discovers the ” correct ” mathematical word or expression for a particular
physical object or phenomena.
So basically, a priori, to a scientist there would exist a large number
of mathematical options/words to accurately describe a particular physical
phenomenon. One tries all. There is bound to be a stage where confusion
reigns. That would be the initial stage wherein more than one mathemat-
ical model or terminology may appear to be applicable. History of science
tells us that slowly with time and much effort, the physical reality will man-
ifest itself by demanding and forcing upon scientists only one particular and
unique mathematical structure. That will be the stage that the scientist
would have discovered the ’’exact” word∕phrase for that particular physical
object∕phenomena. No ambiguity about that ( more on it below ). Thus
nature has allowed the scientist to read that particular ’’word”.
The whole purpose of science is to continue to read nature through this
’’exact” mathematical language. Acquiring a larger vocabulary of this math-
ematical language leads to a greater fluency with nature.
Sometimes scientists would have to develop ab initio the necessary mathe-
matics to understand physical reality. For example, to understand the empir-
ically determined Kepler’s laws of planetary motion, Newton had to develop
the requisite calculus to do so. The very fact that Newton was actually able
to acquire the necessary mathematical vocabulary made it possible for him
to appreciate the effects of gravity. The physical ’book’ of gravity was ’read’
only because the necessary mathematics could be simultaneously developed.
It was to ’read’ the other physical effects as well, that Newton’s contem-
porary, Leibniz was independently developing the required mathematics of
calculus. Hence the requisite mathematical language of calculus was basic
and essential to an understanding of gravity and dynamics in physical nature.
Simply put, had it not been possible to develop the language of calculus, one
would not have been able to read nature any better.
The basic mathematics of calculus could be developed by scientists them-
selves (ie. Newton and Leibniz ) as fortunately it did not necessarily require
a too sophisticated pre-existing mathematical framework. Their work was
simplified by the fact that the foundations of calculus had already been laid
by earlier mathematicians. It was not just for nothing that Newton had
stated that he had risen on the shoulders of giants.
As there appears to be some confusion in the minds of many as to the
issue of priority here, may I quote Richard Courant and Herbert Robbins