Pythagoras – The First True Mathematician
Pythagoras was an ancient Greek philosopher and the first true mathematician, and today his name is one of the most famous in the history of mathematics. Most of the information about him is considered unreliable because he was collected after his death. The authors, who wrote about it, wanted to portray him as a person with superpowers, similar to God.
He was born around 570 BC before a new era on the Greek island of Samos. As a child, he spent a lot of time traveling with his father, Mnesarh, who was a trader by profession.
At 18, he visited Miletus, a Greek city on the west coast of Anatolia, where he met Tales, the first known Greek philosopher and scientist. Tales were quite old at the time, so he was unlikely to teach Pythagoras. Instead, it is considered that only their learning influenced Pythagoras’s interest in mathematics and astronomy. Listening to the Tales Advice, Pythagoras goes on a journey, primarily with the desire to explore Egypt. It was taught there by many distinguished professors and philosophers, and the greatest amount of knowledge and wisdom was adopted by an Egyptian priest.
In Croton, Pythagoras founded his philosophical-religious society, which had strict rules on the way of life of its members (Platform Resp 600 b). This “Pythagorean lifestyle” (as Plato calls it) encompassed a special way of dressing and eating, the obligation of mutual help and fellowship, work on mathematics, music and astronomy. Such a life, according to Plato, was supposed to provide tranquility not only in this, but also in every future life. Pythagoreans were the first to recognize equality in Greek women’s world, and they were also accepted as members of society. The Pythagoreans treated the slaves in a humane way. The number of members of the Pythagorean community grew in many cities in southern Italy. The political thought of the Pythagoreans was conservative and aristocratic, and that is why during the 5th century st. e. Democrats persecuted, burned down their houses, and tried to destroy their alliance. Pythagoras already had such political conflicts that around 509 c. e. from Croton he moved to Metapont, where he died around 494, very famous and deeply respected.
Pythagoras did not leave any written works behind him, and for several books that were circulating under his name in antiquity, they were found to be undoubtedly apocryphal. Pythagoras’ teaching was of a secret nature and was passed only to oral students directly, which his doctrine usually quoted with the term lat. ipse dixit = “personally said”. Heraclitus says (p. 129) that Pythagoras “collected all that was written” and that by studying these writings “he made his own wisdom”.
Under the Pythagorean theory of numbers, one theory of beings is actually understood, the theory of “nature of things”, and it also includes mathematics, music and astronomy. Aristotle says that “those who are called Pythagoreans first devoted themselves to mathematics and improved it, and since they were raised in it, they considered that its principles were at the same time the principles of all things.” Pythagoreans first of all seemed to notice that the tonnage of a lyre depends on the number, namely, as much as it depends on the length of the strings of the instruments, so it is therefore possible that the intervals on the scale are shown by the fraction of the number. Thus, they determined the relationships among the tones (intervals) that were divided into consonant and dissonant ones: the first – in which they counted the quart, quint and octave – were declared compatible because they were jointly in agreement, while all other intervals were considered disagreeable. Pythagoreans continued to tone relationships between the numbers: the double shorter wire gave a higher tone to the octave, so the octave could be numerically interpreted as a 2: 1 ratio. Similarly, the ratio of parts in a quint can be determined as a numerical ratio of 3: 2, and in the quartets as a ratio of 4: 3.
All consonant intervals, therefore, can be numerically expressed by the relations of numbers 1, 2, 3, and 4. Therefore, these first four numbers in a series of natural numbers have gained particular importance in Pythagoras’ teachings: they represent the monad, the dyad, the triad and the tetrad, which all together reveal the secret of the connection of speech, instrumental and vocal music with the structure of the cosmos. Thus, while militant philosophers spoke of a conflict of opposition in the world, Pythagoreans sought the settlement of the “conflict” in numbers. Aristotle (Metaph. 985b 31-983 and 3) says: “After seeing that the properties and musical conditions can be numbered, and how it seemed to them that all other things were all shaped by their nature by numbers, they thought that the ingredients numbers are the ingredients of everything being and that the whole sky is harmony and number. ” Namely, the same as nature, the diode is the same as a pair of primary opposites, the triad is a symbol from the nature of the firstborn (elementary being), and the tetrad is a numerous symbol for the basic manifestations of nature, for four basic elements: water, air, fire and earth.
When Pythagoreans in their theory of beings equated beings with numbers, space opened for various types of arbitrary and completely fantastic ideas. For example, although we can see the Pythagorean argument why nature should be equal to the number four, it is not so easy to see why the “convenient time, opportunity” should be number seven or why life should be equal to number six. Pythagoreans also announced that the wedding was five, because five were the creation of a triple – the first male number and two – the first female figure. Nevertheless, despite these divergences in the fantastic area, Pythagoras and his followers have made a significant contribution to mathematics. Although Pythagoras’ theorem, as a geometric fact, was known even in Sumerian calculations, Pythagoreans rose above mere geometric or arithmetical facts by transforming them into a deductive system. Pythagoras and his followers are significant for their musical and mathematical research, and because they have deviated from the materialism of militant philosophers with their teachings on metempsychosis and mathematical metaphysics. They are also important because they strongly influenced Plato, especially in the part of their science dealing with the soul and its fate: Plato probably from the Pythagoreans accepted the triple structure of the soul. Pythagorean mathematical speculations also had a strong influence on the formation of Plato’s thoughts.