Karlis' "rule of thumb" suggestion is right on. I would like to
extend his idea to the point that mathematics has always been, and
will continue to be the 'language of science'. Numerically modeling
of any significant physical reality, creating reliable predictions
creates the desire language 'rule of thumb' condition, and the
first example of mathematics.
Historically, the above generalization is confirmed by all the
great cultures of history, China, India, Mesopotamia (Sumer), Egypt,
Mesoamerica, Inca and Polynesia first modeling the heavens for human
reasons. Therefore astronomy has long been seen as the birth mother
of mathematics, as attested by several ancient numerical models.
Regards to all,
Milo