Mathematical and Philosophical Ideas of Pythagoras

Pythagoras was considered to be an influencer of many people and things around him. He was said to be interested in philosophy, astronomy, and music. He was greatly motivated by Pherekydes, Thales, and Anaximander. But one of the main achievements that he was known for is being the first real/famous mathematician.

Pythagoras was born approximately 569 BC at the island of Samos Greece. Historians are not really sure when he died but it is said that he died around 500 BC to 475 BC in Metapontum, Lucania, Italy.

He was around 75 years old when he died. Pythagoras’s mother’s name was Parthenis, she was a native of Samos. She was from one of the islands most aristocratic families. His father’s name was Mnesarchus, he was a wealthy merchant of Phoenician heritage who had settled on Samos. Pythagoras father’s business was trade and traveled a lot. It was even said that he had two or three brothers. There also was a theory that he was married to a woman named Theano but others believed that it was one of his students that he was the teacher for (mathopenref.

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com). Some sources said he was treated like a God.

He was also the first to believe that the earth was round.

Pythagoras was most famous for a theory that he did the first proof on called the Pythagorean Theorem. This theory evolved in the world very quickly. This means that a right triangle the square of the hypotenuse is equal to a sum of two squares of other two sides.

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The equation was and still is a^2+b^2=c^2 Once this was put out to the world most people started to experiment with it. This is even still being used to this day in most math school settings like in geometry and algebra classes.

During his lifetime Pythagoras was also famous for some of the quotes that he wrote. One of the quotes was “There is geometry in the humming of the strings, there is music in the spacing of the spheres.” (Pythagoras) Another one was “Geometry is knowledge of the eternally existent.” (Pythagoras)“ He also had many other quotes that did not pertain to math but he was famous for them too. One was “Above the cloud with its shadow is the star with its light.” (Pythagoras)

He and his followers (which were called Pythagoreans) believed that everything can be a made into a number. They were also known for representing numbers by a series of equally spaced numbers by lines, triangles, and so on. This was a way that Pythagoras was able to see and change the shape with every number given. He and the Pythagoreans put the most important numbers into four basic groups. They are triangles, squares, and gnomons. Triangular numbers include any numbers that can form/be shaped into a triangle by a series of dots. An example would be numbers 3 and 10. There are also square numbers that are spaced into squares. An example would be the numbers 4 and 9. He was also known for something called Pythagorean triples. It is described as a group of positive numbers that follow the Pythagorean theorem formula which was a^2+b^2=c^2. One of them is (3,4,5).

Another way Pythagoras discovered math in music was by him to play the instrument called the lyre. When he played it, he realized that when he was playing a tune there are proportional numbers being involved. Some were 2:1 3:2 and 4:3. The ratio 2:1 represents a musical octave, 3:2 represents something called a musical fifth and 4:3 represents something called musical fourth. He even found out that his knowledge can be used in other instruments too. ( With this Pythagoras and the Pythagoreans believed that music was the expression of harmony around the world. This was one of the many things that Pythagoras and the Pythagoreans were able to figure out the official connection with music and numbers. (Karamanides)

Pythagoras was the human being in his time period and was named a philosopher. It basically means a person who loves to search out for wisdom and enlightenment. He and the Pythagoreans (his followers) followed the teachings of the human soul and religion tied together with beliefs and some knowledge of science. Pythagoras was very intrigued with learning religious traditions in some countries and cultures. He believed the soul is made of three main parts. They were emotion, reason, and intelligence. He and the Pythagoreans believed that a person’s soul to be immortal and when dead it can be transmitted from one body to another (Karamanides 54-60). Pythagoras was also a man that believed in many things. One of them was “All things are numbers. Mathematics is the basis for everything, and geometry is the highest form of mathematical studies. The physical world can be understood through mathematics.” Some other ones were “Numbers have personalities, characteristics, strengths and weaknesses.” and “Certain symbols have a mystical significance.” Another one was “All members of the society should observe strict loyalty and secrecy.” One more was “The world depends upon the interaction of opposites, such as the male and female, lightness and darkness, warm and cold, dry and moist, light and heavy, fast and slow ( The last belief he was known for was “The soul resides in the brain, and is immortal. It moves from one being to another, sometimes from a human into an animal, through a series of reincarnations called transmigration until it becomes pure (

In Pythagoras’s lifetime he was also known as an astronomer. Pythagoras showed this belief of astronomy by saying the universe was made of ten spheres. These spheres were the sun, moon, earth and five other planets which were Mercury, Venus, Mars, Jupiter, and Saturn. He even said that there was something called the counter-earth. This was described as a global sphere which was never seen from the earth. Pythagoreans and Pythagoras then mixed astronomy with music. They said or believed that a planet that was moving faster made a very high pitch while it was orbiting the central-hearth. When a planet was moving slower it made less loud pitch of music. As shown above, Pythagoras was a man known for many things.


  • Circumcenter - Math Word Definition - Math Open Reference,
  • Karamanides, Dimitra. Pythagoras: Pioneering Mathematician and Musical Theorist of Ancient Greece. Rosen Central, 2006.
Updated: Feb 13, 2024
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Mathematical and Philosophical Ideas of Pythagoras. (2024, Feb 13). Retrieved from

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