Pythagoras of samos when was he born

An important part of Pythagoreanism was the relationship of all life. A universal life spirit was thought to be present in animal and vegetable life, although there is no evidence to show that Pythagoras believed that the soul could be born in the form of a plant.

It could be born, however, in the body of an animal, and Pythagoras claimed to have heard the voice of a dead friend in the howl of a dog being beaten. The Pythagoreans presented as fact the dualism that life is controlled by opposite forces between Limited and Unlimited. It Pythagoras. Reproduced by permission of the Corbis Corporation.

His study of musical intervals, leading to the discovery that the chief intervals can be expressed in numerical ratios relationships between numbers between the first four integers positive whole numbers , also led to the theory that the number ten, the sum of the first four integers, embraced the whole nature of number.

Pythagoras may have discovered the theorem which still bears his name in right triangles [triangle with one angle equal to 90 degrees], the square on the hypotenuse equals the sum of the squares on the other sides , although this proposal has been discovered on a writing stone dating from the time of the Babylonian king Hammurabi died c.

Regardless of their sources, the Pythagoreans did important work in extending the body of mathematical knowledge. As a more general outline, the Pythagoreans presented the two contraries opposites , Limited and Unlimited, as ultimate principles, or truths. Numerical oddness and evenness are equated with Limited and Unlimited, as are one and plurality many , right and left, male and female, motionlessness and movement, straight and crooked, light and darkness, and good and bad.

It is not clear whether an ultimate One, or Monad, was presented as the cause of the two categories. The Pythagoreans, as a result of their religious beliefs and careful study of mathematics, developed a cosmology dealing with the structures of the universe which differed in some important respects from the world views at the time, the most important of which was their view of the Earth as a sphere which circled the center of the universe.

Pythagoras believed that a person could save and free their soul through physical and moral cleansing. His teachings may be compared to the ancient Vedic knowledge based on the quantitative transmigration of souls; they will get to animal or human bodies until the right to return to God is earned. Pythagoras did not impose his philosophy on ordinary people, who just needed to learn the basics of sciences.

As long as Pythagoras returned to Greece from Babylon, he met a beautiful woman, Theano, who attended his lectures secretly. The philosopher was not young at that time: something about years old. Soon, the lovers married. They had two children, a boy and a girl, together; their names are unknown.

A democratic revolution took place there, and the philosopher had to leave the region; he headed to Metaponto, but the rebellion reached this town soon. The mathematician had many enemies who did not share his life principles. It could be a man whom he rejected to teach secret occult methods. Toggle navigation Logo Biography News About. Celebrities Public Figures Pythagoras. Name: Pythagoras Pythagoras of Samos. Birthplace: Samos, Greece. Tags: philosopher , mathematician.

More info: show. Zhmud argues that the split between acusmatici who blindly followed the acusmata and the mathematici who learned the reasons for them see the fifth paragraph of section 5 below is a creation of the later tradition, appearing first in Clement of Alexandria and disappearing after Iamblichus Zhmud a, — He also notes that the term acusmata appears first in Iamblichus On the Pythagorean Life 82—86 and suggests that it is also a creation of the later tradition.

The Pythagorean maxims did exist earlier, as the testimony of Aristotle shows, but they were known as symbola , were originally very few in number and were mainly a literary phenomena rather than being tied to people who actually practiced them Zhmud a, — Indeed, the description of the split in what is likely to be the original version Iamblichus, On General Mathematical Science So the question of whether Pythagoras taught a way of life tightly governed by the acusmata turns again on whether key passages in Iamblichus On the Pythagorean Life 81—87, On General Mathematical Science If they do, we have very good reason to believe that Pythagoras taught such a life, if they do not the issue is less clear.

The testimony of fourth-century authors such as Aristoxenus and Dicaearchus indicates that the Pythagoreans also had an important impact on the politics and society of the Greek cities in southern Italy. Dicaearchus reports that, upon his arrival in Croton, Pythagoras gave a speech to the elders and that the leaders of the city then asked him to speak to the young men of the town, the boys and the women Porphyry, VP The acusmata teach men to honor their wives and to beget children in order to insure worship for the gods Iamblichus, VP 84—6.

Dicaearchus reports that the teaching of Pythagoras was largely unknown, so that Dicaearchus cannot have known of the content of the speech to the women or of any of the other speeches; the speeches presented in Iamblichus VP 37—57 are thus likely to be later forgeries Burkert a, , but there is early evidence that he gave different speeches to different groups Antisthenes V A On the other hand, it is noteworthy that Plato explicitly presents Pythagoras as a private rather than a public figure R.

It seems most likely that the Pythagorean societies were in essence private associations but that they also could function as political clubs see Zhmud a, — , while not being a political party in the modern sense; their political impact should perhaps be better compared to modern fraternal organizations such as the Masons. Thus, the Pythagoreans did not rule as a group but had political impact through individual members who gained positions of authority in the Greek city-states in southern Italy.

See further Burkert a, ff. 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.

Neither Plato nor Aristotle treats Pythagoras as having contributed to the development of Presocratic cosmology, although Aristotle in particular discusses the topic in some detail in the first book of the Metaphysics and elsewhere.

Thus, for Dicaearchus too, it is not as a mathematician or Presocratic writer on nature that Pythagoras is famous. At first sight, it appears that Eudemus did assign Pythagoras a significant place in the history of geometry.

Eudemus is reported as beginning with Thales and an obscure figure named Mamercus, but the third person mentioned by Proclus in this report is Pythagoras, immediately before Anaxagoras. There is no mention of the Pythagorean theorem, but Pythagoras is said to have transformed the philosophy of geometry into a form of liberal education, to have investigated its theorems in an immaterial and intellectual way and specifically to have discovered the study of irrational magnitudes and the construction of the five regular solids.

Proclus elsewhere quotes long passages from Iamblichus and is doing the same here. Even those who want to assign Pythagoras a larger role in early Greek mathematics recognize that most of what Proclus says here cannot go back to Eudemus Zhmud a, — Thus, not only is Pythagoras not commonly known as a geometer in the time of Plato and Aristotle, but also the most authoritative history of early Greek geometry assigns him no role in the history of geometry in the overview preserved in Proclus.

Eudemus does not assign the discoveries to any specific Pythagorean, and they are hard to date. The crucial point to note is that Eudemus does not assign these discoveries to Pythagoras himself. The first Pythagorean whom we can confidently identify as an accomplished mathematician is Archytas in the late fifth and the first half of the fourth century.

Are we to conclude, then, that Pythagoras had nothing to do with mathematics or cosmology? The evidence is not quite that simple. Several things need to be noted about this tradition, however, in order to understand its true significance. Although a number of modern scholars have speculated on what sort of proof Pythagoras might have used e.

All that this tradition ascribes to Pythagoras, then, is discovery of the truth contained in the theorem. The truth may not have been in general form but rather focused on the simplest such triangle with sides 3, 4 and 5 , pointing out that such a triangle and all others like it will have a right angle. Robson It is possible, then, that Pythagoras just passed on to the Greeks a truth that he learned from the East.

If the story is to have any force and if it dates to the fourth century, it shows that Pythagoras was famous for a connection to a certain piece of geometrical knowledge, but it also shows that he was famous for his enthusiastic response to that knowledge, as evidenced in his sacrifice of oxen, not for any geometric proof.

What emerges from this evidence, then, is not Pythagoras as the master geometer, who provides rigorous proofs, but rather Pythagoras as someone who recognizes and celebrates certain geometrical relationships as of high importance. It is striking that a very similar picture of Pythagoras emerges from the evidence for his cosmology. A famous discovery is attributed to Pythagoras in the later tradition, i.

The only early source to associate Pythagoras with the whole number ratios that govern the concords is Xenocrates Fr. It may be once again that Pythagoras knew of the relationship without either having discovered it or having demonstrated it scientifically.

The relationship was probably first discovered by instrument makers, and specifically makers of wind instruments rather than stringed instruments Barker , Here in the acusmata , these four numbers are identified with one of the primary sources of wisdom in the Greek world, the Delphic oracle.

This acusma thus seems to be based on the knowledge of the relationship between the concords and the whole number ratios. The picture of Pythagoras that emerges from the evidence is thus not of a mathematician, who offered rigorous proofs, or of a scientist, who carried out experiments to discover the nature of the natural world, but rather of someone who sees special significance in and assigns special prominence to mathematical relationships that were in general circulation.

Some might suppose that this is a reference to a rigorous treatment of arithmetic, such as that hypothesized by Becker , who argued that Euclid IX. There is, moreover, no talk of mathematical proof or a deductive system in the passage from Aristoxenus just quoted. Pythagoras is known for the honor he gives to number and for removing it from the practical realm of trade and instead pointing to correspondences between the behavior of number and the behavior of things.

The doxographical tradition reports that Pythagoras discovered the sphericity of the earth, the five celestial zones and the identity of the evening and morning star Diogenes Laertius VIII. In each case, however, Burkert has shown that these reports seem to be false and the result of the glorification of Pythagoras in the later tradition, since the earliest and most reliable evidence assigns these same discoveries to someone else a, ff.

Thus, Theophrastus, who is the primary basis of the doxographical tradition, says that it was Parmenides who discovered the sphericity of the earth Diogenes Laertius VIII. Parmenides is also identified as the discoverer of the identity of the morning and evening star Diogenes Laertius IX. The identification of the five celestial zones depends on the discovery of the obliquity of the ecliptic, and some of the doxography duly assigns this discovery to Pythagoras as well and claims that Oenopides stole it from Pythagoras Aetius II.

As was shown above, Pythagoras saw the cosmos as structured according to number insofar as the tetraktys is the source of all wisdom. His cosmos was also imbued with a moral significance, which is in accordance with his beliefs about reincarnation and the fate of the soul West , —; Huffman , 60— Zhmud calls these cosmological acusmata into question a, — , noting that some only appear in Porphyry, but Porphyry explicitly identifies Aristotle as his source and we have no reason to doubt him VP The best analogy for the type of account of the cosmos which Pythagoras gave might be some of the myths which appear at the end of Platonic dialogues such as the Phaedo , Gorgias or Republic , where cosmology has a primarily moral purpose.

Should the doctrine of the harmony of the spheres be assigned to Pythagoras? Certainly the acusma which talks of the sirens singing in the harmony represented by the tetraktys suggests that there might have been a cosmic music and that Pythagoras may well have thought that the heavenly bodies, which we see move across the sky at night, made music by their motions.

The first such cosmic model in the Pythagorean tradition is that of Philolaus in the second half of the fifth century, a model which still shows traces of the connection to the moral cosmos of Pythagoras in its account of the counter-earth and the central fire see Philolaus. If Pythagoras was primarily a figure of religious and ethical significance, who left behind an influential way of life and for whom number and cosmology primarily had significance in this religious and moral context, how are we to explain the prominence of rigorous mathematics and mathematical cosmology in later Pythagoreans such as Philolaus and Archytas?

It is important to note that this is not just a question asked by modern scholars but was already a central question in the fourth century BCE. What is the connection between Pythagoras and fifth-century Pythagoreans? The tradition of a split between two groups of Pythagoreans in the fifth century, the mathematici and the acusmatici , points to the same puzzlement. The evidence for this split is quite confused in the later tradition, but Burkert a, ff.

The acusmatici , who are clearly connected by their name to the acusmata , are recognized by the other group, the mathematici , as genuine Pythagoreans, but the acusmatici do not regard the philosophy of the mathematici as deriving from Pythagoras but rather from Hippasus.

The mathematici appear to have argued that, while the acusmatici were indeed Pythagoreans, it was the mathematici who were the true Pythagoreans; Pythagoras gave the acusmata to those who did not have the time to study the mathematical sciences, so that they would at least have moral guidance, while to those who had the time to fully devote themselves to Pythagoreanism he gave training in the mathematical sciences, which explained the reasons for this guidance.

This tradition thus shows that all agreed that the acusmata represented the teaching of Pythagoras, but that some regarded the mathematical work associated with the mathematici as not deriving from Pythagoras himself, but rather from Hippasus on the controversy about the evidence for this split into two groups of Pythagoreans see the fifth paragraph of section 4.

For fourth-century Greeks as for modern scholars, the question is whether the mathematical and scientific side of later Pythagoreanism derived from Pythagoras or not. The picture of Pythagoras presented above is inevitably based on crucial decisions about sources and has been recently challenged in a searching critique Zhmud a. In many cases, he argues, the evidence suggests that early Pythagoreanism was more scientific and that religious and mythic elements only gained in importance in the later tradition.

One of the central pieces of evidence for this view is that the tetraktys does not first appear until late in the tradition, in Aetius in the first century CE DK 1. Zhmud himself agrees that sections 82—86 of On the Pythagorean Life as a whole go back to Aristotle but suggests that the acusma about the tetraktys was a post-Aristotelian addition a, — Once again source criticism is crucial. If the acusma in question goes back to Aristotle then there is good evidence for the tetraktys in early Pythagoreanism.

If we regard it as a later insertion into Aristotelian material, the early Pythagorean credentials of the tetraktys are less clear. Although there is no explicit evidence, Pythagoras is the most likely candidate to fill these gaps. Thus between Thales, whom Eudemus identifies as the first geometer, and Hippocrates of Chios, who produced the first Elements , someone turned geometry into a deductive science Zhmud a, In each case Zhmud suggests that Pythagoras is that someone.

Such speculations have some plausibility but they highlight even more the puzzle as to why, if Pythagoras played this central role in early Greek mathematics, no early source explicitly ascribes it to him. Of course, some scholars argue that the majority have overlooked key passages that do assign mathematical achievements to Pythagoras. In order to gain a rounded view of the Pythagorean question it is thus appropriate to look at the most controversial of these passages.

Some scholars who regard Pythagoras as a mathematician and rational cosmologist, such as Guthrie, admit that the earliest evidence does not support this view Lloyd , 25 , but maintain that the prominence of Pythagoras the mathematician in the late tradition must be based on something early.

Others maintain that there is evidence in the sixth- and fifth-century BCE for Pythagoras as a mathematician and cosmologist. Thus the description of Pythagoras as a wise man who practiced inquiry is simply too general to aid in deciding what sort of figure Herodotus and Heraclitus saw him as being. There is more controversy about the fourth-century evidence.

Zhmud argues that Isocrates regards Pythagoras as a philosopher and mathematician a, However, it is hard to see how the passage in question Busiris 28—29 supports this view. Nowhere in it does Isocrates ascribe mathematical work or a rational cosmology to Pythagoras.

What Isocrates emphasizes about Pythagoras is what the rest of the early tradition emphasizes, his interest in religious rites.

The same situation arises with Fr. If the words in question were by Aristotle they would be his sole statement that Pythagoras was a natural philosopher.

The case of Fr. The further problem with Fr. This awkward repetition of the same story about two different people immediately suggests that only one story was in the original and the other was added in the later tradition. This suggestion is strikingly confirmed by the fact that Aristotle does tell this story about Anaxagoras in his extant works Eudemian Ethics a11—16 but not about Pythagoras. Aristotle only knows Pythagoras as a wonder working sage and teacher of a way of life Fr.

What about the pupils of Plato and Aristotle? Pythagoreans contributed to our understanding of angles, triangles, areas, proportion, polygons, and polyhedra. Pythagoras also related music to mathematics.

He had long played the seven string lyre, and learned how harmonious the vibrating strings sounded when the lengths of the strings were proportional to whole numbers, such as , , Pythagoreans also realized that this knowledge could be applied to other musical instruments.

The reports of Pythagoras' death are varied. He is said to have been killed by an angry mob, to have been caught up in a war between the Agrigentum and the Syracusans and killed by the Syracusans, or been burned out of his school in Crotona and then went to Metapontum where he starved himself to death.

At least two of the stories include a scene where Pythagoras refuses to trample a crop of bean plants in order to escape, and because of this, he is caught.

The Pythagorean Theorem is a cornerstone of mathematics, and continues to be so interesting to mathematicians that there are more than different proofs of the theorem, including an original proof by President Garfield.