Robert Recorde

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.

The 16th-Century intellectual Robert Recorde is chiefly remembered for introducing the equals sign into algebra, yet the greater significance and broader scope of his work is often overlooked. This book presents an authoritative and in-depth analysis of the man, his achievements and his historical importance. This scholarly yet accessible work examines the latest evidence on all aspects of Recorde’s life, throwing new light on a character deserving of greater recognition. Topics and features: presents a concise chronology of Recorde’s life; examines his published works; describes Recorde’s professional activities in the minting of money and the mining of silver, as well as his dispute with William Herbert, Earl of Pembroke; investigates Recorde’s work as a physician, his linguistic and antiquarian interests, and his religious beliefs; discusses the influence of Recorde’s publisher, Reyner Wolfe, in his life; reviews his legacy to 17th-Century science, and to modern computer science and mathematics.

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This enthralling biography tells the complete story of one of Tudor England’s most enigmatic figures. A Welshman born in Tenby, south Wales, c.1512, Robert Recorde was educated at both Oxford and Cambridge. This book, a detailed biography of this Tudor scholar, reviews the many facets of his astonishingly wide-ranging career and ultimately tragic life. It presents a richly detailed and fully rounded picture of Recorde the man, the university academic and theologian, the physician, the mathematician and astronomer, the antiquarian, and the writer of hugely successful textbooks. Crown appointments brought Recorde into conflict with the scheming Earl of Pembroke, and eventually set him at odds with Queen Mary I. As an intellectual out of his depth in political intrigue, beset by religious turmoil, Recorde eventually succumbed to the dangers that closed inexorably around him.

The first edition of Robert Recorde's The Pathway to Knowledge was printed in London, at the sign of the Brazen Serpent, by Reynold Wolfe in 1551. This book is the earliest work on geometry in the English language and was used as a standard textbook well into the middle of the seventeenth century. Recorde's prose is delightfully rhythmical and his poetical phrasing perhaps made learning less of a chore than otherwise for his studious readers. That he well knew this book, although modelled after Euclid, was breaking new ground is evidenced by his statement in the preface to the theorems: 'For nother is there anie matter more straunge in the english tongue, than this whereof never booke was written before now, in that tongue, and therefore oughte to delite all them, that desire to understand straunge matters, as most men commonlie doo'. Recorde encountered an unexpected difficulty when setting out to teach Euclidean geometry to English readers. He found that the English language did not (at that time) have a sufficiency of technical terms. But rather than use longstanding Latin or Greek words, he invented his own English equivalents. So for example, obtuse angles are 'blunt corners', an equilateral triangle is a 'threelike' and a square is a 'likeside'. Unfortunately, Recorde's terminology was not taken up and did not survive the passage of time. Hence schoolchildren in geometry lessons today have to wrestle with difficult Latin words like tangent, instead of Recorde's much more homely and easily understood 'touch line'. The mathematical text itself is extremely lucid in both exposition and diagrams, proceeding from a list of definitions through forty-six constructions and seventy-seven theorems. At the start of the definitions is the statement that 'Geometry teacheth the drawyng, measuring and proporcion of figures' and history produced no finer or more eloquent tutor in the subject than Robert Recorde.

First full-length biography of Robert Recorde. This will benefit general readers wanting a chronological history of his life, or those interested in learning more about him in relation to other events in the Tudor period. Two chapters devoted to Recorde’s academic studies at Oxford and Cambridge. This will benefit readers interested in the life of scholars at university during the Tudor period. Describes the training and practice of a physician, of interest to readers pursuing the history of medicine in the Tudor period. Book contains numerous extracts from Recorde’s own writings transcribed into Modern English. Of benefit to readers wanting to read the original texts written in Early Modern English.

The sole edition of Robert Recorde's The Whetstone of Witte was printed at London by John Kingston in 1557. One of Recorde's concerns in this book is to develop not only a means of representing powers of numbers, but also a means of naming them. Prior to the development of a numerical index notation, the names given to the powers was of considerable importance. Hence in these pages we find terminology which is now archaic, for instance the strange word zenzizenzizenzike, the name for the eighth power of a number. It is generally acknowledged that Recorde's treatise on algebra, in the section entitled The arte of cossike numbers, is the first to be printed in the English language. Although this work owes much to the German mathematicians Christoff Rudolff and Michael Stifel, it does have one well known claim to originality; the first use of two parallel lines as the sign for equality (because noe 2 thyngs, can be moare equalle). Recorde's invention of the equals sign =, together with his adoption of the + sign (which betokeneth more) and the minus sign – (which betokeneth less) placed him at the very forefront of European practice. Like most of Recorde's books, The Whetstone is written in the form of a dialogue between a learned master and a clever, but rather precocious, scholar. After being patiently encouraged through the seconde parte of arithmetic (begun by the scholar in Recorde's first book, The Grounde of Artes) followed by the extraction of rootes, the scholar remarks 'I am moche bounde unto you … Trusting so to applie my studie, and emploie my knowlege, that it shall never repente you of your curtesie in this behalfe'. To which the master, about to start an exposition on the difficult and strange cossike arte (algebra), replies 'Then marke well my words, and you shall perceive, that I will use as moche plainesse, as I maie, in teaching : And therefore will beginne with cossick numbers first'. Here Recorde is again using terminology that is now archaic. In his day algebra was called the cossic art, derived from the Latin cosa, meaning 'thing'. The Whetstone also includes a lengthy treatise on the arte of surde nombers, that is, on irrational numbers.

Putting Two and Two Together is a humorous and quirky collection of unusual, ingenious, and beautiful morsels of mathematics. Authors Burkard Polster (YouTube's Mathologer) and Marty Ross delve into mathematical puzzles and phenomena in engaging stories featuring current events, sports, and history, many flavored with a distinctive bit of Australiana. Each chapter ends with “puzzles to ponder” that will spur further reflection. These stories were written for a general audience, and originally appeared in the Maths Masters column in The Age newspaper. The book offers mathematical entertainment for curious readers of all ages, and assumes a minimum of mathematical background. Polster and Ross are masters of the genre this book represents: a cornucopia of offerings, from across the mathematical spectrum. Their articles are entertaining, captivating, and informative, and will appeal to everyone from interested amateurs to old pros. On top of all that, the prose is clear, concise and a lot of fun—happily with a charmingly Aussie flavo(u)r. Crack the spine and enjoy! —Michael Berg, Loyola Marymount University, Los Angeles The American Mathematical Society must be congratulated on publishing a singularly amusing synthesis of cultural anthropology coupled with mathematical entertainment. —Tushar Das, University of Wisconsin–La Crosse Polster and Ross are as good as the original master, Martin Gardner! They are also as good as that other great popularizer of mathematics, Ian Stewart, who took up Gardner's mantle, and as good as Douglas Hofstedter, who also followed in Gardner's footsteps as popularizers of mathematics within regular columns in “Scientific American”, and elsewhere. I recommend this new book very highly! Like Poster and Ross's first collection of columns, it is one that you can happily read from cover to cover, or dip into at any random point, and find treasures. You will then often return, savouring, and often laughing, while also learning, and responding to thoughtful challenges! —John Gough, Deakin University, Geelong, Australia