Recorde, Robert

(c.1512-1558), mathematician

by Stephen Johnston

© Oxford University Press 2004 All rights reserved

Recorde, Robert (c.1512-1558), mathematician, was the second son of Thomas Recorde of Tenby, Pembrokeshire, and Rose, daughter of Thomas Johns of Machynlleth in Montgomeryshire. Little is known about Recorde's personal life and there is no evidence that he married or had children. A portrait formerly identified as of Recorde is now considered to be Flemish and was found on cleaning to depict a seventeenth-century sitter (Cassels, 59-61).

Recorde studied at Oxford; he graduated BA in 1531 and became a fellow of All Souls in that year. He is reported to have taught mathematics at Oxford and must also have begun the study of medicine there. However, he vacated his fellowship in 1535, and at an unknown date moved to Cambridge where he received an MD in 1545. Recorde was presumably pursuing a career as a physician at this time, and his only non-mathematical publication, The Urinal of Physick, appeared in 1547. The book was dedicated to the warden and Company of Surgeons in London and the dedication shows that Recorde was based in London by 1547. The text is a short compendium on the traditional topic of diagnosis from urine; it was evidently popular and was frequently reprinted, the last edition apparently issued under the title The Judgement of Urines in 1679. Recorde's only other medical writing, an unpublished work on anatomy, has been lost.

Active as a technical adviser in the last decade of his life, Recorde was consulted on questions of navigation and dedicated his Whetstone of Witte (1557) to the Muscovy Company. However, his promise to publish a text on navigation remained unfulfilled. He also advised on a voyage in search of the north-west passage, presumably in the 1550s.

Recorde's most prominent service was to the crown as a mint administrator. Shortly after the accession of Edward VI he was appointed as one of the commissioners to investigate the running of the Bristol mint, which had been reopened in 1546. As a result of the commission, the under-treasurer, William Sharington, was sent to the Tower and Recorde was appointed comptroller of the Bristol mint in January 1549. He was also appointed comptroller of a new mint at Durham House in the Strand. Recorde was placed fully in charge of the Bristol mint in June 1549 but the mint was closed in October and he was confined to court for sixty days after supporting Protector Somerset against Edward VI, and refusing to divert money to Lord John Russell and Sir William Herbert (later earl of Pembroke).

Recorde was nevertheless appointed surveyor of the mines and moneys in Ireland in 1551 and placed in charge of both the Dublin mint and a project to develop silver mines at Wexford. The silver mines failed technically and financially and Recorde was recalled in 1553, having also clashed with the earl of Pembroke over the running of the mint. In 1556 Recorde brought a suit of malfeasance against Pembroke, who in return sued for libel in October of that year. After the hearing in January 1557 Pembroke was awarded £1000 in damages, and Recorde was subsequently committed to the king's bench prison, presumably for debt. Recorde's will was written in the king's bench prison, where he died. It was proved on 18 June 1558. Ironically, in 1570 his estate was paid about £1000 in belated recompense for his services in Ireland.

Recorde had a reputation for wide learning among scholarly contemporaries. He was a student of Greek and Old English and also concerned himself with British history; he had a hand in the 1559 edition of Fabyan's Chronicle and made at least one addition to it. His intellectual range is indicated by a list of works announced in 1551:

Of the peregrination of man, and the original of all nations, The state of times and mutations of realms, The image of a perfect commonwealth, with diverse other works in natural sciences, Of the wonderful works and effects in beasts, plants and minerals. (R. Recorde, The Pathway to Knowledge, 1551, sig. a4r)
Recorde also collected manuscripts and his library was used by bibliophiles such as John Bale. Recorde did not shrink from the religious and political issues of the day. Bale mentions that Recorde had composed tracts 'De auriculari confessione' and 'De negotio Eucharistae', and in late 1550 or early 1551 he testified as a prosecution witness in the trial of Bishop Gardiner. His testimony suggests not only that he was a committed protestant but emphasizes that he was a familiar figure at court; in addition, Recorde says that he was then thirty-eight or thereabouts, providing the most direct evidence for his year of birth.

However, despite this wide range of activity, Recorde is primarily remembered for his mathematical texts. His first publication was his most basic and popular, The Grounde of Artes (1543), an elementary introduction to arithmetic written in dialogue form. After several reissues, the book was enlarged in 1552 with a new dedication to Edward VI which draws on Recorde's mint experience. Though referring to inadequacies in mint standards, he deferred such matters (presumably the debasement of the coinage) to further writings which would need crown approval. After Recorde's death the Grounde was edited first by John Dee and then by a string of successors, passing through at least forty-five editions up to 1699.

Recorde had given considerable and independent thought to questions of didactic exposition and his subsequent mathematical works were issued in the sequence he considered appropriate for teaching. After arithmetic came geometry in the two books of The Pathway to Knowledge (1551; reissued 1574 and 1602). Recorde was conscious that he was here treating a subject never before published in English, and dedicated the work to Edward VI. As printed, the Pathway was, like The Grounde of Artes, an introductory text, in this case simplifying and rearranging the first four books of Euclid's Elements. However, Recorde had intended that there should be two further books leading on from elementary geometry to practical matters such as surveying and map-making. These were not published and neither were other planned works advertised in the Pathway on instruments such as geometrical quadrants, the astronomer's staff, sundials, and an unidentified surveying instrument. Some of this material was no doubt incorporated in a lost text, The Gate of Knowledge, which Recorde later referred to as an account of practical geometry and measurement by the quadrant.

Equipped with the rudiments of geometry the mathematical student could pass on in an orderly and methodical progression from the Pathway to The Castle of Knowledge (1556; reissued 1596). Recorde dedicated this astronomical textbook on the sphere to Queen Mary and also included a Latin address to Cardinal Pole. The text itself drew on and critically reviewed a wide range of Greek and Latin sources from antiquity to the Renaissance, as well as offering instructions on the actual construction of an armillary sphere. Though beyond the scope of his elementary treatment, Recorde made a subtly favourable reference to Copernicus, having the master in the dialogue caution his pupil against an over-hasty dismissal of the seeming absurdity of a moving earth. Such sophisticated and controversial issues of astronomy and cosmology were perhaps intended for another projected but unpublished work, The Treasure of Knowledge.

Although abandoning the previous practice of naming his books as a sequence, Recorde's final publication did develop his didactic scheme. The Whetstone of Witte (1557) supplemented The Grounde of Artes by providing a more advanced treatment of arithmetic as well as some algebra. The work, based principally on German cossist authors such as Johann Scheubel and Michael Stifel, introduced the '+' and '-' signs for the first time in England. Recorde's own contribution to notation was the '=' sign still used today, devised to avoid the tedious repetition of the words 'is equal to' and chosen because he could imagine nothing more equal than two parallel lines of the same length.

Recorde's works were intended as an accessible and readable introduction to mathematics, rather than a repository of elevated or novel results. His preferred dialogue form and choice of the vernacular were meant to render a previously forbidding subject familiar to all, especially those unskilful in Latin. His concern with pedagogical order and his own experience of teaching led him to emphasize the presentation of propositions over the proof of their validity; he believed that students could more readily grasp the subject if the exposition of results was separated from demonstration.

Not all of Recorde's innovations were successful. For example, his efforts to replace Latin terminology with vernacular mathematical terms, such as 'cinkeangle' for pentagon and 'siseangle' for hexagon, were not generally adopted. However, his texts became the undoubted starting point for the vernacular tradition of mathematics in England and there are many references to their importance in the formation of succeeding generations of mathematicians and mathematical practitioners. Although his published mathematical works were largely limited to arithmetic, geometry, and spherical astronomy, his complete programme of publication promoted the idea of the mathematical sciences as a much broader field encompassing practical arts such as surveying and navigation.


J. B. Easton, 'Recorde, Robert', DSB
Emden, Oxf.
J. Venn, ed., Grace book D (1910)
G. Howson, A history of mathematics education in England (1982), chap. 1
F. R. Johnson and S. V. Larkey, 'Robert Recorde's mathematical teaching and the anti-Aristotelian movement', Huntington Library Bulletin, 7 (1935), 59-87
J. Williams, 'Mathematics and the alloying of coinage, 1202-1700 [pt 1]', Annals of Science, 52 (1995), 213-63
E. Kaplan, 'Robert Recorde, c.1510-1558: studies in the life and work of a Tudor scientist', PhD diss., New York University, 1960
The acts and monuments of John Foxe, ed. J. Pratt, [new edn], 6 (1877), 155-6
E. G. R. Taylor, Tudor geography, 1485-1583 (1930), 94
Bale, Index
Heraldic visitations of Wales and part of the marches ... by Lewys Dwnn, ed. S. R. Meyrick, 1 (1846), 68-9
R. Fabyan, The new chronicles of England and France, ed. H. Ellis, new edn (1811), 19
will, PRO, PROB 11/40 sig 29
J. W. S. Cassels, 'Is this a Recorde?', Mathematical Gazette, 60 (1976), 59-61

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