William Oughtred born on the 5^{th} March 1575, who Newton regarded along with Christopher Wren and John Wallis as one of the three best seventeenth-century English mathematicians, was the epitome of the so-called English School of Mathematics. The English School of Mathematics is a loose historical grouping of English mathematicians stretching over several generations in the sixteenth and seventeenth centuries who propagated and supported the spread of mathematics, mostly in the vernacular, through teaching and writing at a time when the established educational institutions, schools and universities, offered little in the way of mathematical tuition. These men taught each other, learnt from each other, corresponded with each other, advertised each other in their works, borrowed from each other and occasionally stole from each other building an English language mathematical community that stretched from Robert Recorde (c. 1512 – 1558) who is regarded as its founder to Isaac Newton at the close of the seventeenth century who can be regarded as a quasi member. Oughtred who died in 1660 spanned the middle of this period and can be considered to be one of its most influential members.

Oughtred was born at Eton College where his father Benjamin was a writing master and registrar and baptised there on 5^{th} March 1575, which is reputedly also his birthdate. He was educated at Eton College and at King’s College Cambridge where he graduated BA in 1596 and MA in 1600. It was at Cambridge that he says he first developed his interest for mathematics having been taught arithmetic by his father. Whilst still at Cambridge he also started what was to become his vocation, teaching others mathematics. He was ordained priest in 1603 and appointed vicar of Shalford in Surry. In 1610 he was appointed rector of nearby Albury where he remained for the rest of his life. He married Christgift Caryll in 1606, who bore him twelve or possibly thirteen children, accounts differ. All in all Oughtred lived the life of a simple country parson and would have remained unknown to history if it had not been for his love of mathematics.

Oughtred’s first claim to fame as a mathematician was as a pedagogue. He worked as a private tutor and also wrote and published one of the most influential algebra textbooks of the century his *Clavis Mathematicae* first published in Latin in 1631. This was a very compact introduction to symbolic algebra and was one of the first such books to be written almost exclusively in symbols, several of which Oughtred was the first to use and which are still in use today. Further Latin edition appeared in 1648, 1652, 1667 and 1698 with an English translation appearing in 1647 under the title *The Key to Mathematics*.

The later editions were produced by a group of Oxford mathematicians that included Christopher Wren, Seth Ward and John Wallis. Seth Ward lived and studied with Oughtred for six months and Wallis, Wren and Jonas Moore all regarded themselves as disciples, although whether they studied directly with Oughtred is not known. Wallis probably didn’t but claimed to have taught himself maths using the *Clavis*.

The Latin editions of the *Clavis* were read throughout Europe and Oughtred enjoyed a very widespread and very high reputation as a mathematician.

Although he always preached the importance of theory before application Oughtred also enjoyed a very high reputation as the inventor of mathematical instruments and it is for his invention of the slide rule that he is best remembered today. The international society for slide rule collectors is known as the Oughtred Society. I realise that in this age of the computer, the tablet, the smart phone and the pocket calculator there is a strong chance that somebody reading this won’t have the faintest idea what a slide rule is. I’m not going to explain although I will outline the historical route to the invention of the slide rule but will refer those interested to this website.

The Scottish mathematician John Napier and the Swiss clock and instrument maker Jobst Bürgi both invented logarithms independently of each other at the beginning of the seventeenth century although Napier published first in 1614. The basic idea had been floating around for sometime and could be found in the work of the Frenchman Nicolas Chuquet in the fifteenth century and the German Michael Stifel in the sixteenth. In other words it was an invention waiting to happen. Napier’s logarithms were base ‘e’ now called natural logarithms (that’s the ln key on your pocket calculator) and the English mathematician Henry Briggs (1561 – 1630), Gresham Professor of Geometry, thought it would be cool to have logarithms base 10 (that’s the log key on your pocket calculator), which he published in 1620. Edmund Gunter (1581 – 1626), Gresham Professor of Astronomy, who was very interested in cartography and navigation, produced a logarithmic scale on a ruler, known, not surprisingly, as the Gunter Scale or Rule, which could be read off using a pair of dividers to enable navigators to make rapid calculations on sea charts.

Briggs introduced his good friend Oughtred to Gunter, remember that bit above about teaching, learning etc. from each other, and it was Oughtred who came up with the idea of placing two Gunter Scales next to each other to facilitate calculation by sliding the one scale up and down against the other and thus the slide rule was born. Oughtred first published his invention in a pamphlet entitled *The Circles of Proportion and the Horizontal Instrument* in 1631, which actually describes an improved circular slide rule with the scales now on circular discs rotating about a central pin. This publication led to a very nasty dispute with Richard Delamain, a former pupil of Oughtred’s who claimed that he had invented the slide rule and not his former teacher. This led to one of those splendid pamphlet priority wars with both antagonists pouring invective over each other by the bucket load. Oughtred won the day both in his own time and in the opinion of the historians and is universally acknowledged as the inventor of the slide rule, which became the trusty companion of all applied mathematicians, engineers and physicist down the centuries. Even when I was at secondary school in the 1960s you would never see a physicist without his trusty slide rule.

It still seems strange to me that more than a whole generation has grown up with no idea what a slide rule is or what it could be used for and that Oughtred’s main claim to fame is slowly but surely sliding into the abyss of forgetfulness.

Moment of nostalgia: back in the 60s, you could tell you were in a high school math classroom by the enormous slide rule hanging up by the front blackboard. It was just as emblematic as the stuffed crocodile always seen in old pictures of Baroque Wunderkammern; but unlike the crocodile, the teaching slide rule was perfectly functional. Teachers did problems on them.

Thony, I have notes that suggest (to me) that slide rules were pretty rare in the US up into the last few decades of the 19th C.

For example, Cajori’s HISTORY OF THE LOGARITHMIC SLIDE RULE, (1909),”it appears that, before 1880 or 1885, the slide rule was little known and very little used in the United States. References to it are seldom found in engineering literature. Appleton.s Dictionary of Engineering, Vol. I, New York, 1868, does not name the slide rule, but devotes three or four lines to a description of it under the head of Gunter’s line.. Knight’s American Mechanical Dictionary, Vol. II, 1881, describes Gunter’s line; then, without naming the slide rule, describes it in four lines and ends with the statement to the effect that these “instruments” are now common among intelligent workmen..”

Another says, “In 1929 the slide rule became a formal part of the mathematics program and served as the midshipmen’s primary calculator until 1976.” [From “A Brief History of the Department of Mathematics” by Professor T. J. Benac ]

Was it that much more common in Europe?

Oh yes! Please do not forget the slide rule! A whole lot of physics and invention was needed prior to the manufacture of the first affordable compact calculator capable of raising any number to any power or finding any root of any number, it had all the trig and inverse trig functions and of course logarithms. Not only did I have several slide rules but I also had my trusty book of logarithms. Remember those? Remember the red on black display of the first hand calculators? Thank you Texas Instruments. Remember when calculators were completely and totally banned from mathematics class?

My grandfather carried a wonderful slide rule. It was not one of the plastic versions. It had heft, a high precision cursor slide and a leather case.

“that somebody reading this won’t have the faintest idea what a slide rule is.”

That would be me but then before reading the blog I would have considered the history of maths to be a somewhat obscure and deeply boring subject with no relevance to anyone other than a maths nerd.

But I can label that thought and place it with a vast range of other biases in the stupid and ignorant section.

Still have zero interest in maths, its well beyond my skill set at anything other than a very basic level. Well presented history, presenting the subject in a wider context, provokes a somewhat different emotion.

It also makes people who engage in such weird and deeply strange forms of behavior, such as a love of maths, look almost human and part of (and relevant to the history of) a wider society!

p.s When you look at the contemporary issues in science culture its easy to lose sight of the subjects relevance to understanding the history culture in wider perspective.

It sometimes seems a curse taking an interest. Science is a distinct and and times highly problematic cultural entity. Not easy to understand its contemporary emotive cultural politics or its distinctive sense of self- identity and taste for historical romance.

And of course the slide rule was featured on the greatest

Astounding Science Fictioncover of all time:Returning after fifty years to my shirt pocket K&E I was astounded to discover how enjoyable it was to use! I felt a certain closeness to the mathematics not found at a keyboard. As if I was touching the actual math. I now use it every day. The great sadness is we have denied recent generations the chance to hold mathematics in their hands.

This of course needs to be tied in with the Warrior Chronicles series of books by Bernard Cornwell. Just sayin’. Never pass up an Oughtred (== Uhtred)

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