Because the Greeks had only very clumsy ways of writing down numbers, they didn't like algebra. They found it very hard to write down equations or number problems. Instead, Greek mathematicians were more focused on geometry, and used geometric methods to solve problems that you might use algebra for.
Greek mathematicians were also very interested in proving that certain mathematical ideas were true. So they spent a lot of time using geometry to prove that things were always true, even though people like the Egyptians and Babylonians already knew that they were true most of the time anyway.
The Greeks in general were very interested in rationality, in things making sense and hanging together. They wanted to tie up the loose ends. They liked music, because music followed strict rules to produce beauty. So did architecture, and so did mathematics.

Some famous Greek mathematicians were Pythagoras, Aristotle, Anaxagoras, Euclid, Thales, and Aristarchus. (You will find a geometric proof of the Pythagorean theorem on the Pythagoras page).