Pythagoras of Samos was a famous Greek mathematician and philosopher ( ). He is known best for the proof of the important Pythagorean theorem, which is about right angle triangles. He started a group of mathematicians, called the Pythagoreans, who worshiped numbers and lived like monks. He had an influence on Plato.
He had a great impact on mathematics, theory of music and astronomy. His theories are still used in mathematics today. He was one of the greatest thinkers of his time.
Pythagoras was born in Samos, a little island off the western coast of Asia Minor. There is not much information about his life. It is said that he had a good childhood. Growing up with two or three brothers, he was well educated. He did not agree with the government and their schooling, so he moved to Crotone and set up his own cult (little society) of followers under his rule. His followers did not have any personal possessions, and they were all vegetarians. Pythagoras taught them all, and they had to obey strict rules.
Some say he was the first person to use the term philosophy. Since he worked very closely with his group, the Pythagoreans, it is sometimes hard to tell his works from those of his followers.
Religion was important to the Pythagoreans. They swore their oaths by "1+2+3+4" (which equals 10). They also believed the soul is immortal and goes through a cycle of rebirths until it can become pure. They believed that these souls were in both animal and plant life.
Pythagoras' most important belief was that the physical world was mathematical and that numbers were the real reality.
Pythagoras is most famous for his theorem to do with right triangles. He said that the length of the longest side of the right angled triangle called the hypotenuse (C) squared would equal the sum of the other sides squared. And so a² + b² = c² was born. There are many different proofs for this Pythagorean theorem.
Socrates
Socrates (469 BC – 399 BC) was one of the greatest Greek philosophers. He did not propose any specific knowledge or policy. He showed how argument, debate, and discussion could help men to understand difficult issues. Most of the issues he dealt with were only political on the surface. Underneath, they were moral questions about how life should be lived. Such is the influence of Socrates that philosophers before him are called the Presocratic philosophers.
Socrates made enemies, three of whom brought charges against him. Socrates was tried for his life in 399 BC, found guilty, and put to death by drinking hemlock (a herbal poison). The story of his trial and death is the subject of a tract by Plato which is called the "Apologia".
Most of what we know about Socrates comes from the works of Plato, who was his pupil. Socrates lived in the Greek city of Athens. His method of teaching was to have a dialogue with individual students. They would propose some point of view, and Socrates would question them, asking what they meant. He would pretend "I don't know anything; I'm just trying to understand what it is you are saying", or words to that effect. This is now called the Socratic method of teaching.
Socrates is sometimes called the "father of Western philosophy". This is because in the discussions he uncovered some of the most basic questions in philosophy, questions which are still discussed today. Some of the people he taught came to be important and successful, like Plato and Alcibiades.
Socrates never wrote anything. All of what we know about Socrates is from what other people wrote about him. Our main source of what we know about Socrates is from the writings of his student, Plato. Some of Plato's dialogues, such as the "Crito" and the "Phaedo", are loosely based on fact. They are not written records, but artistic re-creation of Socrates in action.
Another of Socrates' students, Xenophon also wrote about Socrates. Aristophanes, a person who wrote brilliant satirical comedies, wrote about him in play called "The Clouds". Socrates was an easy target for satire. He walked barefoot, and with a swagger. Sometimes he stood in a trance for hours. In "The Clouds" Socrates is a crazy person who tries to scam people out of their money. Plato wrote that Socrates taught for free.
We do not know if Plato's description of Socrates is accurate or not. That is called the 'Socratic problem'. While a lot of what Plato wrote about Socrates is accepted by historians, some believe that Plato (who saw Socrates as a hero) portrayed Socrates as a greater man than he actually was. Some think that Plato was using the character of Socrates as a tool to express his own opinions rather than to accurately write about Socrates. This is what makes Socrates such a mysterious historical figure. Plato's dialogues are works of art, finely written. The general view is that they are based on reality, but no doubt adjusted for the purpose of writing.
Socrates' father was a sculptor, and his mother was a midwife who helped women give birth to children. He may have been a stonemason like his father, and Plato wrote that he served in the Athenian army as a hoplite (heavy infantry). We know he was influenced by an older philosopher, Archelaus, and that he talked with anyone who had interesting ideas in Athens, but beyond that nothing is known.
Socrates was about 50 when he married a much younger woman, Xanthippe. They had three children together. Socrates made complaints about his wife, but no one knew if he was telling the truth.
It is said that one of Socrates' friends went to ask the oracle at Delphi if there was anyone wiser than Socrates in Athens. The oracle said that there was no wiser person. The oracle was well known for saying things that were ambiguous or unclear. It did not say that Socrates was the wisest, just that there was no person wiser.
After being puzzled by this, Socrates finally decided that his wisdom lay in knowing that he was ignorant. His attempts to show the citizens that some of their ideas were nonsense might help explain his unpopularity. In Plato's works, Socrates says he knows nothing, but can draw out other people's ideas just as his mother helped other women to give birth.
In 399 BC, when Socrates was an old man, three citizens—Meletus, Anytus and Lycon—brought charges against Socrates. A trial was held. In ancient Athens the procedure was quite different from the present day. There was a jury of 500 men drawn from the citizens. Both the accusers and the defendant had to make speeches in person to the jury. Guilt or innocence was by majority vote. There was no preset penalty if the verdict was 'guilty'. Both the accuser and the defendant would make speeches proposing what the penalty should be. Again, a vote was taken.
There were two charges against him. The general theme was that Socrates was a menace to society. The first charge was of heresy, disbelief in the Gods. It was probably meant to cause prejudice amongst the jurymen. Actually, Socrates observed all the correct procedures of the religion of his times. The charge had been used successfully against another philosopher, Anaxagoras.
The second charge was that he corrupted the youth with his teachings. What was meant by this? Apparently, this was not about his personal relationship with his pupils. It was about the way he was thought to influence their political views. His circle had included a number of right-wing aristocrats whose ideas were now rejected by most citizens. The brilliant Alcibiades, once a great leader of Athens, was now seen as a traitor.
Crito, a friend of Socrates, illegally paid the prison guards to allow Socrates to escape. Socrates, however, decided not to escape. When Socrates was put on trial, he gave a long speech to defend himself against the claims made by the Athens government.
We have Plato's version of how Socrates defended himself, in the "Apologia". It starts: