# The teaching of mathematics in Britain in the Seventeenth Century.

The real and permanent advances in Scottish Education occurred in the 17th century with the Education Acts of 1616, the first of which required every parish to establish a school and to find a suitable schoolmaster to teach the children of that area. Further Acts were soon required due to the lack of action being taken in response to these Acts but it wasn't until that of 1646, which required landowners to provide a suitable building for a schoolhouse and wages for the schoolmaster, that attempts were made to obey. Efforts did not end with the opening of a school in the parish or burgh; Councils often had to pass acts requiring the parents in the area to send their children to the school so that they might then benefit from this service. In Peebles, for example, the town officer was often required to move through the town and order the children to appear in school the next day or else their parents would be fined, the proceeds of which would then go to the schoolmaster to eke out his salary. By the mid 17th century in the larger towns, where the Burgh Schools were beginning to specialise in the higher studies, Councils were beginning to license private teachers in an effort to regain some form of control over these independent agents. It was now often the case that children would first go to a small private school to learn the basics of reading, writing and counting, before moving to the Grammar School to begin their lessons in Latin. Those being prepared for University would also occasionally get some grounding in further Arithmetic and Euclidean Geometry.

Not everything ran smoothly, however, and despite the Councils' best efforts there was little money to be spent on opening schools in the more rural areas of Scotland and by 1650 only a fraction of the parishes were supplied with any form of school. Additional Acts in 1690, 1693 and 1699 followed before the Union of 1707, after which almost a century went by before the Westminster Parliament produced its first measure dealing with Scottish Schools.

By the beginning of the 17th century the English Universities had partially revised their opinion of Mathematics and had started to increase the quality of Mathematics instruction available. Oxford and Cambridge had both managed to produce several Mathematicians of excellent quality, despite the lack of support and encouragement those wishing to study the subject received. This changed when the first Chair in Geometry was set up in Oxford in 1619, six years after the Mathematics Chair in Aberdeen started being held by a regent who taught Arithmetic, Geometry and Classical Physics. Cambridge was much slower in recognising Mathematics as anything other than a subdivision of the three Philosophies, and the Lucasian Chair in Mathematics was not established until 1662. Although this increase in education in Mathematics was noticeable, the continued separation of University Mathematics and the commercial and industrial needs of the general populace continued and so a new educational establishment was formed.

Gresham College, founded in the late 1650's, was intended to provide a much more practical and useful knowledge of the sciences. It was vastly successful in this aim, giving public lectures in both Latin and English on topics drawn from Geometry, Astronomy and Mathematics which attracted large numbers of people. It was through Gresham's that Logarithms and Trigonometrical advances relating to Navigation were spread so quickly after their development. It was also at Gresham College that what was later called the Royal Society of London started holding their discussions and lectures on Experimental science. The Society was not formally recognised by the crown until 1662, but many of those involved moved in influential circles and did much to improve the state of Mathematical education yet further. One such was Samuel Pepys whose endeavours finally led to the Royal Mathemtical School being established in Christ's Hospital School in 1673. Although this school had a very troubled and chequered start, it did accomplish a lot and the Mathematical education of the prospective officers for the Navy did improve. Other Colleges and Universities proposed to help spread the knowledge of the Mathematical Sciences and other subjects were quashed by Charles II in 1660.

One of the biggest turning points in English Education was the Act of Uniformity passed in 1662. This required all of the clergy and all teachers at all levels to swear that they would in no way seek any changes to Church or State and that they would conform to the Book of Common Prayer and the thirty-nine Articles. Penalties for not swearing to this code of conduct included fining and a possible prison sentence. Approximately 1760 of the clergy and over 150 dons and school teachers were evicted because of their conviction in their beliefs. Many of the evicted teachers chose to set up their own schools until the Five Mile Act of 1665 which restrained the dissenting clergy from coming within five miles of towns or cities. It was also made illegal for any of these dissenters to work in any private (or public) school. These actions led to the foundation of the Dissenting Colleges.

Like all other schools at this time, the early dissenting colleges and institutions varied a great deal in curriculum and standards. Some, like Richard Frankland's Academy, were comparable to Oxford and Cambridge and students were allowed to graduate from Edinburgh University after only a single year's extra study. The courses run were also very similar to those at the two well established Universities and favoured the classics over all else. Not all followed this path, especially after the Toleration Act of 1685 when many Academies followed John Jenning's lead and broadened their syllabuses to include subjects like advanced Algebra and Geometry, Logarithms and Surveying. These topics were taught by educators such as Adam Martindale and Humphrey Ditton (who later became a Mathematics Master at Christ's Hospital).

One of the students to benefit from the knowledge available at Dissenting Colleges and Academies was Isaac Watts. Believing that an understanding of Mathematics was a step towards an acceptance of God, he learnt as much of the subject as he could while at College. In later years he campaigned vigorously for Mathematics to have a place of honour in the curriculum justifying this on utilitarian, liberal, moral and religious grounds. Isaac Watts was joined in these views by other influential Mathematicians, such as the traditionally trained Isaac Newton and fellow educator Philip Dodderidge. However, both Watts and Philip Doddridge argued against allowing students to pursue mathematical truths for too long believing that this led to abstraction from the real world. Similar opinions had been held a hundred years before by Vives, tutor to Henry VIII's daughters, and centuries before by the Romans. Despite all of this when other religious groups started setting up boarding schools they followed the curriculum found in the most modern Dissenting Colleges.

Schools and Colleges were not the only source of learning, private tutors also picked up on the need for a practical mathematical education and rapidly advertised their skills in this area. It took just nine short years from Napier's

Not everything ran smoothly, however, and despite the Councils' best efforts there was little money to be spent on opening schools in the more rural areas of Scotland and by 1650 only a fraction of the parishes were supplied with any form of school. Additional Acts in 1690, 1693 and 1699 followed before the Union of 1707, after which almost a century went by before the Westminster Parliament produced its first measure dealing with Scottish Schools.

By the beginning of the 17th century the English Universities had partially revised their opinion of Mathematics and had started to increase the quality of Mathematics instruction available. Oxford and Cambridge had both managed to produce several Mathematicians of excellent quality, despite the lack of support and encouragement those wishing to study the subject received. This changed when the first Chair in Geometry was set up in Oxford in 1619, six years after the Mathematics Chair in Aberdeen started being held by a regent who taught Arithmetic, Geometry and Classical Physics. Cambridge was much slower in recognising Mathematics as anything other than a subdivision of the three Philosophies, and the Lucasian Chair in Mathematics was not established until 1662. Although this increase in education in Mathematics was noticeable, the continued separation of University Mathematics and the commercial and industrial needs of the general populace continued and so a new educational establishment was formed.

Gresham College, founded in the late 1650's, was intended to provide a much more practical and useful knowledge of the sciences. It was vastly successful in this aim, giving public lectures in both Latin and English on topics drawn from Geometry, Astronomy and Mathematics which attracted large numbers of people. It was through Gresham's that Logarithms and Trigonometrical advances relating to Navigation were spread so quickly after their development. It was also at Gresham College that what was later called the Royal Society of London started holding their discussions and lectures on Experimental science. The Society was not formally recognised by the crown until 1662, but many of those involved moved in influential circles and did much to improve the state of Mathematical education yet further. One such was Samuel Pepys whose endeavours finally led to the Royal Mathemtical School being established in Christ's Hospital School in 1673. Although this school had a very troubled and chequered start, it did accomplish a lot and the Mathematical education of the prospective officers for the Navy did improve. Other Colleges and Universities proposed to help spread the knowledge of the Mathematical Sciences and other subjects were quashed by Charles II in 1660.

One of the biggest turning points in English Education was the Act of Uniformity passed in 1662. This required all of the clergy and all teachers at all levels to swear that they would in no way seek any changes to Church or State and that they would conform to the Book of Common Prayer and the thirty-nine Articles. Penalties for not swearing to this code of conduct included fining and a possible prison sentence. Approximately 1760 of the clergy and over 150 dons and school teachers were evicted because of their conviction in their beliefs. Many of the evicted teachers chose to set up their own schools until the Five Mile Act of 1665 which restrained the dissenting clergy from coming within five miles of towns or cities. It was also made illegal for any of these dissenters to work in any private (or public) school. These actions led to the foundation of the Dissenting Colleges.

Like all other schools at this time, the early dissenting colleges and institutions varied a great deal in curriculum and standards. Some, like Richard Frankland's Academy, were comparable to Oxford and Cambridge and students were allowed to graduate from Edinburgh University after only a single year's extra study. The courses run were also very similar to those at the two well established Universities and favoured the classics over all else. Not all followed this path, especially after the Toleration Act of 1685 when many Academies followed John Jenning's lead and broadened their syllabuses to include subjects like advanced Algebra and Geometry, Logarithms and Surveying. These topics were taught by educators such as Adam Martindale and Humphrey Ditton (who later became a Mathematics Master at Christ's Hospital).

One of the students to benefit from the knowledge available at Dissenting Colleges and Academies was Isaac Watts. Believing that an understanding of Mathematics was a step towards an acceptance of God, he learnt as much of the subject as he could while at College. In later years he campaigned vigorously for Mathematics to have a place of honour in the curriculum justifying this on utilitarian, liberal, moral and religious grounds. Isaac Watts was joined in these views by other influential Mathematicians, such as the traditionally trained Isaac Newton and fellow educator Philip Dodderidge. However, both Watts and Philip Doddridge argued against allowing students to pursue mathematical truths for too long believing that this led to abstraction from the real world. Similar opinions had been held a hundred years before by Vives, tutor to Henry VIII's daughters, and centuries before by the Romans. Despite all of this when other religious groups started setting up boarding schools they followed the curriculum found in the most modern Dissenting Colleges.

Schools and Colleges were not the only source of learning, private tutors also picked up on the need for a practical mathematical education and rapidly advertised their skills in this area. It took just nine short years from Napier's

*Descripto*(the English translation was published two years later) for Logarithms to be advertised and taught by men such as Robert Hartwell. The quality and the quantity of teaching still varied hugely, and a significant number of students entering Oxford and Cambridge in the 1630's still had no prior knowledge of the Hindu-Arabic numeral system. This contrasts greatly with the education available in parts of Hampshire where Sir William Petty was taught all the Rules of common Arithmetic, Practical Geometry and the astronomical parts of Navigation at a school in Romsey. At this stage there was no external examination of schools and the curriculum and syllabus of each was decided by the head teacher.**Article by:***J J O'Connor*and*E F Robertson*based on a University of St Andrews honours project by Elizabeth Watson submitted May 2000.