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Pythagoras: Going Beyond a2 + b2 = c2

November 8, 2021
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By Lillie Therieau 


Pythagoras is one of the most celebrated classical mathematicians and most school children learn about him briefly in the context of their geometry classes. 


However, his life and work was much more complex and multidisciplinary than we know! He led a mysterious spiritual society for most of his life, known as the Pythagoreans. 


His philosophical thought inspired important thinkers around the world and throughout history. Delve into the strange and superstitious world of one of history’s most famous, yet underexplored mathematicians! 

The Mysterious Life of Pythagoras

Little is definitively known about Pythagoras’ early life, as most biographical details come from his students and friends who wrote about him after his death. However, it is believed that Pythagoras was born in about 570 BC in Ancient Greece, on the island of Samos. Before his birth, a prophet is said to have told his mother that the child she was carrying would be wise and important to the development of mankind.


Bust Sculpture of Pythagoras


He traveled to the Middle East, like many other important Greek thinkers. Pythagoras spent a lot of time in Egypt, where he studied from priests in the city of Thebes. There are also many sources who say that he studied in Persia, Crete, and even India. In any event, Pythagoras was greatly influenced by the teachings of Orphism, a sect of Greek religious beliefs originating from the teachings of the legendary Greek prophet and musician, Orpheus, who is said to have journeyed to the Underworld and survived. 


When Pythagoras returned to his native island of Samos in his mid-30s, he discovered that it had been conquered by a tyrant, Polycrates. As a philosophical believer in freedom, Pythagoras disagreed with the way Samos was governed. He decided to leave and move to the Greek colony of Croton, in modern-day Southern Italy. There he would begin a community of like-minded people that lived together and followed his philosophical and religious teachings. 

The Beliefs of the Pythagoreans 

Pythagoras’ beliefs were a unique synthesis of the many places he had traveled, cultures he had experienced, and philosophers that he had learned from. One of the main ideas that he espoused to his followers was metempsychosis, or the idea that all souls are immortal and are reborn in a new body after death. He also taught a strong harmonious connection between religion and the mathematics of the natural world. 


This belief is what animated his idea of the harmony of the spheres, wherein the planets and stars were said to move according to equations that correspond to musical notes, creating a symphony. However, Pythagoras believed that human beings could never hear this celestial music because it surrounds them from birth and they’re oblivious to it. 


Besides reincarnation and natural harmony, Pythagoras taught his followers to observe numerology, drawing meaning from the occurrence of certain numbers. The number one represented the origin of everything, while the number three was considered to be an ideal number with a beginning, middle, and end. To the Pythagoreans, odd numbers were masculine and even numbers feminine. However, ten was the perfect number, which the community celebrated by never gathering in groups that exceeded ten people. 


On Croton, Pythagoras and his followers embraced a radical communal lifestyle. They shared all of their possessions, ate their meals together, and vowed to observe the rules of the community. In many ways, the community was like a monastery. They embraced simplicity and abstained from excess in their daily lives. Each member of the Pythagoreans followed a set of restrictions and rules. They were vegetarians and did not eat fava beans. They also believed strongly in the importance of athletics and quiet walks. 


Many people from all over Greece flocked to Croton to join Pythagoras’ community. Upon joining, members were forbidden to share their ritual teachings with outsiders. If a member did not obey the laws and customs of the community, they would be expelled. The remaining members would erect a tombstone for them and pretend that they had died. 


Pythagoras’ esoteric ideas on living a good life and being a spiritual person are not often what is most remembered about his life. However, his lifestyle and spiritual teachings had enormous impacts on later Greek philosophers, early Christianity, and the Middle Ages. His beliefs in numerology even shaped the world of Greek and early Christian architecture. Many buildings were designed to reflect the meaning of certain numbers, such as Hadrian’s Pantheon in Rome. 


The Ceiling of Hadrian’s Pantheon in Rome

Pythagoras’ Influence on Math and the Natural Sciences 

The most well-known mathematical contribution credited to Pythagoras is his famous theorem. It states that for any right triangle, the length of the hypotenuse (the longest side) squared is equal to the sum of the other two sides squared. This concept is a crucial part of geometry and has many other mathematical applications. 


Pythagorean Theorem


However, some readers may be surprised to find out that Pythagoras most likely did not discover this theorem. There’s evidence that the ancient Babylonians and Indians knew of this equation and were using it centuries earlier than Pythagoras, though he may have been the first to set it out as a proof. 


Pythagoras is also one of the first people to teach that the earth was spherical and to divide it up into 5 climate zones divided by the major circles of latitude. He also was among the first to identify that the Morning Star and the Evening Star were the same celestial body, Venus. 


Finally, he’s also credited with being the first thinker to identify the five Platonic solids. A platonic solid is a three-dimensional shape that must be a regular polyhedron. This means that each of the faces of a Platonic solid is a congruent regular polygon and that the same number of faces meet at each vertex. The five Platonic solids that Pythagoras identified are: a tetrahedron, a cube, an octahedron, a dodecahedron, and an icosahedron. 


The Platonic Solids

The Death and Legacy of Pythagoras 

The death of Pythagoras is widely disputed, as are many other details of his life. However, it is accepted that it had something to do with the revolt in Croton sometime around 510 BC. After an important military victory, some prominent citizens in Croton had suggested a democratic system of government. However, Pythagoras roundly rejected the idea. The supporters of democracy galvanized the public in Croton, turning them against the Pythagoreans. The people attacked Pythagoras and his followers, burning their meeting place to the ground while they were inside. 


Some scholars believe that Pythagoras died in the fire, while others believe that he escaped and died afterwards in hiding, either of his wounds or starvation. After his death, his followers scattered, unable to replace their charismatic leader. 


However, the teachings and influence of Pythagoras lived on, immortalized in important writings like those of Plato and other Greek and Roman philosophers. He inspired the work of some of the most important mathematicians in the Middle Ages, such as Isaac Newton, Nicolaus Copernicus, and Johannes Kepler. Today his theorem is taught in classrooms around the world! 


The Brilliant Lives of Famous Mathematicians 


This article is the fifth in our series exploring the lives and achievements of famous mathematicians throughout history. (Our last article was about the British mathematician Alan Turing!) 


Through the lives of these brilliant folks, we hope you’ll find connections, inspiration, and empowerment.


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