empirical experience would lead to the synthetic a posteriori knowledge and
this would correspond to the applied mathematics. Explicitly or implicitly
such a ’’dichotomous” point of view of the intrinsic structure of mathematics
is held by most scientists, mathematicians and philosophers today. However,
if indeed mathematics is the language of nature, then how come there is a
smaller reservoir of language which nature communicates with ( ie applied
mathematics ) but there is a larger reservoir of unused language ( ie pure
mathematics )? How and why does this unused language ( ” pure mathemat-
ics ” ) come into existence? No one has any reasonable understanding of it
at present. This is an extremely unsatisfactory state of affairs and demands
further inquiry. Though not often explicitly stated, this problem remains
today as one of the most outstanding open issues in science∕mathematics
and its philosophy.
If anyone has doubts as to the seriousness of the issue, one need only read
Reuben Hersh ( Hersh (2005) ). Therein he was reviewing Ronald Omnes’
new book on philosophy of physics and mathematics (Omnes (2005)). He
quotes Omnes, ” The consistency of mathematics is therefore tantamount
to the existence of mathematically expressible laws of nature.” Thereafter
Hersh goes on to say bitterly, ” Minor glitches can be shrugged off. ( A
few oddball branches of math like higher set theory and nonstandard logics
may not be physical, but who cares? ) ”. If this is how leading authorities
feel about the issue, then what could be more urgent? Hersh further quotes
Omnes, ” What exactly is the extent of the present mathematical corpus
that is in relation to the mathematics of physics? I cannot say that I have
analyzed this question carefully, but I considered it from time to time when
reading papers in theoretical physics and mathematics ”. Hence clearly up
to now, no philosopher or mathematician or scientist has understood what
mathematics ” really ” is. Here I offer a novel solution to the conundrum.
Just as a child discovers the ’’correct” words to use for specific objects or
ideas through social interactions, similarly a scientist learns the appropriate
word for a particular physical reality by interacting with nature. However,
while the word ” rose” for a particular flower is culture determined and varies
from language to language, the mathematical word for a particular physical
object is exact and specific. It turns out that nature is very demanding and
requires strict adherence to clear-cut mathematical rules to reveal its reality
to scientists. Only through a tortuous and painstaking process of basically
hit and trial method along with some judicious guesswork is it that a scientist