![]() The nature of the solutions depends on a quantity b 2 –4ac, which is called the discriminant (Sylvester introduced this term). Quadratics have two solutions, called roots. At school we learn to solve quadratic equations like ax 2 +bx+c=0. The theory of algebraic invariants had initially been developed by George Boole while he was at Queen’s College Cork. Cayley and Sylvester inspired each other in some of their best work, on the theory of invariants and matrix theory. The greatest benefit of this period was his encounter with Arthur Cayley, another renowned mathematician, which led to a life-long friendship and collaboration. In 1846, aged thirty-two, Sylvester entered the Inner Temple to pursue a legal career, and was called to the Bar four years later. He supported himself by taking private pupils, the most distinguished of these being Florence Nightingale. He took a post in Virginia, but it turned out badly and he returned from America within a year or so. Sylvester, like many brilliant young people today, had difficulty in finding a suitable position. He was elected a Fellow of the Royal Society at the unusually early age of twenty five. that Cambridge would not bestow unless he subscribed to the Thirty-Nine Articles of the Church of England, which his Jewish convictions precluded. Trinity College Dublin awarded Sylvester the degrees of B.A. He entered Cambridge in 1831, aged just seventeen and came second in the notorious examinations known as the Mathematical Tripos the man who beat him achieved nothing further in mathematics! Sylvester’s mathematical talents became evident at an early age. ![]() The family name was Joseph but, for reasons unclear, Sylvester – the name of an anti-Semitic Pope from the Roman period – was adopted later. James Joseph Sylvester was born in London to Jewish parents in 1814, just 201 years ago today. James Joseph Sylvester (1814-1897) as a graduate of Trinity College Dublin.
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