No serious advance could be made in the application
of algebraic language to the expression of physical phenomena
until it could be so extended as to express variation in
quantities, as well as the quantities themselves. This extension,
worked out independently by Newton and Leibnitz, may be classed as
the most fruitful of conceptions in exact science. With it the way
was opened for the unimpeded and continually accelerated progress
of the last two centuries.
The feature of this period which has the closest relation to the
purpose of our coming together is the seemingly unending
subdivision of knowledge into specialties, many of which are
becoming so minute and so isolated that they seem to have no
interest for any but their few pursuers. Happily science itself
has afforded a corrective for its own tendency in this direction.
The careful thinker will see that in these seemingly diverging
branches common elements and common principles are coming more and
more to light. There is an increasing recognition of methods of
research, and of deduction, which are common to large branches, or
to the whole of science. We are more and more recognizing the
principle that progress in knowledge implies its reduction to more
exact forms, and the expression of its ideas in language more or
less mathematical.
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