History of mathematician pythagoras

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Fr. 191 comes from a book on marvels by Apollonius (2nd BCE?). The harmony of the spheres became a central theme in Pythagorean cosmology and influenced later philosophical and scientific thought, including the works of Plato and Johannes Kepler.

The Pythagoreans also developed a cosmological system that placed fire, rather than the Earth, at the center of the universe.

986a29 is probably an interpolation; Rh. 1398b14 is a quotation from Alcidamas; MM 1182a11 may not be by Aristotle and, if it is, may well be a case where “Pythagoreans” have been turned into “Pythagoras” in the transmission). Álvarez Salas, accepting the three apparent references to Pythagoras in Aristotle’s extant writings which are mentioned above as genuine, suggests that scholars are mistaken to regard Aristotle as slighting Pythagoras, because Aristotle also refers very infrequently to other early figures such as Thales.

Aristotle simply does not include Pythagoras in his account of the Presocratic philosopher/scientists. In some cases, the fragments of these early works are clearly identified in the later lives, but in other cases we may suspect that they are the source of a given passage without being able to be certain. His followers, the Pythagoreans, believed that numbers and mathematical relationships were fundamental to understanding the universe.

He reports that “once when he [Pythagoras] was present at the beating of a puppy, he pitied it and said ‘stop, don’t keep hitting him, since it is the soul of a man who is dear to me, which I recognized, when I heard it yelping’” (Fr. It is true that there is little if any fifth- and fourth-century evidence for Pythagoreans living according to the acusmata and Zhmud argues that the undeniable political impact of the Pythagoreans would be inexplicable if they lived the heavily ritualized life of the acusmata, which would inevitably isolate them from society (Zhmud 2012a, 175–183).

There is no direct evidence for these restrictions in the pre-Aristotelian evidence, but both Aristotle and Aristoxenus discuss them extensively. This picture can then be tested by the most fundamental evidence of all, the testimony of authors that precede even Aristotle, testimony in some cases that derives from Pythagoras’ own contemporaries.

First, Proclus does not ascribe a proof of the theorem to Pythagoras but rather goes on to contrast Pythagoras as one of those “knowing the truth of the theorem” with Euclid who not only gave the proof found in Elements I.47 but also a more general proof in VI. 31. 23).

Fr. 20 comes from Iamblichus’ Protrepticus, large parts of which are likely to derive from Aristotle’s lost Protrepticus but, as is his practice, Iamblichus does not make any explicit reference to Aristotle. Moreover, the story depends on a conception of a philosopher as having no knowledge but being situated between ignorance and knowledge and striving for knowledge.

For Aristotle Pythagoras did not belong to the succession of thinkers starting with Thales, who were attempting to explain the basic principles of the natural world, and hence he could not see what sense it made to call a fifth-century thinker like Philolaus, who joined that succession by positing limiters and unlimiteds as first principles, a Pythagorean.

570–475 BCE) and Heraclitus (fl. That there should be secret teachings about the special nature and authority of the master is not surprising. There he began teaching and soon had a clutch of students who lived a structured life of study and exercise, inspired by a philosophy based around mathematics. The only thing that could prove this in Pythagoras’ case is reliable early evidence for a rational cosmology and that is precisely what is lacking.

There is more controversy about the fourth-century evidence.

It should be clear from the discussion above that, while the early evidence shows that Pythagoras was indeed one of the most famous early Greek thinkers, there is no indication in that evidence that his fame was primarily based on mathematics or cosmology. He knew that all the philosophers before him had ended their days on foreign soil so he decided to escape all political responsibility, alleging as his excuse, according to some sources, the contempt the Samians had for his teaching method. Pythagoras founded a philosophical and religious school in Croton (now Crotone, on the east of the heel of southern Italy) that had many followers.

the dependence of the dynamics of world structure on the interaction of contraries, or pairs of opposites; the viewing of the soul as a self-moving number experiencing a form of metempsychosis, or successive reincarnation in different species until its eventual purification (particularly through the intellectual life of the ethically rigorous Pythagoreans); and the understanding ...that all existing objects were fundamentally composed of form and not of material substance.