Jones, William Hogarth 1740

William Jones was born in a cottage at Llanfihangel Tre’r Beirdd on the Isle of Anglesey, to Elizabeth Rowland and John George Jones. His primary school education was in Llanfechell, where he quickly demonstrated a high ability in arithmetic, sufficient for the local landowner, Lord Buckley, to arrange for him to go to London. There, he gained employment with a merchant who, after a while, sent him to sea on trade routes. This experience enabled him to apply his innate mathematical ability to the point of being able to write a book, A New Compendium of the Whole Art of Navigation, in 1702. When he returned from his time at sea, he set up as a teacher of mathematics in London coffee houses. In this respect he was like Robert Recorde, taking delight in communicating his discipline to ordinary folk. Also somewhat like Recorde, Jones soon moved in high circles; social and scientific. He became a Vice-President of the prestigious Royal Society and, in that role, he chaired a committee that was set up to resolve a dispute on the matter of who created the differential calculus (a topic in mathematics). Was it Isaac Newton or was it Gottfried Wilhelm Leibniz? His death in 1749 had none of the sadness and trauma of that of Recorde.

For our purposes now, we note that it was William Jones who first formally introduced the symbol π to the world, in his 1706 work Synopsis Palmariorum Matheseos; in which he used the Greek letter π as an abbreviation for perimeter. Most people today have a recollection of Pi, albeit faint, from school geometry, concerned with circles. What is the area of a circle of radius r? What is the perimeter of a circle of radius r?

Among ancient hints at Pi are verses in the Hebrew/Christian Bible, for example, in the first book of Kings, Chapter 7, Verses 23-26, 'He then made the Sea of cast metal … it was round … the diameter … being ten cubits … it took a line thirty cubits long to go round it'. These figures give the ratio of perimeter to diameter (which is the definition of π) as 3. This is close, but Pi is an irrational number, i.e. one that cannot be presented as the ratio of two integers. Most of us remember π as 22/7 or 333/106 (unlikely!) or 52163/16604 (you must be joking!). The interesting feature of the decimal presentation of Pi is that it never ends and never settles into a repeating pattern. It starts 3.14159265359 ... and so on for trillions of digits. Keep it going! What else is your life for?

It has been a source of endless delight for some people to create mnemonics for the Pi sequence. For example, for a 7-digit sequence the mnemonic is – How I wish I could calculate Pi – the number of letters in each word matches the digits in the sequence, thus, How (3) I (1) wish (4) ... For a 15 digit sequence we have this one which is favoured by physics undergraduates, - How I like a drink, alcohol of course, after the heavy lecture involving quantum mechanics.

Your homework is to do likewise for longer sequences. I have a few in English and in Welsh and one each in German and French.