Mathematical Treasure: A Letter of James Joseph Sylvester to Leopold Kronecker

James Joseph Sylvester (1814-1897)
(Source: MacTutor History of Mathematics Archive)

James Joseph Sylvester, a short biography

James Joseph Sylvester was born James Joseph on September 3, 1814 in London; he died March 15, 1897. James assumed the last name Sylvester when his older brother chose that name upon immigrating to the United States; at the time, immigration required a first name, middle name, and last name. When he was 14, Sylvester became a student of Augustus De Morgan (1806-1871) at the University of London. He withdrew from the University after being accused of stabbing a student. 

Sylvester formally began his study of mathematics a few years later, in 1831, at St. John’s College, Cambridge. At St. John’s he ranked second in Cambridge's rigorous mathematical examination, the Tripos. Despite his stellar performance, he was not awarded a degree because, as a Jew, he could not see his way clear to the mandatory swearing to the Thirty-Nine Articles of the Church of England. Moreover, because of his refusal on religious grounds, he was unable to compete for a Fellowship at Cambridge. In 1838 he became Professor of Natural Philosophy at University College London. In 1841, he was awarded a BA and an MA by Trinity College, Dublin. That same year he moved to the United States where he briefly served as a professor at the University of Virginia, returning to England in November 1843.

On his return to England he pursued law, studying at the Inns of Court in London at the same time as fellow mathematician Arthur Cayley (1821-1895). The two became friends and together they made major contributions to linear algebra, particularly in matrix theory. It is interesting to note that Sylvester’s private students, taken on to supplement his income, included Florence Nightingale (1820-1910), one of the founders of modern nursing. In 1855, he was appointed Professor of Mathematics at the Royal Military Academy, Woolwich; he left in 1870 because he had reached the required retirement age of 55.

In 1872, Sylvester finally received his B.A. and M.A. from Cambridge. In 1876 he returned to the United States to become the first Professor of Mathematics at the newly formed Johns Hopkins University in Baltimore, Maryland; the university wanted him to start a graduate program in mathematics. While at Johns Hopkins he founded the American Journal of Mathematics. The website of the Johns Hopkins University Mathematics Department has an image of the letter featured in this article; see http://mathematics.jhu.edu/wp-content/uploads/sites/62/2015/05/jjletter.pdf

In 1880, the Royal Society of London presented the Copley Medal, its highest award for scientific achievement, to Sylvester. In 1883, Sylvester returned to England to assume the Savilian Professorship of Mathematics at Oxford University, which he held until 1894. As Savilian Professor of Geometry beginning in 1884, Sylvester was required to deliver a public lecture, and he initially chose the topic “Descartes as Geometer.” He was anxious about delivering the lecture and thus solicited suggestions from his mathematical colleagues; in the letter featured in this article Sylvester asked Leopold Kronecker (1823-1891) for help with the public lecture.

Sylvester invented a great number of mathematical terms such as “matrix” and “discriminant”. His collected scientific work fills four volumes; The Collected Mathematical Papers of James Joseph Sylvester are available on Google Books.

For more information:

J. J. O'Connor and E. F. Robertson, "James Joseph Sylvester," MacTutor History of Mathematics Archive, 2005

Karen Hunger Parshall, James Joseph Sylvester: Jewish Mathematician in a Victorian World, Johns Hopkins University Press, 2006

Letter from Sylvester to Kronecker (1884)

The three-page letter reproduced here is in the collection of the author. You may use these images in your classroom; all other uses require the permission of the author.

Transcription of Letter from Sylvester to Kronecker

Keswick Cumberland 4^th Sept^r 1884

Dear Professor Kronecker – ¹

Having chosen “Descartes as a Geometer” as the subject of a Public Lecture which I am compelled by the Statutes to deliver at Oxford next term² if you could suggest any moderately sized book or books or article in some mathematical notice or review which would be likely to be useful in enabling me to say anything worth hearing on the subject (with which I have no special acquaintance) you would be rendering me a great service. I have Baillet, Millet and Liard³ (the last I think of no value except to contradict).