MATHEMATICS AS AN EXACT AND PRECISE LANGUAGE OF NATURE



When the quark model of particle/high energy physics was being devel-
oped to understand the structure of the umpteen number of particles being
discovered experimentally in the 1950’s and 1960’s, a priori there were sev-
eral group theoretical mathematical candidates for a scientific description of
reality : the groups G2, F2, SU(2)xU(l) and SU(3) were good candidates for
it. It was basically through the method of hit and trial that it was found
that SU(3) group was the correct candidate for such a description. It was
found that to understand the structure of particles like proton, neutron etc
it was necessary to assume that they were made up of three kind of quarks
which were named as up, down and strange ( in the accepted nomenclature
at present ). As such nature ’forced’ the scientists to read the word ”SU(3)”
in the quark model. Plainly stated they found that no other mathematical
’word’ can do the job appropriately!

It maybe noted here that two scientists, Murray Gell-Mann and G. Zweig,
independently and practically simultaneously, had come to the same conclu-
sion that indeed SU(3) was the relevant group as discussed above. So to say,
they both had been able to ’’read” nature correctly. Hence this is another
example, in addition to the cases of Newton/Leibniz and Einstein/Hilbert as
pointed out above, where proper mathematics, being the language of nature,
allows itself to be ’’read” by more than one person at the same time.

Another example from particle/high energy physics is that of Quantum
Chromodynamics, the theory of the strong interaction. In the 1970’s and
1980’s a priori several groups SU(2) U(2), SO(3) and SU(3) were reasonable
candidates as the group theoretical∕mathematical words to describe strong
interaction consistently. But experimental information and mathematical
consistency forced the group SU(3) as the relevant group for the theory of
the strong interaction to be built upon. It has been meticulously checked and
found that SU(3) and none other is the right ’’word” for Quantum Chromo-
dynamics or the theory of strong interaction. No scientist could have even
in his wildest dreams ever thought of such a scenario right up to the 1960’s.

So also is the example of the so called the Standard Model of particle
physics which is built around the group SU(3)xSU(2)xU(l). This is the most
successful model in particle physics as of now. This mathematical structure
or word is the result of judicious speculation, meticulous experimentation
and sheer hard work on the part of scientists all over the world during the
last 100 years or so. It is important to realize that no other mathematical
description can do what the Standard Model can do. Not that scientists did



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