I think it would be both churlish and unfair to Paul not to
cite the following which I recently came across:
"No better proof of the Pythagorean idea that number underlies
physical attributes: specific weight, specific heat, the
constants of elasticity, viscosity, etc. In this respect the
full implications of Pythagoras' conception were not realised
until modern times...
"We may say, then, that from the standpoint of modern science,
the scientific method of the Pythagoreans was correct. True,
the special field of investigation chosen by them does not
appear to us to be a suitable starting-point for a systematic
study of the physical world as a whole. Yet we observe that
their approach was the same as ours: starting from experiments
on various instruments, they expressed their findings in
general terms and aimed at the mathematical formulation of
universally applicable laws. Their fondness for numerical
mysticism in now way detracts from their scientific qualities;
on the contrary, in so far as it stimulated them to search for
causal laws in nature, it contributed to the progress of
science. The theoretical physicists of our time, who have so
greatly advanced the understanding of nature, likewise believe
almost religiously in the power of the mathematical symbol and
the validity of formulae and calculations. For this reason we
are so surprised that the Pythagorean beginnings should just
have petered out, instead of providing the starting-point for a
detailed quantititative study of natural phenomena in all the
fields of science, and not only in astronomy. What was the
cause of the decline of the Pythagorean School and the
"religion of numbers"? And why did the mystic element in it
eventually prevail over the scientific"
Sambursky, S. `The Physical World of the Greeks", Princeton UP
1987. (p41)
I think the question at the end of this passage, is the
question we ought to ask. But it may have been intemperate to
blame Pythagoras himself for the whole succeeding development.
There is a mystic element in the use of mathematics today, and
we need to understand where it comes from.
Alan