"The decisive step leading to the construction of precise and verifiable scientific theories in place of vague and largely speculative accounts was the involvement of mathematics. This step was made by the Pythagoreans. ...In their philosophy of nature the Pythagoreans began with the principle that number is the essence of all substance. ...forms reduced to numbers. Since number is the essence of any object, the explanation of natural phenomena could be achieved only through number. ...Whether by a lucky stroke or by intuitive genius the Pythagoreans did hit upon two doctrines which later proved to be all important. The first is that nature is built in accordance with mathematical principles, and the second that number relationships reveal the order in nature. They underlie and unify the seeming diversity exhibited by nature."