Why is pythagoras famous

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, If, however, the Pythagorean way of life was little out of the ordinary, why do Plato and Isocrates specifically comment on how distinctive those who followed it were?

The silence of fifth-century sources about people practicing acusmata is not terribly surprising given the very meager sources for the Greek cities in southern Italy in the period.

We would then have lots of people who followed the acusmata of the name in the catalogue appear nowhere else. Moreover, other scholars argue that archaic Greek society in southern Italy was pervaded by religion and the presence of similar precepts in authors such as Hesiod show that adherence to taboos such as are found in the acusmata would not have caused a scandal and adherence to many of them would have gone unobserved by outsiders Gemelli Marciano , — Once again a problem of source criticism raises its head.

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. Special relativity is still based directly on an empirical law, that of the constancy of the velocity of light.

The fact that such a metric is called Euclidean is connected with the following. The postulation of such a metric in a three-dimensional continuum is fully equivalent to the postulation of the axioms of Euclidean Geometry. The defining equation of the metric is then nothing but the Pythagorean Theorem applied to the differentials of the co-ordinates. Such transformations are called Lorentz transformations.

From the latest results of the theory of relativity, it is probable that our three-dimensional space is also approximately spherical , that is, that the laws of disposition of rigid bodies in it are not given by Euclidean geometry, but approximately by spherical geometry. According to the general theory of relativity , the geometrical properties of space are not independent, but they are determined by matter.

I wished to show that space time is not necessarily something to which one can ascribe to a separate existence, independently of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended. The above excerpts — from the genius himself — precede any other person's narrative of the Theory of Relativity and the Pythagorean Theorem. Accordingly, I now provide a less demanding excerpt, albeit one that addresses the effects of the Special and General theories of relativity.

The system of units in which the speed of light c is the unit of velocity allows to cast all formulas in a very simple form. The Pythagorean Theorem graphically relates energy, momentum and mass. Euclid of Alexandria was a Greek mathematician Figure 10 , and is often referred to as the Father of Geometry. The date and place of Euclid's birth, and the date and circumstances of his death, are unknown, but it is thought that he lived circa BCE.

His work Elements , which includes books and propositions, is the most successful textbook in the history of mathematics. In it, the principles of what is now called Euclidean Geometry were deduced from a small set of axioms. When Euclid wrote his Elements around BCE , he gave two proofs of the Pythagorean Theorem: The first, Proposition 47 of Book I, relies entirely on the area relations and is quite sophisticated; the second, Proposition 31 of Book VI, is based on the concept of proportion and is much simpler.

He may have used Book VI Proposition 31, but, if so, his proof was deficient, because the complete theory of Proportions was only developed by Eudoxus, who lived almost two centuries after Pythagoras.

Euclid's Elements furnishes the first and, later, the standard reference in geometry. It is a mathematical and geometric treatise consisting of 13 books. It comprises a collection of definitions, postulates axioms , propositions theorems and constructions and mathematical proofs of the propositions. Euclid provided two very different proofs, stated below, of the Pythagorean Theorem.

This is probably the most famous of all the proofs of the Pythagorean proposition. In right-angled triangles the figure on the side opposite the right angle equals the sum of the similar and similarly described figures on the sides containing the right angle.

In right-angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle. Euclid I 47 is often called the Pythagorean Theorem , called so by Proclus — a Greek philosopher who became head of Plato's Academy and is important mathematically for his commentaries on the work of other mathematicians — and others centuries after Pythagoras and even centuries after Euclid.

Although many of the results in Elements originated with earlier mathematicians, one of Euclid's accomplishments was to present them in a single, logically coherent framework, making them easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics twenty-three centuries later.

Although best known for its geometric results, Elements also includes number theory. It considers the connection between perfect numbers and Mersenne primes, the infinitude of prime numbers and the Euclidean algorithm for finding the greatest common divisor of two numbers.

The geometrical system described in the Elements was long known simply as geometry , and was considered to be the only geometry possible. Today, however, this system is often referred to as Euclidean Geometry to distinguish it from other so-called Non-Euclidean geometries that mathematicians discovered in the nineteenth century.

At this point in my plotting of the year-old story of Pythagoras, I feel it is fitting to present one proof of the famous theorem. For me, the simplest proof among the dozens of proofs that I read in preparing this article is that shown in Figure Start with four copies of the same triangle. See upper part of Figure See lower part of Figure In the seventeenth century, Pierre de Fermat — Figure 14 investigated the following problem: for which values of n are there integer solutions to the equation.

Fermat conjectured that there were no non-zero integer solutions for x and y and z when n was greater than 2. He did not leave a proof, though. Instead, in the margin of a textbook, he wrote that he knew that this relationship was not possible, but he did not have enough room on the page to write it down.

His conjecture became known as Fermat's Last Theorem. This may appear to be a simple problem on the surface, but it was not until when Andrew Wiles of Princeton University finally proved the year-old marginalized theorem, which appeared on the front page of the New York Times.

Today, Fermat is thought of as a number theorist, in fact perhaps the most famous number theorist who ever lived. It is therefore surprising to find that Fermat was a lawyer , and only an amateur mathematician. Also surprising is the fact that he published only one mathematical paper in his life, and that was an anonymous paper written as an appendix to a colleague's book.

Because Fermat refused to publish his work, his friends feared that it would soon be forgotten unless something was done about it. His son Samuel undertook the task of collecting Fermat's letters and other mathematical papers, comments written in books and so on with the goal of publishing his father's mathematical ideas. Samuel found the marginal note the proof could not fit on the page in his father's copy of Diophantus's Arithmetica. In this way the famous Last Theorem came to be published.

His graduate research was guided by John Coates beginning in the summer of Together they worked on the arithmetic of elliptic curves with complex multiplication using the methods of Iwasawa theory. He further worked with Barry Mazur on the main conjecture of Iwasawa theory over Q and soon afterwards generalized this result to totally real fields.

Taking approximately 7 years to complete the work, Wiles was the first person to prove Fermat's Last Theorem, earning him a place in history. It seems that he also visited Italy with his father. Little is known of Pythagoras's childhood. All accounts of his physical appearance are likely to be fictitious except the description of a striking birthmark which Pythagoras had on his thigh. It is probable that he had two brothers although some sources say that he had three.

Certainly he was well educated, learning to play the lyre, learning poetry and to recite Homer. There were, among his teachers, three philosophers who were to influence Pythagoras while he was a young man.

One of the most important was Pherekydes who many describe as the teacher of Pythagoras. The other two philosophers who were to influence Pythagoras, and to introduce him to mathematical ideas, were Thales and his pupil Anaximander who both lived on Miletus. In [ 8 ] it is said that Pythagoras visited Thales in Miletus when he was between 18 and 20 years old. By this time Thales was an old man and, although he created a strong impression on Pythagoras, he probably did not teach him a great deal.

However he did contribute to Pythagoras's interest in mathematics and astronomy, and advised him to travel to Egypt to learn more of these subjects. Thales 's pupil, Anaximander, lectured on Miletus and Pythagoras attended these lectures.

Anaximander certainly was interested in geometry and cosmology and many of his ideas would influence Pythagoras's own views. In about BC Pythagoras went to Egypt. This happened a few years after the tyrant Polycrates seized control of the city of Samos. There is some evidence to suggest that Pythagoras and Polycrates were friendly at first and it is claimed [ 5 ] that Pythagoras went to Egypt with a letter of introduction written by Polycrates.

In fact Polycrates had an alliance with Egypt and there were therefore strong links between Samos and Egypt at this time. The accounts of Pythagoras's time in Egypt suggest that he visited many of the temples and took part in many discussions with the priests. According to Porphyry [ 12 ] and [ 13 ] Pythagoras was refused admission to all the temples except the one at Diospolis where he was accepted into the priesthood after completing the rites necessary for admission.

It is not difficult to relate many of Pythagoras's beliefs, ones he would later impose on the society that he set up in Italy, to the customs that he came across in Egypt.

For example the secrecy of the Egyptian priests, their refusal to eat beans, their refusal to wear even cloths made from animal skins, and their striving for purity were all customs that Pythagoras would later adopt. Porphyry in [ 12 ] and [ 13 ] says that Pythagoras learnt geometry from the Egyptians but it is likely that he was already acquainted with geometry, certainly after teachings from Thales and Anaximander.

Polycrates abandoned his alliance with Egypt and sent 40 ships to join the Persian fleet against the Egyptians. Pythagoras was taken prisoner and taken to Babylon. Iamblichus writes that Pythagoras see [ 8 ] Whilst he was there he gladly associated with the Magoi He also reached the acme of perfection in arithmetic and music and the other mathematical sciences taught by the Babylonians Pythagoras believed that 10 was the ideal number.

Plato may also have obtained the idea that mathematical and dynamic ideas are behind logic, science, and morality from Pythagoras. Plato and Pythagoras shared a magical way to deal with the spirit and its place in the material world, and it is likely that both were impacted by Orphism, a set of religious beliefs and practices originating in the ancient Greek world. Pythagoras established the mysterious society of the Pythagoreans in southern Italy. The Pythagoreans put forward a hypothesis that stated that everything known to humankind could be clarified with numbers, explicitly entire numbers.

This rationale made perfect sense to them, and it is easy to see why. Even today, we use numbers for everything from working out wind speeds in a storm to calculating the speed of a vehicle.

Pythagoras made huge contributions in the fields of astronomy, mathematics, philosophy, music and many other areas. His impact on later philosophers such as Plato cannot be underestimated, and his influence was significant to the point that he could be seen as the most persuasive intellectual of all time. Save my name and email in this browser for the next time I comment. Here is a list of the top 11 contributions of Pythagoras: Contents hide.

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