Symposium ``James Joseph Sylvester (1814-1897)''
Friday the 9th of April 1999
during the 1999 Dutch Mathematical Congress
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
Robin J. Wilson (Open University UK): ``Sylvester's years in Oxford ''.
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
Martyn Mulder (Erasmus University, Rotterdam): ``Sylvester and the emergence of
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
Teun Koetsier (Vrije Universiteit Amsterdam): ``Sylvester's role in the
development of the theory of mechanisms''
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:
``Glancing Back: The Mathematics of James Joseph Sylvester''
James Joseph Sylvester, one of Britian's nineteenth-century
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.