sense. But this ether may not be thought of as endowed with the
quality characteristic of ponderable media, as consisting of parts
which may be tracked through time. The idea of motion may not be
applied to it.




GEOMETRY AND EXPERIENCE

An expanded form of an Address to the Prussian Academy of Sciences
in Berlin on January 27th, 1921.



One reason why mathematics enjoys special esteem, above all other
sciences, is that its laws are absolutely certain and indisputable,
while those of all other sciences are to some extent debatable and
in constant danger of being overthrown by newly discovered facts.
In spite of this, the investigator in another department of science
would not need to envy the mathematician if the laws of mathematics
referred to objects of our mere imagination, and not to objects
of reality. For it cannot occasion surprise that different persons
should arrive at the same logical conclusions when they have already
agreed upon the fundamental laws (axioms), as well as the methods
by which other laws are to be deduced therefrom. But there is another
reason for the high repute of mathematics, in that it is mathematics
which affords the exact natural sciences a certain measure of
security, to which without mathematics they could not attain.