Robert Recorde

Quick Info

Tenby, Wales
London, England

Recorde was a Welsh doctor and mathematician who invented the "equals" symbol '=' which appears in his book The Whetstone of Witte (1557).


Robert Recorde's parents were Thomas Recorde and Rose Jones. Thomas Recorde's father was from Wales and Rose Jones was the daughter of Thomas Jones from Machynlleth in Montgomeryshire. Robert was the second son of Thomas and Rose and, although the date is not definitely known, it is thought that he entered the University of Oxford in about 1525. Again we do not know the topics he studied but we do know that he graduated with a B.A. in 1531 and was elected a Fellow of All Souls College, Oxford in that year.

All Souls was a graduate College at this time endowed for the study of Church music. It trained men in theology, law and medicine. Certainly we know that he studied medicine at Oxford and was a highly educated man. In later life he was interested in history, collecting British antiquities and manuscripts, and he was an expert in the Anglo-Saxon language. It is reasonable to suppose that he gained his love of antiquities at All Souls College for John Leyland, who was in 1531 chaplain and librarian to King Henry VIII employed by the King for his expertise in antiquities and manuscripts, had studies at All Souls at the same time as, or slightly before, Recorde.

It is likely that following his election to a fellowship in 1531 Recorde taught at Oxford for a few years but there are no records to prove this. The next that we know for certain is that he went to Cambridge and studied there for his M.D. There is a record at Cambridge which states that Recorde received a license in medicine in Oxford twelve years earlier and this almost certainly means that Recorde received the degree of B.M. from Oxford although again no record of this has been found. He graduated from Cambridge in 1545, receiving the degree of M.D. He may have taught at Cambridge following the award of his degree but all we know for certain is that some time during two years following 1545 he moved to London where he practised medicine.

Henry VIII died on 28 January 1547 and his son Edward, by his third wife Jane Seymour, succeeded to the throne. Edward was only ten years old and Edward Seymour, duke of Somerset, was appointed regent with the title of protector. Recorde was in London, practicing medicine at the time of Edward's succession. In the following year the privy council asked Recorde to examine someone who had been imprisoned in the Tower of London charged with claiming to be a false prophet. In 1549 Recorde was appointed controller of the Bristol mint.

Seymour effectively governed the country until October 1549 when he was overthrown by John Dudley, earl of Warwick who later received the title duke of Northumberland. Sir William Herbert was a governor to the young king Edward VI, and helped to suppress the rebellion in Wiltshire, Devon, and Cornwall in 1549. He tried to get money diverted to support his army in this venture but Recorde refused on the grounds that the orders were not from the King. Herbert accused Recorde of treason, removed him from control of the Bristol mint which ceased production. Recorde was confined to the court for sixty days.

In 1551 Recorde was back in favour for he was appointed by the King to be general surveyor of the mines and monies in Ireland. In this capacity he was in charge of silver mines in Wexford and technical supervisor of the Dublin mint. Silver was important in the King's financial strategy for Edward VI restored an English coinage of silver. It is interesting that he introduced the silver crown of five shillings which was the first English coin to have a date written in Arabic numerals rather than Roman numerals. When we say that Recorde was back in favour, it must be understood that his quarrel with Sir William Herbert had never been settled and there continued to be animosity between the two. Herbert became of increasing importance in the country and, in October 1551, was created Baron Herbert of Cardiff and Earl of Pembroke.

The silver mines in Wexford did not become a successful venture for Recorde. There were a great many problems, all outside his control, which meant that the project never had a chance to succeed. The technology needed to mine the silver was the subject of a dispute with German miners who operated the mines. In addition the treasury would have needed to invest a great deal of money in the venture before they would have seen a return and this they were not able, or perhaps not willing, to do. The Earl of Pembroke certainly did not give Recorde support and by 1553, with the mines showing a loss, the project was closed down and Recorde was recalled to England.

There were other difficulties which were caused by the illness of Edward VI. He showed the first signs of tuberculosis in January 1553 and various factions sought to influence his successor, particularly after May when it was clear to everyone that he was quite close to death. Edward VI died on 6 July and Lady Jane Grey, the duke of Northumberland's daughter-in-law, ruled from 10 July to 19 July before being overthrown by Mary I, a daughter of King Henry VIII. The Church of England had been established in 1534 by Mary's father and Recorde was a supporter of the Reformation. However, Mary sought to reestablish the Roman Catholic Church in England and after she married Philip II of Spain in 1554 they brought back the laws against heresy. During the next three years over 300 heretics were burned at the stake earning her the title "bloody Mary".

The Earl of Pembroke, Recorde's enemy, attended the proclamation of Mary I in London. Mary rewarded his loyalty by making him a privy councillor. When it became clear that Mary would marry Philip there was a rebellion and Pembroke led Mary's troops against the rebels in early in 1554. It was really a very stupid move on Recorde's part, therefore, when in 1556 he attempted to charge Pembroke with misconduct in order to regain his court position. Of course it is almost certain that Recorde had a valid case against Pembroke but there was no way that someone so close to Mary and Philip would allow a minor civil servant like Recorde to get the better of him.

Pembroke countered Recorde's charges by suing Recorde for libel, the bill being served on 16 October 1556. The hearing took place in January 1557 and, almost inevitably, the Earl of Pembroke won his action against Recorde. The award of £1000 which Recorde was ordered to pay to Pembroke was made on 10 February. Either Recorde could not pay this sum, or he chose not to, for he was imprisoned. If indeed he could not pay it was doubly unfortunate for Recorde since he was owed exactly this amount for his services in Ireland which he had never received. In fact the £1000 for his work in Ireland was paid to his estate in 1570, but this was not much use to him as, by this time, he had been dead for twelve years. In the King's Bench prison in Southwark, he made a will on 28 June 1558 leaving small amounts of money to his four sons and five daughters. He died in the prison, probably no more than a few weeks later.

If Recorde showed little common sense in his argument with the Earl of Pembroke, this was in stark contrast to the remarkable good sense and learning which he showed in all his academic work. Recorde virtually established the English school of mathematics and first introduced algebra into England.

He wrote many elementary textbooks and he did this with a very deliberate policy in mind. Firstly he wanted to produce a complete course of mathematical instruction and he wrote his books in the order in which he thought that they should be studied in a mathematics course. It was a course of study which he wanted to be available to everyone, not just the few educated men who could read Latin or Greek. He therefore wrote all his books in English and, in addition, he tried to use clear and simple expressions. In order to do this he had to introduce many new English words to be the equivalent of the Latin or Greek terms in use at that time. It would be nice to think that some of these carefully chosen terms might have survived, but sadly none of them have.

Anyone who reads Recorde's works will be led to believe that, although no evidence survives, he must have taught for some time since he has a deep understanding of how to teach. Ideas are developed clearly step by step, with difficult points being left until the student has gained enough experience to understand them. Although he used the works of others as a basis for much of his work, he certainly did not follow these slavishly, rather picking the best ideas and discarding others. It is clear that when he read a book he always did so critically which, although not remarkable today, certainly was in the 16th century when education was still largely based on slavishly following the classic writers without question.

Recorde published The Grounde of Artes in 1543 which was a very successful commercial arithmetic book:-
... teaching the perfect work and practice of Arithmeticke etc.
in Recorde's own words. The book discusses operations with Arabic numerals, computation with counters, proportion, the 'rule of three', all arithmetic being studied for the natural numbers in the first version which had second and third editons in 1549 and 1550. In 1552 Recorde published a second enlarged version of The Grounde of Artes extending the work of the first edition to rational as well as whole numbers and including such topics as 'false position'.

In 1551 Recorde wrote Pathwaie to Knowledge which some consider an abridged version of Euclid's Elements . It is the only one of his books not written in the form of a dialogue between a master and scholar. No proofs are given in this book but instead Recorde explains why the theorems are true and gives examples to aid a student to understand not only what was being taught, but also why it was being taught.

The Castle of Knowledge was first published in 1556 and gives an elementary introduction to Ptolemy's version of astronomy. It is therefore essentially a mathematical work on the sphere and Recorde certainly read works by Ptolemy, Proclus, Sacrobosco and Oronce Fine before writing his text. We know that he had read these works for he states this in the text and also gives a critical account of the works correcting textural errors in them. It is in this work that Copernicus's heliocentric theory is mentioned, and although Recorde does not say that he himself believes the theory, many historians feel that he probably did. We mentioned above how Mary I had reestablished the Catholic Church and the laws of heresy in 1554 and that many heretics were burned. It may be that here Recorde showed more common sense than he did over the Pembroke affair of 1556, and chose not to commit himself to Copernicus's theory. He wrote:-
Copernicus a man of great learning, of much experience, and of wonderful diligence in observation, hath renewed the opinion of Aristarchus Sainius, and affirmith that the earth not only moveth circularly about his own centre, but also may be, yea and is, continually out of the precise centre of the world 38 hundred thousand miles: but because the understanding of that controversy dependeth upon profounder knowledge than in this Introduction may be uttered conveniently, I will let it pass till some other time.
The 'equals' symbol '=' appears in Recorde's book The Whetstone of Witte published in 1557. He justifies using two parallel line segments:-
... bicause noe 2 thynges can be moare equalle .
The symbol = was not immediately popular. The symbol || was used by some and ae ( or oe), from the word 'aequalis' meaning equal, was widely used into the 1700s.

There is more to The Whetstone of Witte than the equals sign of course. First let us comment on the title which greatly puzzles many people. It is actually a clever pun by Recorde which, sadly, is incomprehensible to people today without explanation. Cosa is Latin for a 'thing' which was used for the unknown in early algebra. Algebraists were called cossists and algebra was known as the cossic art for many years. For example in 1525 Rudolff published the book Coss which was the first German algebra text. The word cos is Latin for whetstone, a stone for sharpening razors and tools. Hence the pun - it was an algebra book on which to sharpen one's mathematical wit!

The book was dedicated to the Muscovy Company which was an association of merchant adventurers founded by the explorer Sebastian Cabot in 1555 and given a monopoly of Anglo-Russian trade. The Company also had as one of its aims to the search for the Northeast Passage. It seems that Recorde advised the Muscovy Company on navigation.

The book was the Second Part of Arithmetic, The Grounde of Artes being the first, covering the extraction of roots, the theory of equations and arithmetic with surds. In his study of quadratic equations, Recorde does not allow solutions which are negative, but he does allow negative coefficients. He makes good use of the sum and product of the roots stressing that for the equation
x2=pxqx^{2} = px - q
the sum of the roots is pp and their product is qq.

One further comment on this algebra book. For many years Stifel was considered as Recorde's major source, but in [5] Hughes argues convincingly that Algebrae compendiosa by J Scheubel published in Paris in 1551 is Recorde's major source.

Finally we note that Recorde did write a medical text The Urinal of Physick (1547) which is [1]:-
A traditional medical work on the judgement of urines, full of sensible nursing practice, [but] less modern than his mathematical works and less critical of authority.

References (show)

  1. J B Easton, Biography in Dictionary of Scientific Biography (New York 1970-1990).
    See THIS LINK.
  2. Biography in Encyclopaedia Britannica.
  3. E Kaplan, Robert Recorde (c. 1510-1558) : studies in the life and works of a Tudor scientist (PhD Thesis New York University, 1960).
  4. M Brooke, A matter of Recorde, J. Recreational Math. 15 (2) (1982/83), 109-111.
  5. B Hughes, Robert Recorde and the first published equation, in Vestigia mathematica (Amsterdam, 1993), 163-171.
  6. S V Larkey, Robert Recorde's Mathematical Teaching and the Anti-Aristotelian Movement, Huntington Library Bulletin 7 (1935), 59-87.

Additional Resources (show)

Honours (show)

Honours awarded to Robert Recorde

  1. Popular biographies list Number 118

Cross-references (show)

Written by J J O'Connor and E F Robertson
Last Update April 2002