Archimedes (ca. 287–212 BCE) was a relative of the ruler of Syracuse, Hieron II, and his father was the astronomer Phidias. Belonging to one of Syracuse’s most aristocratic families, Archimedes didn’t have to work, and mathematics became his passion. In fact, he is believed to have cared so little about daily life that he left meals uneaten when a mathematical problem occupied his mind. Archimedes is famous for a great discovery he made while taking a bath. The episode with the bath actually begins with a request by Hieron to his bright relative to help him determine whether a goldsmith had stolen some of his gold. The king had apparently asked the goldsmith to make him a new crown, providing him with the needed gold. When the king got his new crown from the goldsmith, he became suspicious that the goldsmith had replaced some of the gold inside the crown with silver or another cheaper metal and then pocketed the missing gold. The king needed Archimedes to find a way to compare the
Eudoxus was born in 408 BCE to an impoverished family in Knidus, Asia Minor. Because of his family’s low socioeconomic status, he would have had no chance at a successful life if it weren’t for his powerful mathematical skills. As a young adult, Eudoxus heard about Plato’s Academy and borrowed money to travel there. Many of the philosophers at the Academy ignored the young man, but Plato recognized his genius and supported him in his mathematical pursuits. There was no remuneration for membership in the esteemed Academy, and Eudoxus had so little money that he could not afford to live with the other members in Athens. He was forced to rent a small room in the nearby city of Piraeus, where rents were low and basic food could be obtained inexpensively. He commuted daily to Athens to attend the discussions at the Academy. Eventually, after having proved several major theorems in geometry that no one had been able to tackle, Eudoxus earned the respect of the other philosophers. Thanks in p