**Alexander Macfarlane** began his research on experimental physics but moved to mathematics and logic. He is best known for his two famous posthumous publications on British mathematicians of the nineteenth century, many of whom he had personally known.

- Alexander was educated at the James Street Free Church school at Blairgowrie where he showed such outstanding abilities that, at the age of thirteen, he was employed as a pupil-teacher.
- A very successful year in studying Greek, Latin and Mathematics, saw Macfarlane compete in the scholarships at the beginning of his third year and was awarded the prestigious Spence Scholarship.
- Macfarlane took Kelland's course which introduced his students to the quaternions.
- Macfarlane purchased Tait's Treatise on Quaternions believing that since Tait was Professor of Natural Philosophy, the book would be addressed to physicists but found that Tait approached the topic in a very mathematical way.
- John Stevenson (1695-1775) was Professor of Logic and Metaphysics at Edinburgh University and he invited Macfarlane to present a paper criticising the statement of the law of the excluded middle given by William Stanley Jevons in his book Elementary Lessons on Logic (1870).
- Macfarlane had been intending to take honours in logic but this experience made him realise that he needed a solid background in mathematics and science.
- Tait was very impressed by his student's work in experimental physics and, in 1874, Macfarlane was awarded the Neil Arnott scholarship for Experimental Physics.
- In 1875 Macfarlane graduated with an M.A. with First Class Honours in Mathematics and Physics.
- It was followed in the same year by a paper, jointly authored by Macfarlane, Knott and Charles Michie Smith (1854-1922) (known as Michie), entitled On the Electric Resistance of Iron at a High Temperature.
- Macfarlane was awarded a D.Sc. on 23 April 1878 for his thesis On the Disruptive Discharge of Electricity which was published in the Transactions of the Royal Society of Edinburgh.
- This was one of six papers Macfarlane published in 1878, all in the Proceedings or the Transactions of the Royal Society of Edinburgh.
- We note that by this time Macfarlane had both an M.A. and a B.Sc. In the same year, on 6 May, he was elected a fellow of the Royal Society of Edinburgh.
- He was proposed by Peter Guthrie Tait, Philip Kelland, Alexander Crum Brown and John Hutton Balfour.
- We note that Alexander Crum Brown was the Professor of Chemistry at Edinburgh, while John Hutton Balfour was the Professor of Botany.
- In 1880 Macfarlane was appointed as temporary professor of physics at the University of St Andrews, a position he held for a year.
- In 1885 Macfarlane was appointed to the chair of physics at the University of Texas in Austin, Texas, United States.
- Macfarlane's appointment came through his correspondence with Halsted on the algebra of logic.
- Macfarlane read the paper On the definitions of the trigonometric functions to the International Mathematical Congress in Chicago in August 1893.
- In 1894, Macfarlane resigned his chair of physics at the University of Texas.
- Macfarlane was appointed to Mathematical Physics and organised the programme from 1895 to 1897.
- This is not clarified by the fact that in 1900, when Macfarlane attended the International Congress of Mathematicians in Paris, he gave his address as Lehigh University, South-Bethlehem, Pennsylvania.
- In Chatham, Ontario, Macfarlane devoted much time to writing and during the years 1901-1904 delivered at Lehigh University lectures on twenty-five British mathematicians of the nineteenth century.
- Macfarlane attended the International Congress of Mathematicians in Paris in 1900, in Heidelberg in 1904, in Rome in 1908 and Cambridge, England, in 1912.
- Macfarlane received widespread recognition for his contributions.

Born 21 April 1851, Blairgowrie, Scotland. Died 28 August 1913, Chatham, Ontario, Canada.

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Origin Scotland

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive