The book may not have received critical acclaim, but it’s safe to assume he had fun writing it. He even wrote his own book, The Laws of Verse, which was an attempt to turn some of his mathematical concepts into a more artful form with rhyming lines. Totient (for Leonhard Euler’s totient function)Īs a hobby, Sylvester’s love of words found him translating poetry from other languages into English.Graph (in the context of combinatorics).Some of Sylvester’s more common terms include: He described mathematical factors as allotrius and multiplication as zetaic. To get a sense of his unique style, some of the colorful mathematical terms Sylvester coined include combiants and plagiograph, or skewn pantograph. James Joseph Sylvester also wrote a lot of poetry and, while his musings about algebra were often hard to follow due to his eccentric and poetic writing style, his contributions were nevertheless valued considerably by the mathematical community. Also, a lecture and accompanying syllabus he gave on Newtonian algebra was published by the newly established London Mathematical Society, of which Sylvester became president in the 1860s. During his many years as a professor there, he kept busy, becoming an editor of the Quarterly Journal of Pure and Applied Mathematics and a math correspondent to the French Academy of Sciences. In 1855, he accepted a position as a professor of mathematics at the Royal Military Academy, Woolwich, which he held until 1870. While Sylvester had been successful in the private sector, his advances in math on the side led him to circle back to academics. Before Sylvester and Cayley came along, many mathematicians focused on the theory of equations, but thanks to their work, people began to think about the theory of invariants and forms, as well as linear associative algebra. This collaboration helped change the way algebraists think about math and the applications of equations. The two collaborated for many years (wherever they could squeeze in the time between legal proceedings) and produced contributions to both invariant theory and matrix theory as a result. Sylvester and Cayley would often bounce ideas off each other as they each developed theorems. Partnering with his friend Arthur Cayley, who was a lawyer and mathematician as well, Sylvester began some of his most significant work in the theory of invariants. Between tutoring pupils, working as an actuary at an insurance company, and later becoming a law student and working as a lawyer, it’s a wonder he was able to have the time or energy to come up with mathematical theories - but that’s just what he did. Once a Mathematician, Always a Mathematician…Īlthough James Joseph Sylvester changed his career path in the 1840s, he still taught mathematics through private tutoring (with Florence Nightingale as one of his promising students). From there, he had a short stint teaching at the University of Virginia in the United States before returning to England to focus on mathematics outside of academia. The next year, when he was just 25 years old, he was chosen as a fellow of the Royal Society based on papers he had written right after his tripos exam: one on Fresnel’s theory and the other on the motion of fluids and rigid bodies.
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In 1838, he was able to accept a teaching position at University College in London. Image in the public domain in the United States, via Wikimedia Commonsĭespite the lack of many nonsectarian colleges at the time, Sylvester earned his degree from Trinity College, Dublin. However, he could not get a degree or an appointment there because of a religious requirement to the Church of England that would have compromised his beliefs. When he took the University of Cambridge’s mathematical tripos examination in 1837, he ranked second and should have been well on his way to graduating at the top of his class. By the time he was a teenager, Sylvester was winning prizes for his work in mathematics. He spent his childhood in England with his family and was educated in both London and Liverpool. James Joseph Sylvester was born on September 3, 1814, in Liverpool, England. Tripos Triumph and Other Academic Achievements His interest in poetry and verse likely helped him in coining new mathematical terms, but it was his prolific output on proofs and elliptical functions that stole the show for his lifetime achievements. His genius is most obvious in his cofounding of invariant theory, but he also contributed greatly to number theory, partition theory, and matrix theory.
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English mathematician and expert algebraist James Joseph Sylvester imagined new ways of thinking about numbers and their applications.