scientists for a long time. For example Galileo Galilie had said ( Galileo
(1616) ), ” Philosophy ( ie physics) is written in this grand book - I mean
the universe - which stands continually open to our gaze, but it cannot be
understood unless one first learns to comprehend the language and interpret
the characters in which it is written. It is written in the language of mathe-
matics, and its characters are triangles, circles, and other geometrical figures,
without which it is humanly impossible to understand a single word of it;
without these, one is wandering around in a dark labyrinth”.
Bertrand Russell ( Russell (1931) ) said, ’’Ordinary language is totally un-
suited for expressing what physics really asserts, since the words of everyday
life are not sufficiently abstract. Only mathematics and mathematical logic
can say as little as the physicist means to say”. James Jeans enthusiastically
stated ( Jeans (1930) ), ”God is a mathematician”. And work to show that
indeed mathematics is the language of nature has been actively pursued (
Redhead (1975), Alan and Peat(1988), French (1999), Omnes (2005) ).
It is clear that just about all the scientists and most of the philosophers
would feel that mathematics is indeed the language of nature. However
the mathematics that is usable as a language of nature is called ’’applied
mathematics”. Inherent in this word ” applied” is the fact that there is a lot of
mathematics which is not applied. This is the so called ’’pure” mathematics.
That is, mathematics which has found no application in a description of
nature. It acts outside any physical framework - a pure construct of human
intellect as many a mathematician would have us believe. In fact, it is a
dream of every mathematician to discover/invent a mathematics which can
be labelled as ’’pure” - that is uncorrupted by any ’’lowly” application to the
real world. There must be a thrill in creating something that is absolutely
independent of any existing thing∕concept∕idea. Hardy boasted ( Hardy
(1940) ), ” I have never done anything ’ useful ’. No discovery of mine has
made, or is likely to make, directly or indirectly, for good or ill, the least
difference to the amenity of the world. ”
So clearly - though mathematics may be the language of nature ( ie. the
’’applied” part), most of it is not (ie the ’’pure” part). What is that mathe-
matics ? It seems to have a Platonic world of its own. The logical positivists (
Carnap ( 1995 Edition ) ) tried to understand this dichotomy by arguing that
knowledge has two sources - the logical reasoning and the empirical experi-
ence. According to them logical reasoning shall lead to the analytical a priori
knowledge. That would embrace the field of pure mathematics. While the