Final answer:
It is false that Plato gathered and published Socrates' writings; Socrates never wrote anything down, and his teachings were transmitted through Plato's dialogues.
Step-by-step explanation:
The statement that Plato gathered Socrates' writings and published them under his own name is false. In reality, Socrates never wrote anything down, preferring oral dialogues and the process of memorization over written texts. His philosophical ideas and methodologies were instead documented by his student, Plato, in the form of dialogues. These dialogues dramatize Socrates' life and present his philosophy, although they reflect Plato's philosophical system as well. It was through Plato's works, along with those of Xenophon, that Socrates' teachings have been passed down to us, making Plato not just a disciple, but one of the primary reasons why Socrates is remembered today.