Recent research has revealed new information about the Welsh Tudor mathematician, Robert Recorde who invented the equals sign (=) what inspired his work and what was its influence on the development of mathematics education in the English-speaking world. The findings of that research, presented at a commemorative conference in 2008, form the core of this publication. The book begins with an account of Recorde’s life and an overview of his work in mathematics, medicine and cosmography. Individual chapters concentrate on each of his books in turn, taken chronologically, and are supplemented by chapters that present historical perspectives of Recorde’s work and its wider European links and one that sets Recorde’s work within the general knowledge economy.
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About the Author
Gareth Roberts is professor emeritus of education at Bangor University, UK. Fenny Smith is an independent scholar specializing in ancient and medieval numerical notation and arithmetic techniques and Italian Renaissance algebra.
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The Life and Times of a Tudor Mathematician
By Gareth Roberts, Fenny Smith
University of Wales PressCopyright © 2012 The Contributors
All rights reserved.
The lives and works of Robert Recorde
The conference referred to in the Introduction marked the 450th anniversary of the death of Robert Recorde. It is therefore appropriate to open this first chapter with an account of that event. We have Recorde's undated will, probate for which was first granted on 18 June 1558. A second probate was granted on 6 November 1570, but more of that later. The will was made while Recorde served time as a debtor in the King's Bench Prison at Southwark, south London, unable to pay a fine of £1,000 imposed as a result of his having been found guilty of slandering Sir William Herbert, first Earl of Pembroke (1501–70).
The King's Bench Prison was run as a private enterprise with inmates paying for the services provided. Such services included the possibility, under certain circumstances and within specified 'Rules', for inmates to live outside the prison, provided that the services could be paid for. This situation appears to be reflected in Recorde's will, which lists payments of various sorts to prison officials.
The will also lists bequests to members of his family, including one of £20 to 'my widowe mother and stepfather'. Recorde himself was not married and minor goods and chattels were gifted to his cousins and their children. His executors were his brother Richard, and his nephew and namesake, Robert. The cause of his death is not known. However the years 1557–8 were epidemic years in London. In 1558 the country as a whole was smitten with what is believed to have been an outbreak of influenza, which had ravaged the Continent the previous year. Prison would not have been a good place to be during such a season. One of the side effects of such epidemics was that records of births, deaths and burials were not kept, even in parishes more salubrious than Southwark, so it is not surprising that it is not known of what Recorde died or when and where he was buried.
The closest to an obituary for Recorde was written by the physician and author, William Bullein (c. 1520–1575/6). In the Preface to the second book of his Bulwarke of Defence, published in 1562 but compiled earlier while he was in prison, Bullein lists some medical worthies, including Robert Recorde, to whom he devoted most space:
How well was he seen in tongues, Learned in Artes and in Sciences, natural and moral. A father in Physicke whose learning gave liberty to the ignorant with his Whetstone of Witte and Castle of Knowledge and finally giving place to eliding nature, died himself in bondage or prison. By which death he was delivered and made free, and yet liveth in the happy land amongst the Laureate learned, his name was Dr. Recorde.
If this list of abilities is augmented by those attributed to him a few years before Recorde's death by the courtier and religious radical, Edward Underhill (1512–c. 1576),' ... singularly sene in all of the seven sciences, and a great divine ...', together they give some feel for the regard in which Recorde was held across the breadth of his many 'lives'.
Evidence relating to the year of Recorde's birth is found in accounts of one of the defining show trials of the reign of Edward VI, that of Stephen Gardiner (c. 1497–1555), bishop of Winchester, the leading English religious conservative of his time. As a staunch Roman Catholic, Gardiner steadfastly opposed the policy of the Administration to complete the Reformation. To resolve the situation he was asked by the Privy Council to preach a sermon endorsing the religious policy of the regime. He delivered his sermon before king and court on 29 June 1548, but stopped short of compliance with his instructions on a number of issues. He was re-imprisoned, during which time further unsuccessful attempts were made to bring him to heel. Gardiner was then brought to trial at Lambeth on 15 December 1550 and deprived of his bishopric. Depositions relating to the content of the sermon of 1548 were made by members of the Privy Council and their officials, members of the king's court and divines. Twelfth in the list of depositions, sandwiched between those of a high-ranked cleric and a long-established courtier, was one by a 'Dr Robert Recorde, doctor of physicke of the age of 38 years or thereabouts'. The boy from Tenby had travelled a long way geographically, socially and intellectually in his thirty-eight years. If thirty-eight was his age at the time of the sermon then he was born in 1509–10; if at his trial, he was born in 1512.
The Recorde family was deeply embedded in the community of Tenby from well before Robert Recorde's birth, and became even more so after his death. Its genealogy is to be found in Lewys Dwnn's Heraldic Visitations. The earliest member of the family noted in the Visitations is Roger Record of East Wel in Kent, whose one surviving son Thomas Recorde married twice. Thomas had no children by Joan, daughter and co-heiress of Thomas Ysteven of Tenby Gent. but, by Ros Johns, daughter of Thomas of Machynlleth ap Sion, he had two sons, Richard and Robert. The latter is our subject. Richard married Elizabeth, daughter of William Baenam of Tenby, by whom he had a son and heir named Robert, presumably after his uncle.
Nothing is known of Robert Recorde's youth. How he obtained an education adequate to enter Oxford is a matter for speculation. There is no evidence of the existence of lay schools in the vicinity of Tenby and its church was not collegiate, in the formal sense of that designation. There may have been a modest chantry school, held in the west porch of the church or in the closely associated college.
Robert probably arrived at Oxford about 1525. He was awarded the degree of Bachelor of Arts on 16 February 1531 and elected a Fellow of All Souls in the same year. The annual income from land and properties held by All Souls College in south Wales, Montgomeryshire and Denbighshire allowed it to provide generously funded scholarships and fellowships for Welsh students throughout the period. For example, a holding at St. Clears – only about sixteen miles from Tenby, albeit in Carmarthenshire rather than Pembrokeshire – provided the college with an annual income of about £40 during the sixteenth century.
It seems that Recorde undertook medical studies while at All Souls, but there are no records at Oxford of this activity. The qualification he earned at Oxford for a licence to practise medicine proves that he had, as a minimum, carried out two dissections and effected three cures. There is no firm evidence of when he left Oxford. The probable course of Recorde's subsequent academic career has to be deduced from his records at Cambridge. In 1545 he was awarded the degree of MD by Cambridge on the basis that, by then, he had had twelve years of medical practice after being granted his licence by Oxford to start such activities.
Recorde's subsequent career encompassed a bewildering combination of 'lives' as a mathematician, astronomer and physician, and are discussed elsewhere within these proceedings. This chapter focuses initially on his work in the service of the Crown and its attendant difficulties, then on his interests as an antiquary and linguist and, finally, on what is known about the readers of Recorde's own books.
2. Crown service and its consequences
Robert Recorde and William Herbert, Earl of Pembroke
It was his abilities as an applied scientist that drew Recorde into Crown service and into the unlikely conflict with Sir William Herbert, yet to become Earl of Pembroke. Nowadays Recorde's work for the Crown could be described as that of an iron-founder, a production manager, an accountant and an extraction metallurgist. All of these activities arise in the context of his dispute with Pembroke and are catalogued in the account of the proceedings that led to Recorde's committal for trial.
Recorde brought the dispute to a head in a letter he wrote on 10 June 1556, during the reign of Queen Mary, to William Ryse, a knight of the Queen's Privy Chamber. Recorde complained bitterly about harassment by Pembroke on issues dating back to the previous reign (that of Edward VI) and of an impending lawsuit. He also included a text in Latin that reads like an extract from a book of prophecies warning of danger to the Crown. He asked to be allowed to answer for his complaints before the Privy Council. Queen Mary passed the letter to certain Privy Councillors and Recorde was called before them only ten days later, when he confirmed that he had indeed written the letter. On 16 October 1556 Pembroke's attorney presented a bill against Recorde alleging that the letter made the Earl appear a traitor, to have injured the Crown and to deserve imprisonment. Damages of £12,000 were claimed.
Recorde replied with a detailed list of allegations, largely involving defrauding of the Crown by Pembroke during the previous reign. Final judgement was passed on 10 February 1557 and is merely appended as a brief note to the summary of the case presented to the hearing of October 1556. No detailed record of the trial proceedings has come to light. The judgement found that Recorde's letter had damaged the Earl without good reason and awarded damages of £1,000 and £10 costs. It fell far short of what Pembroke had asked. There is however no question of Recorde's financial probity ever being an issue. The alacrity of the royal reaction and the speed of the dispatch of judgement indicated the seriousness with which it was taken. How many members of the Administration other than Pembroke and including the Crown were involved? Analysis of the accusations levelled by Recorde throws much-needed light on his work for the Crown and on his possibly misguided loyalty to it.
The incident at Pentyrch
The first of Recorde's accusations against Pembroke reads as follows:
From an iron mill at Pentyrch on 3 February 1549 the earl took a barrel of iron worth £10 being Crown property to his own use, and drove off the workers there, to the King's loss of £2000. At Westminster 20 March 1550 the earl persuaded Recorde to give him the profits of the said iron-working which should have been allowed for in the accounts to the profit of the Crown to the value of £200.
The price of iron quoted of about £7 a ton is the rate that held for both wrought and cast iron at the time. Correspondence shows that Pembroke was still pursuing Recorde at the end of 1550 for the balance of the profits he claimed.
There seems to be no reason to doubt Recorde's account of events. If, as the use of the name 'iron mill' suggests, the plant was a bloomery producing wrought iron, then it would have been following the practice at nearby Miskin and it establishes Recorde as being in charge of the earliest known iron-making plant in the lower Taff valley. Assuming a profit of about 50 per cent, corresponding to £3.50 per ton of iron, and using Recorde's figure, a profit of £200 would have arisen from the production of about 60 tons of finished iron, which would have been typical of two years' production of a traditional bloomery. However the capital cost of such a plant would have been far less than the £2,000 that Recorde claimed to have been lost. Such expenditure would have been closer to that of a blast-furnace complex. Whether bloomery or blast furnace, there seems to be no obvious explanation for Pembroke's behaviour. He owned the land if not the mining rights, and had the reversion of such rights. In a previous reign, Henry VIII had been keen to control the use of iron, and here Pembroke had taken Crown property presumably for his own use.
A short digression on monetary matters may help us to understand the nature of the viper's nest Recorde had entered. By the time of Edward VI's accession in 1547 the Crown was almost bankrupt as a result of Henry VIII's military adventures and other extravagances. One means Henry had used to generate revenue was by debasing the currency. The essential details may be summarized as follows. A coin had two values: on the one hand its intrinsic value determined by the weight of precious metal it contained; and on the other, its face value stipulated by whatever the authorities said it was worth. Intrinsic value depends on the weight of the coin and its composition. Time was when a silver penny weighed a pennyweight and was of sterling silver composition, 92.5 per cent silver and 7.5 per cent copper. Towards the start of Henry VIII's reign the weight of a silver penny had been approximately halved. The debasement of the currency was further aggravated by coming off the sterling standard as the percentage of silver was progressively reduced. This provided the Crown with additional revenue, for each time there was a coinage or recoinage it claimed its right to a seigniorage over and above the gain from debasement. Between 1544 and 1551 it is estimated that the total revenue to the Crown from debasement amounted to approximately £1.27m, a sum greater than the total of all Crown taxes and income generated from the sale of Crown lands taken together. The ultimate depth of debasement was reached with the Irish harp pennies whose intrinsic value was less than a seventh of their face value. One practical result of such debasement was a significant rise in inflation – the cost of basic commodities such as bread rose by a factor of three over a period of twenty years. It also provided mint officials with potentially very rich pickings. Corruption was rife at all levels and manifested itself in many ways.
The Bristol mint
Recorde's first appointment as comptroller of the Bristol mint was a direct result of the corrupt behaviour of its under-treasurer Sir William Sharrington, who admitted defrauding the Crown to the tune of about £6,000, to the advantage of both himself and Thomas Seymour, Pembroke's brother-in-law. The appointment was dated 29 January 1549 just a few days before the raid on Pentyrch. Recorde was paid the same annual salary as the new under-treasurer, Sir Thomas Chamberlayne, viz. £133 6s. 8d. The division of responsibilities between them is not clear, but generally the comptroller seems to have had more immediate control of operations. Whatever the split, the outcome was that the mint at Bristol, while operational, turned in an outstanding performance. The quality of product was very high, and when the financial accounts for this period were scrutinized in 1551, they were found to be in surplus to the extent of £218 13s. 2d, an extremely unusual occurrence in mint accounts at the time. The accounts cover the first three-quarters of that year and show a gross profit of some £43,000 and a net profit of a little more than £5,100.
Recorde's charges against Pembroke also accuse him of having played a key role in closing the mint at Bristol, the events being closely associated with the overthrow of Protector Somerset (Edward Seymour, Thomas Seymour's older brother) who had been effectively ruling the country during Edward VI's period as a minor. Pembroke's part in the overthrow has been well explored and opinion on it is still divided. The coup was being organized from London by the Earl of Warwick. The support of Pembroke and Bedford (John Russell, Earl of Bedford) was twice requested by Somerset. They brought their forces as far as Andover by 8 October 1549, from where they responded somewhat coolly to Somerset's request, saying that they were staying put. The following day they retreated a little to Pembroke's manor at Wilton. On 11 October, Warwick (who was made the Duke of Northumberland on that same date) and his followers arrested Somerset at Windsor, where he had fled for safety. Pembroke and Bedford gave their approval to the coup. On 14 October, Somerset was taken to the Tower and Northumberland took over the reins. The evidence deposed by Recorde reveals a sub-plot that exposes Pembroke's attention to raw self-interest. Basically the evidence alleges that, starting on the very day of the coup, Pembroke began to act as if the operation and contents of the Bristol mint were his personal property and lists some four acts by Pembroke to this end.
Excerpted from Robert Recorde by Gareth Roberts, Fenny Smith. Copyright © 2012 The Contributors. Excerpted by permission of University of Wales Press.
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Table of Contents
List of illustrations
Notes on contributors
1. The lives and works of Robert Recorde
2. Robert Recorde and his remarkable Arithmetic
John Denniss and Fenny Smith
3. Recorde and The Vrinal of Physick: context, uroscopy and the practice of medicine
4. The Pathway to Knowledge and the English Euclidean tradition
5. The Castle of Knowledge: astronomy and the sphere
6. The Whetstone of Witte: content and sources
7. The Welsh context of Robert Recorde
Nia M. W. Powell
8. Commonwealth and Empire: Robert Recorde in Tudor England
Howell A. Lloyd
9. Data, computation and the Tudor knowledge economy
John V. Tucker
Appendix: From Recorde to relativity: a speculation
Gareth Wyn Evans