I am sorry, I did not mean to sound dismissive or supercilious; far from it. Kaptaan has a knack for articulating difficult ideas and putting them together in an eminently accessible way. As he so well put it, Pythagoras believed that the entire universe, including such diverse elements as the health of humans, music and the astronomical system, was possible to understand through the use of what we call 'mathematics' today: he himself used the term in its Greek sense of 'seeker'. 'Mathematikoi' is a term for the collective group of seekers that he drew around himself, in an inner circle with strict rules of living, including one demanding silence if uncertain on any matter, on pain of death. He has not been well documented; what we know is simply that he took it that numbers underlaid nature, and that understanding nature was best done through understanding numbers very well. Understanding numbers covered arithmetic and geometry; algebra was not known or practised then.
The simplest possible summary is that the only way to understand the physical universe is to model it mathematically; for instance, the General and Special Theories of Relativity, the Laws of Motion, Gravity, and almost everything that we take for granted today is represented for quick understanding as a mathematical model.
I hope that was more useful.