James Joseph Sylvester
In my experience, many people picture mathematicians as cold, isolated, geniuses. Though Sylvester was an extremely capable man, he got things wrong and was far from cold and isolated. One student said about him,
Sylvester’s methods! He had none. “Three lectures will be delivered on a New Universal Algebra,” he would say; then, “The course must be extended to twelve.” It did last all the rest of that year. The following year the course was to be Substitutions-Théorie, by Netto. We all got the text. He lectured about three times, following the text closely and stopping sharp at the end of the hour. Then he began to think about matrices again. “I must give one lecture a week on those,” he said. He could not confine himself to the hour, nor to the one lecture a week. Two weeks were passed, and Netto was forgotten entirely and never mentioned again. Statements like the following were not unfrequent in his lectures: “I haven’t proved this, but I am as sure as I can be of anything that it must be so. From this it will follow, etc.” At the next lecture it turned out that what he was so sure of was false. Never mind, he kept on forever guessing and trying, and presently a wonderful discovery followed, then another and another. Afterward he would go back and work it all over again, and surprise us with all sorts of side lights. He then made another leap in the dark, more treasures were discovered, and so on forever.
-Ellery W. Davis
James Joseph Sylvester, was born on 3 September 1814 and grew up to become a bright, passionate man. He died on 15 March 1897, but not before leaving his mark on the world of mathematics. His major mathematical contributions were in the theory of equations, matrix theory, determinant theory, and invariant theory (which was discovered with Cayley). Sylvester loved poetry and his proofs were often described as, "flowery and eloquent", and were said to match his sensitive and enthusiastic personality.
We will often see terms that Sylvester coined such as matrix, invariant, discriminant, commutant, and more. There have also been ideas named after Sylvester such as Sylvester's determinant identity, the Sylvester-Gallai theorem, Sylvester Matrix, Sylvester's theorem and the list can go on. Taking a look at Sylvester's work, we can see his finger prints on Abstract Algebra today. And Sylvester's contributions to things like invariant theory are a branch of Abstract Algebra. Another reminder that the math we study now was built from the shoulders of those who proceeded us.
In 1837 Sylvester earned second place in the Mathematical Tripos Examination but did not graduate with a degree as he was Jewish and refused to subscribe to the Thirty-Nine Articles of the Church of England, which was required to graduate at the time. However, Sylvester continued to spread his influence despite the roads that were closed to him because of his religious beliefs.
For three years Sylvester was the chair of natural philosophy at the University of London, then in 1841 he finally was able to receive his B.A. and his M.A. from Trinity College, Dublin. By the time Sylvester was 27 he applied to be the chair of mathematics in the University of Virginia in Charlottesville in the United States. In 1843 he left the U.S. and returned to England. There he got into actuary work and decided to study law. This happened to be a very lucky choice on his part as it was what the mathematician Arthur Cayley was doing as well. They met, and though very different in many ways, became great friends who would end up doing lots of research together. Among Sylvester's many accomplishments in 1876 he was appointed to a prestigious position at the Johns Hopkins University, he founded the American Journal of Mathematics, and held a teaching position at Oxford from 1884 until he died.
What did I learn from studying Sylvester? It is okay to not get things right the first time... keep trying, you never know how much your contributions can benefit others.
Thanks bunches!
-Haylee Jo Lau
Works Cited:
https://mathigon.org/timeline/sylvester
https://mathigon.org/timeline/sylvester
Contemporary Abstract Algebra, Joseph A. Gallian, Ninth Edition
Sounds like he'd be a fun guy to take an elective from :)
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