Anaximander was born about 610 BC in the Greek city of Miletus, in what is now Turkey. So he was able to have the great mathematician Thales of Miletus as his teacher. Thales was probably about 35 when Anaximander was twenty years old. The two mathematicians worked together for most of their lives.
Anaximander lived just a little bit after Lao Tzu wrote about Taoism in China. Possibly Anaximander had heard some Taoist ideas carried by travelers. Like Lao Tzu, Anaximander thought nature worked towards a balance, just as a swinging pendulum will stop in the middle. So for every hot thing like fire there was a cold thing like ice to balance it. You could see this as an early version of the conservation of energy.
But Anaximander went on from there. Earlier Greek scientists saw nature as random and chaotic. They thought of men as creating order out of chaos. For example, nature created random noise, but men created music. But Anaximander proposed – correctly – that nature also worked according to rational laws. Anaximander’s ideas about order and law could have influenced Confucius, who lived just slightly later, in China. Anaximander was also the first West Asian mathematician who worked with Indian mathematicians‘ idea of infinity. He called infinity epeiron in Greek. Anaximander – like Confucius and Lao Tzu – wrote a book about his work, but almost all of Anaximander’s book has been lost.
When Anaximander was 64 years old, Cyrus the Persian conquered Miletus. Afterwards Miletus wasn’t as rich a city. Not as many families could afford to send their boys to school. Teachers began to move to richer towns like Athens. Thales died three years later, and Anaximander took over Thales’ school. Anaximander taught Anaximenes, and probably Pythagoras there. But then Anaximander himself died three years after Thales, about 546 BC, when he was 70 years old. Then Anaximenes took over Miletus’ school.