Socrates legacy in the world
Socrates maybe was sentenced to death by his fellow Athenian citizens, but his way of thinking created logic and science. That came out mainly through two persons: his student Plato, his student, Aristotle, and Alexander the Great. 

Plato did not have easy times, as many may suppose so. After a trip to Sicily he was sold as a slave, and was bought by a philosopher named Anniceris, for the amount of 30 mnas. Plato gathered money from his friends to repay him, but Anniceris denied them, so it was the first capital to fund his Academy. Academy was the world’s first University and had famous students such as Aristotle. His method was dialogue, so there was not a teacher higher than his students, but all were equal. Of course mathematics were included in the academy’s program as well. Academy was operating as a legal, rhetorical and political sciences School, so Aristotle as a student he wrote laws for his homeland in Macedonia, Stageira. Plato’s competitors were orators and rhetorical schools, such as this of Isocrates.
Aristotle was born in 384 BC. At seventeen or eighteen years of age, he joined Plato’s Academy in Athens and remained there until the age of thirty-seven (c. 347 BC). After leaving Academy, since Plato’s successor was appointed his nephew Speusippus, Aristotle either go with his student Theofrastus to Lesvos for research or met him there.
His fame soon grew bigger and in 343 BC, Aristotle was invited while being to Lesvos by Philip II of Macedon to become the tutor to his son Alexander, between 343-340. His school was located in Mieza, near modern Naousa, Greece. Alexander the Great was 13 years old at that time and later he was given the regency of Macedonia in his father’s absence at age 16. He was tutored by Aristotle, and had some appreciation for Athens as a center of learning. After Athens revolt again, he decided to bring the city down, as he did with Thebes, but General Phocion changed his mind and made him to see Persia instead of Greece.

Lyceum and Aristotle 
Aristotle after few years returned to Athens in 334-335 BC, aged 50, funded by Alexander the Great to manage Lyceum, which was already had been used as a school before. It was the time that scientific method was born, since Aristotle made not only observations, but also experiments, since Alexander was providing him with plant and animals specimens from his conquest in various regions. So the first zoo and botanical garden was developed in Athens as well. A year after Alexander’s death, in 322 BCE, Aristotle was forced to flee Athens with his family. Athenians reacted against Macedonians and he was considered as a target. He passed on Lyceum to notable student Theophrastus and died later that year in Chalcis.
These two schools (Academy and Lyceum) marked the western civilization, during Enlightenment, since neoplatonism was spread across Italy.

Christianity and Neoplatonists 

In 529 AD all Athens philosophical schools were forced to close, because they were challenging the Christian doctrine of the so-called medieval Byzantine Empire, where the ancient religion collapsed.

Until 500 years ago, Socrates and Plato teachings were being taught by Christian researches, who are described as neoplatonists. Their work was transferred to the west after the Latin occupation of Constantinople, that bear Renaissance. Today Socrates is admired by the whole world.