# Robert Recorde - Mathematician

Created | Updated Aug 16, 2012

The single greatest thing that Robert Recorde left behind was indeed great. He changed mathematical notation forever. He invented the equals sign (=). He was also practically the only Welsh mathematician to have gained any fame whatsoever. He worked as a civil servant for most of his life, but in parallel with this life he wrote a succession of excellent (though not always revolutionary) and clearly-explained mathematical texts.

### Life

Robert Recorde was born in 1510, in Tenby, Pembrokeshire, the second son of Thomas Recorde and Rose Jones. Very little else is known of his early childhood, so the next major step in his life that we can be certain of is his entrance into Oxford University in about 1525. Once again, information is hazy, so we do not know which topics he studied, but he graduated with a BA in 1531 and was elected a Fellow of All Souls College in the same year. He would probably have taught at Oxford for a few years, though again we have no evidence to prove this.

The next we see of Recorde is in Cambridge, where he studied for an MD and graduated in 1545 at the age of 35. After graduating he travelled to London, where he spent two years practising medicine. Then came one of the defining events of his life: he was appointed Controller of the Bristol Mint in 1549. It was during his time at the Mint that he made an enemy.

At this time Edward VI was on the throne^{1}. In the same year that Recorde took the job at the Mint, there was an attempted revolt by John Dudley, Earl of Warwick^{2}. A certain Sir William Herbert was one of the principal suppressors of the rebellion in Wiltshire, Devon and Cornwall. Sir William demanded that Recorde divert funds so that he could support his army, but Recorde refused on the grounds that the orders were not from the king. Sir William countered and accused Recorde of treason. He was confined to court for 60 days.

However, royal favour changed quickly in those days and in 1551 Recorde was appointed general surveyor of mines of monies in Ireland, in charge of the Wexford silver mines and the technical supervisor to the Dublin Mint. There was continued animosity with Sir William Herbert, who was created Baron Herbert of Cardiff and Earl of Pembroke for his services to the crown during the rebellion.

Although the silver mines at Wexford had great potential, the enterprise had no great success, mainly due to a lack of royal investment and technology. The mines were closed in 1553 and Recorde was recalled to England.

Then King Edward died and Lady Jane Grey (the Duke of Northumberland's daughter-in-law) ascended to the throne for a grand total of nine days before being overthrown by Mary I, one of the daughters of Henry VIII. Recorde's old enemy the Earl of Pembroke was made a privy councillor for his support of Mary's claim to the monarchy. Mary was a Catholic and was determined to convert the United Kingdom from the Protestantism Edward had supported. To do this, she needed a Catholic husband to provide her with a Catholic heir — and so she announced her planned marriage to Philip II of Spain. There was a rebellion in 1554 when the masses heard the news^{3}. The Earl of Pembroke led his army to put down the rebellion. He did so efficiently, thus gaining royal favour.

For some reason, Recorde chose the moment when Pembroke was strongest to get his own back, charging him with misconduct in order to try to regain his court position. The allegations were almost certainly valid, but Pembroke was in favour with the monarchy and so had almost perfect immunity. Pembroke responded, suing Recorde for libel. There was a hearing in January 1557 and on 10 February, Recorde was ordered to pay the huge sum of £1,000. Recorde either could not or would not pay and was imprisoned^{4}.

Recorde made a will in King's Bench Prison in Southwark, on 28 June, 1558, leaving a little money to each of his four sons and five daughters. We do not know precisely when he died, but it is supposed to have been only a few weeks later, in prison.

### Works

This is where Recorde's genius shows. He almost single-handedly established the English school of mathematics and introduced algebra to England. He also wrote many textbooks with the ambitious aim of producing a complete course of mathematics. He wrote in English so as to be available to any who wished to read his works^{5}. These textbooks were groundbreaking. They were not the impenetrable volumes that most scholars produced then^{6}. Instead, each point was clearly explained and separated from other parts of the text, making it clear and easy to follow.

#### The Ground of Artes - 1543

In Recorde's own words, '... teaching the perfect work and practice of Arithmeticke, etc.' *The Ground of Artes* dealt primarily with operations using Arabic numerals^{7}, proportion, the 'rule of three'^{8} and computation using counters.

*Pathwaie to Knowledge* - 1551

This is considered by some to be an abridged version of Euclid's *Elements*. It is the only one of Recorde's books not to be written in the format of a dialogue between the master and the student. No mathematical proofs are given; instead, theories are explained and reasoned. Examples are given so the student is aware of why this particular branch of mathematics is being taught.

*Castle of Knowledge* - 1556

Including a short introduction to the astronomy of Ptolemy, this is essentially a mathematical study of the sphere. Recorde also mentions Copernicus' heliocentric theory. He probably believed in the theory, but he had enough sense^{9} to remain ambiguous in judgement, saying:

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.

Followers of Copernicus ran the risk of being branded as heretics.

*The Whetstone of Witte* - 1557

This is the first book where the modern equals (=) sign is used. He justifies his choice thus:

bicause noe 2 thynges can be moare equalle

However, it did not become immediately popular. Each mathematician had his own preference. Many preferred two vertical parallel lines (II), and others used '*ae*', from the Latin *aequalis*.

Many are now puzzled by the title of this book, which is in fact a rather nifty pun, only funny when either it is explained or one is well versed in Latin. *Cosa* is the Latin for 'thing', which was used for the unknown in early algebra. Algebraists were therefore often termed cossists and algebra was known as the cossic art. *Cos* is the Latin for 'whetstone'. Thus, the book could be used to sharpen one's mathematical wit.

The actual mathematical subjects of the book are extraction of roots, theories behind equations (this is where the '=' sign comes into its own) and arithmetic with surds. *The Whetstone of Witte* was the second Part of Arithmetic, the first being *The Grounde of Arte*.

Finally, it is also worth noting that Recorde also wrote one book on the subject of medicine, *The Urinal of Physick*, a more traditional volume discussing the judgement of urine as a means of diagnosis. Compared with his mathematical works, it is unremarkable, but still a decent attempt, full of good advice and the like.

^{1}Though the king was too young to rule, and Edward Seymour, Duke of Somerset was the Regent, with the title of 'Protector'.

^{2}And later Duke of Northumberland.

^{3}Having the Welsh Tudors on the throne was tolerable, but a monarch from the Catholic Continent was clearly unacceptable.

^{4}If he could not pay, then it is ironic, because he was actually owed £1,000 for his services to the crown in Ireland. This was eventually paid in 1570, but Recorde had been dead for 12 years so it was doubtless little consolation.

^{5}At this time, most scholarly works were written in Latin or Greek and therefore could only be read by society's learned men. In fact, so little academic study was done in English that Recorde found it necessary to invent new words to equate to the Latin ones. Unfortunately, none of these words survive today.

^{6}And now, and probably in the foreseeable future as well.

^{7}More correctly Indian numerals, these are the numbers we use today. They are far less cumbersome than Roman numerals when it comes to producing large numbers and performing calculations.

^{8}Finding the fourth term of mathematical proportion when three other terms are given, where the products of the first and fourth terms are equal to the product of the second and third.

^{9}More sense than he showed in accusing the Earl of Pembroke of misconduct, at least.