In an account that appeared five hundred years after the event, Diodorus Siculus wrote that the philosopher Pythagoras, who spent much of his life at Croton, urged the Croton assembly to protect the banished citizens of Sybaris.

Philochorus also wrote on oracles, divination and sacrifices ; the mythology and religious observances of the tetrapolis of Attica ; the myths of Sophocles ; the lives of Euripides and Pythagoras ; the foundation of Salamis, Cyprus.

If Pythagoras wrote of his tenets, his writings have not descended to us.

According to this account, one Scythianos, a Saracen, husband of an Egyptian woman, " introduced the doctrine of Empedocles and Pythagoras into Christianity "; that he had a disciple, " Buddas, formerly named Terebinthus ," who travelled in Persia, where he alleged that he had been born of a virgin, and afterwards wrote four books, one of Mysteries, a second The Gospel, a third The Treasure, and a fourth Heads.

In chapter 2, she describes man's gradual domination of women, starting with the statue of a female Great Goddess found in Susa, and eventually the opinion of ancient Greeks like Pythagoras who wrote, " There is a good principle that created order, light and man and a bad principle that created chaos, darkness and woman.

Syrianus also wrote works on The Theology of Orpheus, and On the Harmony of Orpheus, Pythagoras and Plato with the Oracles.

He wrote a great work on the doctrines of the Pythagoreans, and tried to show that the successors of Pythagoras had made no additions to the views of their founder, but had merely borrowed and altered the phraseology.

Then on Oct 23, 1972, Balliett's student, Dr. Juno Jordan, changed Numerology further and helped it to become the system known today under the title " Pythagorean ", although Pythagoras himself had nothing to do with the system.

There is nothing extant of the writing of Thales ; work done in ancient Greece tended to be attributed to men of wisdom without respect to all the individuals involved in any particular intellectual constructions — this is true of Pythagoras especially.

For example, a professor of music may perhaps know nothing of mathematics, but would probably know that Pythagoras was the earliest known contributor to the mathematical theory of music.

Pythagoras believed that behind the appearance of things, there was the permanent principle of mathematics, and that the forms were based on a transcendental mathematical relation.

In the 6th century BC, the ancient Greek philosopher Pythagoras wanted to know why some musical intervals seemed more beautiful than others, and he found answers in terms of numerical ratios representing the harmonic overtone series on a string.

In the 6th century BC, " Pythagoras himself established a small community that set a premium on study, vegetarianism, and sexual restraint or abstinence.

Diophantus is also known to have written on polygonal numbers, a topic of great interest to Pythagoras and Pythagoreans.

Image: Pythagorean. svg | Pythagoras ' theorem: The sum of the areas of the two squares on the legs ( a and b ) of a right triangle equals the area of the square on the hypotenuse ( c ).

Vincenzo, through his tuning research, found the underlying truth at the heart of the misunderstood myth of ' Pythagoras ' hammers ' ( the square of the numbers concerned yielded those musical intervals, not the actual numbers, as believed ), and through this and other discoveries that demonstrated the fallibility of traditional authorities, a radically empirical attitude developed, passed on to Galileo, which regarded " experience and demonstration " as the sine qua non of valid rational enquiry.

" Having an interest in Rosicrucianism, a prominent magico-religious tradition within Western esotericism, Gardner decided to attend one of the plays performed by the group ; in August 1939, Gardner took his wife to a theatrical performance based on the life of Pythagoras.

" Alberti's thoughts on harmony were not new — they could be traced back to Pythagoras — but he set them in a fresh context, which fit in well with the contemporary aesthetic discourse.

After criticizing the approaches of his predecessors, Ptolemy argued for basing musical intervals on mathematical ratios ( in contrast to the followers of Aristoxenus and in agreement with the followers of Pythagoras ) backed up by empirical observation ( in contrast to the overly theoretical approach of the Pythagoreans ).

However, Pythagoras believed that the mathematics of music should be based on the specific ratio of 3: 2 whereas Ptolemy merely believed that it should just generally involve tetrachords and octaves.

Authorities have not agreed on how the notion arose in Greece: sometimes Pythagoras is said to have been Pherecydes ' pupil, sometimes to have introduced it with the doctrine of Orphism, a Thracian religion that was to be important in the diffusion of reincarnation, or else to have brought the teaching from India.

For science and mathematics to concentrate on what the world ought to be like in the way that religion does can be inappropriate and may lead to improperly ascribing properties to the natural world as happened among the followers of Pythagoras in the sixth century B. C.

However the Chinese culture already featured the same mathmatical positions on the Guqin and the tone holes in flutes, so Pythagoras was not the first.

* c. 570 BC — Birth of Pythagoras on the island of Samos, visionary mathematician ( d. c. 475 BC )

The only complete work of his which has been preserved is the commentary on the Chrysa Epe ( Golden Verses ) of Pythagoras.

According to Herodotus the Greeks of the Hellespont and the Black Sea tell that Zalmoxis was a slave on Samos of Pythagoras, son of Mnesarchos.

* Some authors insist on Zalmoxis ' relation with Pythagoras, stating that he has founded a mystical cult ; partly this theory may be found in Eliade's work ;

Modern mathematicians admire Euclid's practices, and usually frown on those of both Fermat and Pythagoras.

The mathēmatikoi were supposed to have extended and developed the more mathematical and scientific work begun by Pythagoras, while the akousmatikoi focused on the more religious and ritualistic aspects of his teachings.

The mathēmatikoi, on the other hand, allowed that the akousmatikoi were Pythagorean, but felt that their own group was more representative of Pythagoras.

The legacy of Pythagoras, Socrates and Plato was claimed by the wisdom tradition of the Hellenized Jews of Alexandria, on the ground that their teachings derived from those of Moses.

Hippodamus does not seem to have been involved in politics, but several writings attributed to him dealt with issues of the state, including Περί Πολιτείας ( On the State ), Περί Ευδαιμονίας ( On Happiness ), Πυθαγορίζουσαι Θεωρίαι ( Pythagoras Theorems ).

He was mentioned in the writings of Heraclitus and Epicharmus, and had himself mentioned Thales, Epimenides, and Pythagoras.

" According to one statement, Hippasus left no writings, according to another he was the author of the Mystic Discourse, written to bring Pythagoras into disrepute.

The writings attributed to Theano were: Pythagorean Apophthegms, Female Advice, On Virtue, On Piety, On Pythagoras, Philosophical Commentaries, and Letters.

Stobaeus, in his Eclogae, preserves a fragment of his writings ; further extracts survive in the form of quotations in Porphyry's Life of Pythagoras and Simplicius's commentary on Aristotle's Physics.

Some ancient authorities in the doxographic tradition credited the Greek philosophers Pythagoras, in the 6th century BC, and Parmenides, in the 5th, with recognizing that the Earth is spherical.

Heraclitus must have lived after Xenophanes and Pythagoras, as he condemns them along with Homer as proving that much learning cannot teach a man to think ; since Parmenides refers to him in the past tense, this would place him in the 5th century BCE.

After Anaximenes, Pythagoras, Xenophanes and Parmenides all held that the universe was spherical.

Thinkers and teachers like the Buddha, Pythagoras, Heraclitus, Parmenides, and Anaxagoras contributed to such awakenings which Plato would later call anamnesis, or a remembering of things forgotten.

* The Pre-Socratics ( including Thales, Pythagoras, Heraclitus, Parmenides, Empedocles, Anaximander, Anaximenes, Anaxagoras, Leucippus, Democritus and Protagoras )