Let's start with the first sentence of the text:
"Building on Socrates' ideas, his student Plato made significant contributions to the intellectual climate that would eventually lead to the development of note-taking systems."
My suggestion for revision would be:
"Expanding on Socrates' ideas, Plato, his student, significantly contributed to the intellectual atmosphere, paving the way for the development of note-taking systems."
What do you think about this revision?