# Mathematics in Scotland in 1883

In 1883 there were four universities in Scotland: the Universities of Aberdeen, Edinburgh, Glasgow and St Andrews.

You can read here extracts from the respective Calendars of 1883 about the founding of these universities at THIS LINK.

Let us give some details of the Departments in the four universities and number of students who were graduating with a mathematics degree in the preceding couple of years. We also see which of these students became involved in the Edinburgh Mathematical Society.

At Aberdeen the Professor of Mathematics in 1883 is George Pirie who had been appointed in 1878, replacing Frederick Fuller who retired in that year. The Professor of Natural Philosophy is Charles Niven who was appointed in 1880 to replace David Thomson who died in 1880.

In 1881, seven students had graduated with an M.A. with Honours in Mathematics, while in 1882 there were also seven. In both years four of the students were First Class, while the other three were Second Class. One of the students graduating in 1881 was Alexander Yule Fraser, who was a Boxill Mathematical Prizeman, and went on to become a mathematics master at George Watson's College, Edinburgh, and was one of the three signatories of the letter proposing to set up the Edinburgh Mathematical Society. Another graduating in the same year was John Jack who joined the Edinburgh Mathematical Society in November 1895 when Professor of Mathematics at Wilson College, Bombay. W Cooper Dickson, one of the First Class students of 1882 was a founder member of the Edinburgh Mathematical Society, joining in February 1883 while training for ministry in the Church.

At Edinburgh George Chrystal is the professor of mathematics in 1883. He was appointed in 1879 replacing Philip Kelland who had been the professor for over forty years from 1838 to 1879. The Professor of Natural Philosophy is Peter Guthrie Tait who was appointed in 1860 to replace James David Forbes who had moved to St Andrews University to become Principal of the University.

In 1882 one student graduated from Edinburgh with an M.A. with Honours in Mathematics, namely R Edgar Allardice who graduated First Class in 1882, joined Edinburgh Mathematical Society as a founder member in February 1883, and became Assistant to the Professor of Mathematics in the University of Edinburgh. In the following year of 1883 three students graduated from Edinburgh with an M.A. with Honours in Mathematics. Two, who were both awarded First Class degrees, became members of the Edinburgh Mathematical Society. C W Crossley Barlow joined as a founder member in February 1883 when at St Peter's College, Cambridge and George N Stewart joined in November 1884, and then went to Owen's College, Manchester a couple of years later.

At Glasgow the Professor of Mathematics in 1883 is William Jack, who had been appointed in 1879, replacing Hugh Blackburn who had been the professor of mathematics for thirty years 1849-1879. The Professor of Natural Philosophy is Sir William Thomson (Lord Kelvin) appointed 1846 to replace W Meikleham who had held the position from 1803 to 1846.

Five students had graduated with an M.A. with Honours in Mathematics and Natural Philosophy in 1881, two with a First Class and three with a Second Class degree. One of the First Class students was Robert Franklin Muirhead who joined the Edinburgh Mathematical Society in February 1884. The other was Alexander Russell who joined the Society in March 1884 while at Caius College, Cambridge. Of the Second Class students, one was James Hamilton, who joined the Edinburgh Mathematical Society in April 1885 when a Mathematical Master at Kensington Grammar School, London. In 1882 only one student graduated with an M.A. with Honours in Mathematics and Natural Philosophy. He was John Weir who was awarded First Class Honours and joined the Edinburgh Mathematical Society in December 1884 when at St Peter's College, Cambridge.

At St Andrews the Regius Professor of Mathematics in 1883 is R P Scott Lang who was appointed in 1879 to replace George Chrystal who, after two years as Regius Professor had moved to Edinburgh. Before George Chrystal the Regius Professor had been William L F Fischer who held the position from 1859 to 1877. The Professor of Natural Philosophy is Arthur S Butler, who was appointed in 1880 to replace William Swan who was Professor from 1859 to 1880.

Two students had graduated with an M.A. with Honours in Mathematics and Natural Philosophy in 1881, both with a First Class degree. One of these students was R C Buist, who joined Edinburgh Mathematical Society in December 1884. Similarly two students had graduated with an M.A. with Honours in Mathematics and Natural Philosophy in 1882, both with a First Class degree. One of these students was David Rintoul who joined the Edinburgh Mathematical Society as a founder member in February 1883 when he was at Corpus Christi College, Cambridge.

To sum up the results over these two years, it works out that the four Scottish Universities are producing on average about 14 Honours Mathematics per year, approximately 9 of First Class and two of Second Class. It is interesting to note that over these two years Aberdeen produced as many honours mathematics graduates as the other three universities put together.

To see the structure of the courses these students were taking we quote from the respective university Calendars of 1883.

Mathematics in Aberdeen University in 1883

Mathematics in Edinburgh University in 1883

Mathematics in Glasgow University in 1883

Mathematics in St Andrews University in 1883

Some sample questions from the Mathematics and Natural Philosophy examination papers set at Scottish Universities from around this time can be found at THIS LINK

Finally we look at the position of women with regard to university level mathematics in Scotland in 1883. They were not entitled to graduate with a degree. This was not the decision of the individual universities but rather it required an act of Parliament to allow women to graduate. All four universities did, however, offer certificates for women of degree standard.

In 1883 the University of Aberdeen had a "Higher Certificate for Women". The regulations state that:

In 1883 the University of Edinburgh had an "Ordinary Certificate in Arts for Women" and an "Honour Certificate in Arts for Women". The regulations state that:

In 1883 the University of Glasgow held local examinations for Certificates:

Women were admitted to the M.A. classes of the University of Glasgow in 1896. The first woman to graduate M.A. with Honours in Mathematics and Natural Philosophy was Elizabeth Pettigrew Taylor (First Class) in 1898.

The University of St Andrews appears to have made the most progress in women's university level education. They had introduced a Higher Certificate For Women, with the title of L.L.A. (

The centres for Examination in 1882 were St Andrews, London, Halifax, Bristol, and Belfast. Clearly the L.L.A. was popular since by 1885 the centres were Aberdeen, Barbados, Belfast, Birmingham, Bristol, Cheltenham, Edinburgh, Eisenach, Halifax, Hildesheim, Leicester, Lerwick, Liverpool, London, Paris, Pietermaritzburg, and St Andrews.

By 1885 some other changes had been introduced:

You can read here extracts from the respective Calendars of 1883 about the founding of these universities at THIS LINK.

Let us give some details of the Departments in the four universities and number of students who were graduating with a mathematics degree in the preceding couple of years. We also see which of these students became involved in the Edinburgh Mathematical Society.

**Aberdeen**

At Aberdeen the Professor of Mathematics in 1883 is George Pirie who had been appointed in 1878, replacing Frederick Fuller who retired in that year. The Professor of Natural Philosophy is Charles Niven who was appointed in 1880 to replace David Thomson who died in 1880.

In 1881, seven students had graduated with an M.A. with Honours in Mathematics, while in 1882 there were also seven. In both years four of the students were First Class, while the other three were Second Class. One of the students graduating in 1881 was Alexander Yule Fraser, who was a Boxill Mathematical Prizeman, and went on to become a mathematics master at George Watson's College, Edinburgh, and was one of the three signatories of the letter proposing to set up the Edinburgh Mathematical Society. Another graduating in the same year was John Jack who joined the Edinburgh Mathematical Society in November 1895 when Professor of Mathematics at Wilson College, Bombay. W Cooper Dickson, one of the First Class students of 1882 was a founder member of the Edinburgh Mathematical Society, joining in February 1883 while training for ministry in the Church.

**Edinburgh**

At Edinburgh George Chrystal is the professor of mathematics in 1883. He was appointed in 1879 replacing Philip Kelland who had been the professor for over forty years from 1838 to 1879. The Professor of Natural Philosophy is Peter Guthrie Tait who was appointed in 1860 to replace James David Forbes who had moved to St Andrews University to become Principal of the University.

In 1882 one student graduated from Edinburgh with an M.A. with Honours in Mathematics, namely R Edgar Allardice who graduated First Class in 1882, joined Edinburgh Mathematical Society as a founder member in February 1883, and became Assistant to the Professor of Mathematics in the University of Edinburgh. In the following year of 1883 three students graduated from Edinburgh with an M.A. with Honours in Mathematics. Two, who were both awarded First Class degrees, became members of the Edinburgh Mathematical Society. C W Crossley Barlow joined as a founder member in February 1883 when at St Peter's College, Cambridge and George N Stewart joined in November 1884, and then went to Owen's College, Manchester a couple of years later.

**Glasgow**

At Glasgow the Professor of Mathematics in 1883 is William Jack, who had been appointed in 1879, replacing Hugh Blackburn who had been the professor of mathematics for thirty years 1849-1879. The Professor of Natural Philosophy is Sir William Thomson (Lord Kelvin) appointed 1846 to replace W Meikleham who had held the position from 1803 to 1846.

Five students had graduated with an M.A. with Honours in Mathematics and Natural Philosophy in 1881, two with a First Class and three with a Second Class degree. One of the First Class students was Robert Franklin Muirhead who joined the Edinburgh Mathematical Society in February 1884. The other was Alexander Russell who joined the Society in March 1884 while at Caius College, Cambridge. Of the Second Class students, one was James Hamilton, who joined the Edinburgh Mathematical Society in April 1885 when a Mathematical Master at Kensington Grammar School, London. In 1882 only one student graduated with an M.A. with Honours in Mathematics and Natural Philosophy. He was John Weir who was awarded First Class Honours and joined the Edinburgh Mathematical Society in December 1884 when at St Peter's College, Cambridge.

**St Andrews**

At St Andrews the Regius Professor of Mathematics in 1883 is R P Scott Lang who was appointed in 1879 to replace George Chrystal who, after two years as Regius Professor had moved to Edinburgh. Before George Chrystal the Regius Professor had been William L F Fischer who held the position from 1859 to 1877. The Professor of Natural Philosophy is Arthur S Butler, who was appointed in 1880 to replace William Swan who was Professor from 1859 to 1880.

Two students had graduated with an M.A. with Honours in Mathematics and Natural Philosophy in 1881, both with a First Class degree. One of these students was R C Buist, who joined Edinburgh Mathematical Society in December 1884. Similarly two students had graduated with an M.A. with Honours in Mathematics and Natural Philosophy in 1882, both with a First Class degree. One of these students was David Rintoul who joined the Edinburgh Mathematical Society as a founder member in February 1883 when he was at Corpus Christi College, Cambridge.

**Totals for the four universities**

To sum up the results over these two years, it works out that the four Scottish Universities are producing on average about 14 Honours Mathematics per year, approximately 9 of First Class and two of Second Class. It is interesting to note that over these two years Aberdeen produced as many honours mathematics graduates as the other three universities put together.

**Structure of the mathematics courses**

To see the structure of the courses these students were taking we quote from the respective university Calendars of 1883.

Mathematics in Aberdeen University in 1883

Mathematics in Edinburgh University in 1883

Mathematics in Glasgow University in 1883

Mathematics in St Andrews University in 1883

**Examination questions**

Some sample questions from the Mathematics and Natural Philosophy examination papers set at Scottish Universities from around this time can be found at THIS LINK

**Women and the Scottish universities in 1883**

Finally we look at the position of women with regard to university level mathematics in Scotland in 1883. They were not entitled to graduate with a degree. This was not the decision of the individual universities but rather it required an act of Parliament to allow women to graduate. All four universities did, however, offer certificates for women of degree standard.

In 1883 the University of Aberdeen had a "Higher Certificate for Women". The regulations state that:

The University of Aberdeen is prepared to grant a Higher Certificate for Women to all Candidates who shall pass in three of more of the Subjects prescribed.Women were admitted to the M.A. course in the University of Aberdeen in 1896. The first woman to graduate M.A. with Honours in Mathematics and Natural Philosophy was Emily C Riddoch (Third Class) in 1899.

In 1883 the University of Edinburgh had an "Ordinary Certificate in Arts for Women" and an "Honour Certificate in Arts for Women". The regulations state that:

Candidates, before they can receive the certificates, must have studied in at least three of the Classes of the "Edinburgh Association for the University Education of Women," that are recognised by the Senatus Academicus; and they must also have passed the Local Examinations of the University of Edinburgh, or of one of the other Scottish Universities, or of the Universities of Oxford or Cambridge.The mathematics examinations topics for the Ordinary Certificate for October 1883 were:

Arithmetic, Euclid, Books I., II., III., IV., and VI., or their equivalent. Algebra to Quadratics equations, including the Progressions.The mathematics examinations topics for the Honour Certificate for October 1883 were:

Euclid, I., II., III., IV., VI., and XI., or their equivalent; The advanced portions of the Elements of Algebra, Trigonometry, and Conic Sections, treated geometrically and analytically.Women were admitted to the M.A. classes of the University of Edinburgh in 1896. The first woman to graduate M.A. with Honours in Mathematics and Natural Philosophy was Jessie Chrystal Macmillan (First Class) in 1900.

In 1883 the University of Glasgow held local examinations for Certificates:

- Junior (for both boys and girls),

- Senior (for both boys and girls),

- Higher (for women),

- Certificate in Degree Subjects (for women).

Women were admitted to the M.A. classes of the University of Glasgow in 1896. The first woman to graduate M.A. with Honours in Mathematics and Natural Philosophy was Elizabeth Pettigrew Taylor (First Class) in 1898.

The University of St Andrews appears to have made the most progress in women's university level education. They had introduced a Higher Certificate For Women, with the title of L.L.A. (

*Ladies' Licentiate in Arts*). Here is an extract from the regulations:

**HIGHER CERTIFICATE FOR WOMEN, WITH TITLE OF L.L. A.**

**UNIVERSITY EDUCATION FOR WOMEN AT ST ANDREWS.**

**1882.**

*The University of St Andrews grants a Higher Certificate to all Candidates who pass in one or more of the subjects undermentioned.*

*The following are the conditions of Examination:-*

*In each subject there is a Pass and an Honour Standard.*

*The subjects are, for the most part, those taught in the University; but History, and the French, German, and Italian Languages and Literatures, have been added.*

*The standard of attainment both for Pass and Honours is the same as that required for the M.A. Degree in the subjects included in the University curriculum; the books provided, the questions set, and the hours of Examination, being identical; and in the subjects not at present included in the University curriculum, the standard required is analogous.*

*Any Candidate who passes in four subjects (one at least being a language), or gains Honours in any one subject, and passes in two more (one of the three being a language), will receive the title of Literate in Arts (L.L.A.) To women who propose to become teachers this title is equivalent to a diploma, or licence to teach, in the subjects in which they have passed, or taken honours.*

By 1885 some other changes had been introduced:

The Senatus Academicus has authorised the use of an Academic Badge, in the form of a Sash, of the colours of the Universities of Paris and St Andrews, with a St Andrews University cross in silver, to be worn by all who take the title and receive the Diploma of L.L.A.The following (which appeared in the University of St Andrews Calendar for 1881-82 and for several years after that) is interesting in regards to the university education of women.

At the request of several L.L.A.'s throughout the country, the Committee has agreed that a Register should be kept of those who have taken the L.L.A. Title, and are desirous of finding employment as teachers in the Schools or Colleges of the country. Any who wish to be thus enrolled may have their names put on the Register - with a statement of the subjects in which they have passed - on sending their application to Mr Smith, University Library, St Andrews, and remitting to him a registration fee of 2s. 6d.

**UNIVERSITY EDUCATION OF WOMEN AT THE UNIVERSITY OF ST ANDREWS.**

The Senatus of the University of St Andrews having received six Petitions on the subject of University Education of Women - one from the L.L.A.'s of the University, with 34 signatures attached; one from the Association for the Higher Education of Women in Dundee, signed by the Countess of Airlie, president; one from a similar Association for the city and county of Perth, signed by Mrs Drummond of Megginch, president; one from Arbroath, with 15 signatures; one from Dunfermline, with 85; and one from Cupar-Fife, with 54 signatures - expresses its gratification at the desire for the Higher Education embodied in these Petitions.Women were admitted to the M.A. degree course in the University of St Andrews in 1896. The first woman to graduate M.A. with Honours in Mathematics and Natural Philosophy was Margaret Murray (First Class) in 1898.

The Petitioners ask two things:-

First,- They all ask for such a course of University Instruction as the Senatus may think fit to grant.

Second,- Some of them ask for admission to Degrees in Arts.

As to the First, the Senatus expresses its willingness to grant separate Courses of systematic University Instruction to Women - provided a sufficient sum of money is raised by the Petitioners (or others) to enable this to be done - especially as during the earlier stages of the experiment the attendance at the several classes might not be so large as to furnish adequate remuneration to the Professors without such a fund.

As to the Second, the Senatus resolves as follows:-

I. That, in the meantime, as an equivalent for Graduation, women students be recommended to take the L.L.A. Examination in all the subjects necessary for the M.A. Degree, inasmuch as the examination papers used in the two cases are the same.

II. The Senatus is further willing to urge upon Parliament the claims of women to the privileges of Matriculation and Graduation, provided that the attendance of Students, the demand for Graduation, and the existing interests of the University warrant such a step; and provided that every female Student attending the University shall lodge or board in some house in St Andrews, to be approved of by the Senatus.