ABSTRACTS SAMENVATTINGEN

---

Symposium ``James Joseph Sylvester (1814-1897)''

Friday the 9th of April 1999

during the 1999 Dutch Mathematical Congress
(Utrecht)



PROGRAMMA

---

Within the framework of the 34th Dutch Mathematical Congress, a historical symposium was held, to commemmorate J.J. Sylvester (1814-1897). About 50 people partcipated and enjoyed the lectures. Abstracts of the lectures follow below.


First Lecture
Robin J. Wilson (Open University UK): ``Sylvester's years in Oxford ''.
Abstract
In 1883 Sylvester was elected Savilian Professor of Geometry at Oxford University at the age of 69, after a period as the first professor of mathematics at the newly formed Johns Hopkins University in Baltimore. In this talk we summarize his achievements in Oxford, from the time of his appointment to his retirement through failing eyesight in 1894. In particular, we discuss his unusual inaugural address, outline his research work and its frustrations, and describe his founding of the Oxford Mathematical Society

Second lecture
Martyn Mulder (Erasmus University, Rotterdam): ``Sylvester and the emergence of graph theory''
Abstract
Sylvester may be considered as the founding father of Graph Theory. He coined the terms tree and graph. He envisaged a great future for the newly introduced theory as the common foundation of such diverse topics as algebra, kinematics and chemistry. But his main contribution was his stimulating exchange of ideas with notably his friend Arthur Cayley and the Danish mathematician Julius Petersen to use graphs in a non-trivial way for solving mathematical problems. In this talk we discuss Sylvester's contributions, the work of Cayley on trees, Petersen's highly non-trivial work on regular graphs, and the adventures of Petersen's work in subsequent decades.

Third Lecture
Teun Koetsier (Vrije Universiteit Amsterdam): ``Sylvester's role in the development of the theory of mechanisms''
Abstract
In 1784 James Watt invented the so called ``parallel motion'', a linkage connecting the piston rod of a steam engine with the working beam. A modified version of the linkage, 'Watt's parallellogramme' was successfully applied in many steam engines and widely admired. The two linkages are straight-line mechanisms that produce only approximately a straight line. Independently the Frenchman Peaucellier (in the 1860s) and the Russian Lipkin (in 1870) invented the same exact straight-line linkage, somethinmg Chebyshev had considered impossible. James Joseph Sylvester learned about this linkage through Chebyshev and was immensely impressed. His enthusiasm and his results in this area stimulated young mathematicians like A. B. Kempe and H. Hart to study linkages. Sylvester's work also contributed to a more complete analysis by Samuel Roberts in the 1870s of the sixth degree curve that is in Watt's linkages over a considerable distance almost straight.

---

The symposium was followed by the closing lecture of the congress:

Karin Parshall:
``Glancing Back: The Mathematics of James Joseph Sylvester''

Abstract
James Joseph Sylvester, one of Britian's nineteenth-century mathematical characters, did seminal work in a number of pricipally algebraic fields. This talk will examine the development of his mathematical thought from his early work in the theory of determinants, through his founding (with Arthur Cayley) of the British approach to invariant theory, to his work on partition theory and the theory of algebras. It will also set Sylvester's mathematical achievements within the context of his complex life story in an effort to highlight the interplay between the actual production of mathematics and extra-mathematical factors.

---