Why pythagoras is famous

The basic unit, the monad, spoke of the birthplace of all things, and the number two, the dyad, referred to matter. According to the German scholar Burkert, Pythagoras did not deal with mathematics as we understand it today. Burkert contends that the Pythagoreans were mainly concerned with basic arithmetic, which eventually led to the beginnings of modern mathematics.

Both Plato and the ancient orator Isocrates suggest that Pythagoras was an advocate for a new way of life. The school, or organization, that Pythagoras established at Croton operated much like a monastery, and its members shared their assets in much the same way.

They were also committed to one another to the exclusion of outsiders. There were two groups within Pythagoreanism: the mathematikoi students and the akousmatikoi listeners. The pursuit of music may have been associated with the love of Apollo. The Pythagoreans believed that music was a purification for the spirit and had a similar effect to that which medicine produced on the body. Pythagoras was the first person to recommend music as a prescription. He connected music to craftsmanship, design, government, raising a family, fellowship, and self-improvement.

He believed that music was an outflow of harmonia, the divine rule seeking to banish confusion and conflict in the cosmos. Along these lines, music was seen to have a double function as, like science, it empowered people to see into the structures of nature. The Pythagoreans also set great store by physical exercise and recommended daily morning walks and sporting activities.

Periods of self-examination at the beginning and end of every day were likewise advised. Pythagoras was the first person to suggest that the earth was a sphere, but it is not clear what led him to that conclusion. It is possibly connected to his belief that circles were the strongest shape. His experience of the universe was most likely exceptionally basic: at that time, the earth was still thought to be the focal point of the universe with everything revolving around it.

The Pythagorean view of the universe was pretty straightforward and did not take into account any observation of the movements of the planets. Pythagoras escaped to Metapontium and the most authors say he died there, some claiming that he committed suicide because of the attack on his Society.

The evidence is unclear as to when and where the death of Pythagoras occurred but his society expended rapidly after BC and its contributions to mathematics are still recognized and respected. Yes, really! You can learn how to use Pythagoras theorum with chocolate with this great video by 3P Learning. Your email address will not be published. This site uses Akismet to reduce spam.

Learn how your comment data is processed. Skip to content Introduction Pythagoras of Samos is one of the most famous names in the history of mathematics and is recognized as the first true mathematician.

Works In around BC Pythagoras settled in Croton- Italy, where he founded a philosophical and religious school that instantly attracted many followers. Pythagoras and Chocolate Yes, really! Leave a Reply Cancel reply Your email address will not be published. Plato is often thought to be heavily indebted to the Pythagoreans, but he is almost as parsimonious in his references to Pythagoras as Aristotle and mentions him only once in his writings.

In the Philebus , Plato does describe the philosophy of limiters and unlimiteds, which Aristotle assigns to the so-called Pythagoreans of the fifth century and which is found in the fragments of Philolaus, but like Aristotle he does not ascribe this philosophy to Pythagoras himself.

Scholars, both ancient and modern, under the influence of the later glorification of Pythagoras, have supposed that the Prometheus, whom Plato describes as hurling the system down to men, was Pythagoras e. The fragments of Philolaus show that he was the primary figure of this group.

For both Plato and Aristotle, then, Pythagoras is not a part of the cosmological and metaphysical tradition of Presocratic philosophy nor is he closely connected to the metaphysical system presented by fifth-century Pythagoreans like Philolaus; he is instead the founder of a way of life. References to Pythagoras by Xenophanes ca.

For the details of his life we have to rely on fourth-century sources such as Aristoxenus, Dicaearchus and Timaeus of Tauromenium. There is a great deal of controversy about his origin and early life, but there is agreement that he grew up on the island of Samos, near the birthplace of Greek philosophy, Miletus, on the coast of Asia Minor.

There are a number of reports that he traveled widely in the Near East while living on Samos, e. To some extent reports of these trips are an attempt to claim the ancient wisdom of the east for Pythagoras and some scholars totally reject them Zhmud , 83—91 , but relatively early sources such as Herodotus II. Aristoxenus says that he left Samos at the age of forty, when the tyranny of Polycrates, who came to power ca. This chronology would suggest that he was born ca. He then emigrated to the Greek city of Croton in southern Italy ca.

There are a variety of stories about his death, but the most reliable evidence Aristoxenus and Dicaearchus suggests that violence directed against Pythagoras and his followers in Croton ca. There is little else about his life of which we can be confident. The evidence suggests that Pythagoras did not write any books. No source contemporaneous with Pythagoras or in the first two hundred years after his death, including Plato, Aristotle and their immediate successors in the Academy and Lyceum, quotes from a work by Pythagoras or gives any indication that any works written by him were in existence.

Several later sources explicitly assert that Pythagoras wrote nothing e. This fragment shows only that Pythagoras read the writings of others, however, and says nothing about him writing something of his own. The second of these is a Sacred Discourse , which some have wanted to trace back to Pythagoras himself. The idea that Pythagoras wrote such a Sacred Discourse seems to arise from a misreading of the early evidence.

Herodotus says that the Pythagoreans agreed with the Egyptians in not allowing the dead to be buried in wool and then asserts that there is a sacred discourse about this II. For an interesting but ultimately unconvincing attempt to argue that the historical Pythagoras did write books, see Riedweg , 42—43 and the response by Huffman a, — One of the manifestations of the attempt to glorify Pythagoras in the later tradition is the report that he, in fact, invented the word philosophy.

This story goes back to the early Academy, since it is first found in Heraclides of Pontus Cicero, Tusc. 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. Such a conception is thoroughly Platonic, however see, e. For a recent attempt to defend at least the partial accuracy of the story, see Riedweg 90—97 and the response by Huffman a—; see also Zhmud a, — Even if he did not invent the word, what can we say about the philosophy of Pythagoras?

For the reasons given in 1. The Pythagorean Question and 2. There is general agreement as to what the pre-Aristotelian evidence is, although there are differences in interpretation of it. It is crucial to decide this question before developing a picture of the philosophy of Pythagoras since chapter 19, if it is by Dicaearchus, is our earliest summary of Pythagorean philosophy.

Porphyry is very reliable about quoting his sources. He explicitly cites Dicaearchus at the beginning of Chapter 18 and names Nicomachus as his source at the beginning of chapter The material in chapter 19 follows seamlessly on chapter the description of the speeches that Pythagoras gave upon his arrival in Croton in chapter 18 is followed in chapter 19 by an account of the disciples that he gained as the result of those speeches and a discussion of what he taught these disciples.

Thus, the onus is on anyone who would claim that Porphyry changes sources before the explicit change at the beginning of chapter Wehrli gives no reason for not including chapter 19 and the great majority of scholars accept it as being based on Dicaearchus see the references in Burkert a, , n. Zhmud a, following Philip , argues that the passage cannot derive from Dicaearchus, since it presents immortality of the soul with approval, whereas Dicaearchus did not accept its immortality.

However, the passage merely reports that Pythagoras introduced the notion of the immortality of the soul without expressing approval or disapproval.

Zhmud lists other features of the chapter that he regards as unparalleled in fourth-century sources a, but, since the evidence is so fragmentary, such arguments from silence can carry little weight. In the face of the Pythagorean question and the problems that arise even regarding the early sources, it is reasonable to wonder if we can say anything about Pythagoras. A minimalist might argue that the early evidence only allows us to conclude that Pythagoras was a historical figure who achieved fame for his wisdom but that it is impossible to determine in what that wisdom consisted.

We might say that he was interested in the fate of the soul and taught a way of life, but we can say nothing precise about the nature of that life or what he taught about the soul Lloyd There is some reason to believe, however, that something more than this can be said.

The earliest evidence makes clear that above all Pythagoras was known as an expert on the fate of our soul after death. Herodotus tells the story of the Thracian Zalmoxis, who taught his countrymen that they would never die but instead go to a place where they would eternally possess all good things IV.

Among the Greeks the tradition arose that this Zalmoxis was the slave of Pythagoras. Ion of Chios 5 th c. Although Xenophanes clearly finds the idea ridiculous, the fragment shows that Pythagoras believed in metempsychosis or reincarnation, according to which human souls were reborn into other animals after death. According to Herodotus, the Egyptians believed that the soul was reborn as every sort of animal before returning to human form after 3, years.

Without naming names, he reports that some Greeks both earlier and later adopted this doctrine; this seems very likely to be a reference to Pythagoras earlier and perhaps Empedocles later. Many doubt that Herodotus is right to assign metempsychosis to the Egyptians, since none of the other evidence we have for Egyptian beliefs supports his claim, but it is nonetheless clear that we cannot assume that Pythagoras accepted the details of the view Herodotus ascribes to them.

Similarly both Empedocles see Inwood , 55—68 and Plato e. Did he think that we ever escape the cycle of reincarnations? We simply do not know. The fragment of Ion quoted above may suggest that the soul could have a pleasant existence after death between reincarnations or even escape the cycle of reincarnation altogether, but the evidence is too weak to be confident in such a conclusion.

In the fourth century several authors report that Pythagoras remembered his previous human incarnations, but the accounts do not agree on the details. Dicaearchus Aulus Gellius IV. Dicaearchus continues the tradition of savage satire begun by Xenophanes, when he suggests that Pythagoras was the beautiful prostitute, Alco, in another incarnation Huffman b, — It is not clear how Pythagoras conceived of the nature of the transmigrating soul but a few tentative conjectures can be made Huffman Transmigration does not require that the soul be immortal; it could go through several incarnations before perishing.

It has often been assumed that the transmigrating soul is immaterial, but Philolaus seems to have a materialistic conception of soul and he may be following Pythagoras. Similarly, it is doubtful that Pythagoras thought of the transmigrating soul as a comprehensive soul that includes all psychic faculties.

His ability to recognize something distinctive of his friend in the puppy if this is not pushing the evidence of a joke too far and to remember his own previous incarnations show that personal identity was preserved through incarnations.

Thus, it would appear that what is shared with animals and which led Pythagoras to suppose that they had special kinship with human beings Dicaearchus in Porphyry, VP 19 is not intellect, as some have supposed Sorabji , 78 and but rather the ability to feel emotions such as pleasure and pain.

There are significant points of contact between the Greek religious movement known as Orphism and Pythagoreanism, but the evidence for Orphism is at least as problematic as that for Pythagoras and often complicates rather than clarifies our understanding of Pythagoras Betegh ; Burkert a, ff.

There is some evidence that the Orphics also believed in metempsychosis and considerable debate has arisen as to whether they borrowed the doctrine from Pythagoras Burkert a, ; Bremmer , 24 or he borrowed it from them Zhmud a, — Dicaearchus says that Pythagoras was the first to introduce metempsychosis into Greece Porphyry VP Moreover, while Orphism presents a heavily moralized version of metempsychosis in accordance with which we are born again for punishment in this life so that our body is the prison of the soul while it undergoes punishment, it is not clear that the same was true in Pythagoreanism.

It may be that rebirths in a series of animals and people were seen as a natural cycle of the soul Zhmud a, — One would expect that the Pythagorean way of life was connected to metempsychosis, which would in turn suggest that a certain reincarnation is a reward or punishment for following or not following the principles set out in that way of life.

However, there is no unambiguous evidence connecting the Pythagorean way of life with metempsychosis. It is crucial to recognize that most Greeks followed Homer in believing that the soul was an insubstantial shade, which lived a shadowy existence in the underworld after death, an existence so bleak that Achilles famously asserts that he would rather be the lowest mortal on earth than king of the dead Homer, Odyssey XI.

The doctrine of transmigration thus seems to have been extended to include the idea that we and indeed the whole world will be reborn into lives that are exactly the same as those we are living and have already lived. Kingsley argues that the visit of Abaris is the key to understanding the identity and significance of Pythagoras. Abaris was a shaman from Mongolia part of what the Greeks called Hyperborea , who recognized Pythagoras as an incarnation of Apollo.

The stillness of ecstacy practiced by Abaris and handed on to Pythagoras is the foundation of all civilization. Whether or not one accepts this account of Pythagoras and his relation to Abaris, there is a clear parallel for some of the remarkable abilities of Pythagoras in the later figure of Empedocles, who promises to teach his pupils to control the winds and bring the dead back to life Fr.

There are recognizable traces of this tradition about Pythagoras even in the pre-Aristotelian evidence, and his wonder-working clearly evoked diametrically opposed reactions.

Similarly Pythagoras may have claimed authority for his teachings concerning the fate of our soul on the basis of his remarkable abilities and experiences, and there is some evidence that he too claimed to have journeyed to the underworld and that this journey may have been transferred from Pythagoras to Zalmoxis Burkert a, ff. The testimony of both Plato R.

It is plausible to assume that many features of this way of life were designed to insure the best possible future reincarnations, but it is important to remember that nothing in the early evidence connects the way of life to reincarnation in any specific fashion.

One of the clearest strands in the early evidence for Pythagoras is his expertise in religious ritual. Herodotus gives an example: the Pythagoreans agree with the Egyptians in not allowing the dead to be buried in wool II.

It is not surprising that Pythagoras, as an expert on the fate of the soul after death. A significant part of the Pythagorean way of life thus consisted in the proper observance of religious ritual.

The earliest source to quote acusmata is Aristotle, in the fragments of his now lost treatise on the Pythagoreans. It is not always possible to be certain which of the acusmata quoted in the later tradition go back to Aristotle and which of the ones that do go back to Pythagoras. Thus the acusmata advise Pythagoreans to pour libations to the gods from the ear i. A number of these practices can be paralleled in Greek mystery religions of the day Burkert a, Indeed, it is important to emphasize that Pythagoreanism was not a religion and there were no specific Pythagorean rites Burkert , Pythagoras rather taught a way of life that emphasized certain aspects of traditional Greek religion.

A second characteristic of the Pythagorean way of life was the emphasis on dietary restrictions. There is no direct evidence for these restrictions in the pre-Aristotelian evidence, but both Aristotle and Aristoxenus discuss them extensively. Unfortunately the evidence is contradictory and it is difficult to establish any points with certainty. One might assume that Pythagoras advocated vegetarianism on the basis of his belief in metempsychosis, as did Empedocles after him Fr.

This makes it sound as if Pythagoras forbade the eating of just certain parts of animals and certain species of animals rather than all animals; such specific prohibitions are easy to parallel elsewhere in Greek ritual Burkert a, Some have tried to argue that Aristoxenus is refashioning Pythagoreanism in order to make it more rational e.

Certainly animal sacrifice was the central act of Greek religious worship and to abolish it completely would be a radical step. The later tradition proposes a number of ways to reconcile metempsychosis with the eating of some meat. Pythagoras may have adopted one of these positions, but no certainty is possible. For example, he may have argued that it was legitimate to kill and eat sacrificial animals, on the grounds that the souls of men do not enter into these animals Iamblichus, VP Perhaps the most famous of the Pythagorean dietary restrictions is the prohibition on eating beans, which is first attested by Aristotle and assigned to Pythagoras himself Diogenes Laertius VIII.

Aristotle suggests a number of explanations including one that connects beans with Hades, hence suggesting a possible connection with the doctrine of metempsychosis. A number of later sources suggest that it was believed that souls returned to earth to be reincarnated through beans Burkert a, There is also a physiological explanation. Beans, which are difficult to digest, disturb our abilities to concentrate. Moreover, the beans involved are a European vetch Vicia faba rather than the beans commonly eaten today.

Certain people with an inherited blood abnormality develop a serious disorder called favism, if they eat these beans or even inhale their pollen. The discrepancies between the various fourth-century accounts of the Pythagorean way of life suggest that there were disputes among fourth-century Pythagoreans as to the proper way of life and as to the teachings of Pythagoras himself. The acusmata indicate that the Pythagorean way of life embodied a strict regimen not just regarding religious ritual and diet but also in almost every aspect of life.

Some of the restrictions appear to be largely arbitrary taboos, e. On the other hand, some aspects of the Pythagorean life involved a moral discipline that was greatly admired, even by outsiders. Pythagorean silence is an important example.

The ability to remain silent was seen as important training in self-control, and the later tradition reports that those who wanted to become Pythagoreans had to observe a five-year silence Iamblichus, VP Isocrates is contrasting the marvelous self-control of Pythagorean silence with the emphasis on public speaking in traditional Greek education. In addition to silence as a moral discipline, there is evidence that secrecy was kept about certain of the teachings of Pythagoras.

Indeed, one would expect that an exclusive society such as that of the Pythagoreans would have secret doctrines and symbols. That there should be secret teachings about the special nature and authority of the master is not surprising. This does not mean, however, that all Pythagorean philosophy was secret. Aristotle singles out the acusma quoted above Iamblichus, VP 31 as secret, but this statement in itself implies that others were not.

For a sceptical evaluation of Pythagorean secrecy see Zhmud a, — There is some controversy as to whether Pythagoras, in fact, taught a way of life governed in great detail by the acusmata as described above.

Plato praises the Pythagorean way of life in the Republic b , but it is hard to imagine him admiring the set of taboos found in the acusmata Lloyd , 44; Zhmud a. Although acusmata were collected already by Anaximander of Miletus the younger ca.

However, the early evidence suggests that Pythagoras largely constructed the acusmata out of ideas collected from others Thom ; Huffman b: Gemelli Marciano , so it is no surprise that many of them are not uniquely Pythagorean. Moreover, Thom suggests a middle ground between Zhmud and Burkert whereby, contra Zhmud, most of the acusmata were followed by the Pythagoreans but contra Burkert, they were subject to interpretation from the beginning and not followed literally, so that it is possible to imagine people living according to them Thom, 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 a, — He suggests that the Pythagorean way of life differed little from standard aristocratic morality Zhmud a,