28 Annwersary Address by Sir William Huggins. 
of workers, and has devoted himself with great energy and with all his 
available resources to following out lines of work similar to those of Mendel. 
The result has been the supporting of Mendel’s conclusions and the bringing 
to light of a much wider range of facts in general harmony with them. It is 
not too much to say that Mr. Bateson has developed a school of research to 
which many biologists are now looking as the source from which the next 
ereat advance in our knowledge of organic evolution will come. 
SYLVESTER MEDAL. 
The Sylvester Medal is awarded to Georg Cantor, Professor in the 
University of Halle, on account of his researches in Pure Mathematics. His 
work shows originality of the highest order, and is of the most far-reaching 
importance. He has not only created a new field of mathematical 
investigation, but his ideas, in their application to analysis, and in some 
measure to geometry, furnish a weapon of the utmost power and precision for 
dealing with the foundations of mathematics, and for formulating the 
necessary limitations to which many results of mathematics are subject. 
In 1870 he succeeded in solving a question which was then attracting 
much attention—the question of the uniqueness of the representation of a 
function by Fournier’s series. The extension of the result to cases in which 
the convergence of the series fails, at an infinite number of suitably 
distributed points, led him to construct a theory of irrational numbers, which 
has since become classical. From the same starting point he developed, in a 
series of masterly memoirs, an entirely new branch of mathematics—the 
Theory of Sets of Points. 
Having established the fundamental distinction between those aggregates 
which can be counted and those which cannot, Cantor showed that the 
ageregates of all rational numbers and of all algebraic numbers belong to the 
former class, and that the arithmetic continuum belongs to the latter class, 
and further, that the continuum of any number of dimensions can be 
represented point for point by the linear continuum. Proceeding with these 
researches he introduced and developed his theory of “ transfinite” ordinal 
and cardinal numbers, thus creating an Arithmetic of the Infinite. His later 
abstract theory of the order-types of aggregates, in connection with which he 
has given a purely ordinal theory of the arithmetic continuum, has opened up 
a field of research of the greatest interest and importance. 
4 
