ProofWiki:Mathematicians/James Joseph Sylvester

English mathematician who contributed to matrix theory, invariant theory, number theory, partition theory and combinatorics.

Contributed notably to the growth of mathematics in the USA.

Tutor of Florence Nightingale.

Also had a passion for poetry.

Nationality

English

History

• Born: 3 Sept 1814, London, England
• 1841 - 43: Professorship at the University of Virginia, USA
• 1877 - 83: Professor of mathematics at the new Johns Hopkins University in Baltimore, Maryland, USA
• Died: 15 March 1897, London, England

Theorems and Definitions

• Chebyshev-Sylvester Constant (with Pafnuty Lvovich Chebyshev)
• Coin Problem
• Sylvester's Sequence
• Sylvester's Formula, or Sylvester's Matrix Theorem
• Sylvester's Determinant Theorem
• Sylvester Matrix
• Sylvester-Gallai Theorem (with Tibor Gallai)
• Sylvester's Law of Inertia
• Sylvester's Criterion

• Rediscovered the Greedy Algorithm for Egyptian Fractions
• First to construct a Hadamard Matrix

Books and Papers

• 1839: On rational derivation from equations of coexistence, that is to say, a new and extended theory of elimination, Part I
• 1852: On the principle of the calculus of forms
• 1852: A demonstration of the theorem that every homogeneous quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares (in which he proved Sylvester's Law of Inertia)
• 1853: On the theory of syzygetic relations and two rational integer functions
• 1857: On the partition of numbers
• 1869: Presidential address to Section A of the British Association
• 1870: The Laws of Verse: or Principles of Versification
• 1878: Founded the American Journal of Mathematics which, as of the time of this article, is still going strong.
• 1884: Question 7382 in Mathematical Questions from the Educational Times, in which he provided a partial solution to the Coin Problem
• 1897: Outlines of seven lectures on the partition of numbers

Also see

• John J. O'Connor and Edmund F. Robertson: "James Joseph Sylvester": MacTutor History of Mathematics archive

• Eric Temple Bell: Men of Mathematics (1937): Chapter $\text{XXI}$