Protagoras denies a perfect form for all things, while Pythagoras clearly presents the better case with harmonia.

Pythagoras, known as “the father of numbers” through his Pythagorean Theorem is regarded as the first to seek for the form of all things . From Protagoras’s perspective, named as one of the “Sophists” by Plato, there would probably be no exact form for anything. Without an understanding of a true source from which all form flows with, we eliminate all possibility of discovering the greater truth form carries with it. Pythagoras on the other hand deeply searches for a reason for the cosmos in every function of life, and that, carries a significant purpose for form.

Mathematical formulas and ratios, Pythagoras claimed were at the very center of the physical world through which the form of matter could be explained. The Pythagorean perspective stresses that number is universal, "the principle, source, and root of all things" . The formula of the Tetras in which the number 10 is held as the nature of a number can be seen by far as the most solid argument for the form of all things. All four numbers which include one, two, three, and four when added come to equal ten, thus reflecting the essential source of nature and reality together, in which all the cosmos are arranged according to harmonia. Harmonia consists of a melodic framework of three chords where the ratio of the octave is 1:2, the fifth 2:3, and the fourth 3:4 . This phenomenon represents perfect proportionality to the universe by means of form. Now each chord retains its individual identity, but all are still proportionally connected together to form a larger musical scale, thus all three chords needing to be interdependent of one another. Like an ecosystem that works together with its given environment, it most importantly has to function as a unit, via symbiotic relationships . You see, our society works in a similar way as well by functioning as a whole. The trees...