Ancient Science: Geometry
The era of classical Greek culture which spread around the Mediterranean basin from around 750 BCE onwards gave rise to a wealth of scientific and philosophical creativity. Revolutionary thinkers changed the way we think about various sciences including mathematics, showing that math is not just about performing calculations but a way of understanding the reality of the world.
One such thinker was Plato. Plato founded his Academy in Athens in 387 BCE, where he stressed that mathematics is a way of understanding reality. In particular, he was convinced that geometry was the key to unlocking the secrets of the universe.
In Plato's Socratic dialogue Meno, Socrates proves the Theory of Recollection which claims that knowledge is a form of recollection.
Meno: Yes, Socrates, but what do you mean when you say that we don’t learn–that what we call ‘learning’ is actually ‘recollection’? Can you teach me how this is so?
Socrates: Didn’t I describe you a moment ago as mischievous, Meno? And now, just when I’m insisting that there’s no such a thing as teaching, only recollection, you’re asking me whether I can teach you something. You’re trying to catch me out in an immediate contradiction.
This theory asserts teaching does not make one knowledgeable but asking leading questions does as the mind is already in possession of knowledge. Searching for truths within "our souls," brings us to recover pieces of knowledge.
It is assumed that Euclid had studied at Plato's Academy in Athens. Although little is known of the details of Euclid's life, he is credited to have created one of the greatest mathematics texts of all time. Euclid is considered the 'father of geometry' not because he was the first person to study geometry but because of his writings in The Elements, the oldest, continuously used geometry textbook, written around 300 BCE.
Most of the theorems which appear in The Elements are a compilation of the work by Plato and earlier mathematicians. Euclid is credited with arranging the theorems in a logical manner, demonstrating that they can be derived from basic assumptions, called common notions and postulates.
Kraut, Richard. “Plato (Stanford Encyclopedia of Philosophy).” Stanford.edu, 2017, plato.stanford.edu/entries/plato/.
Brickhouse, Thomas, and Nicholas D. Smith. “Plato | Internet Encyclopedia of Philosophy.” Internet Encyclopedia of Philosophy, iep.utm.edu/plato/.
“Euclid’s Elements, Introduction.” Aleph0.Clarku.edu, aleph0.clarku.edu/~djoyce/elements/elements.html.
Ornes, Stephen. “Science and Culture: Researchers Find History in the Diagrams of Euclid’s Elements.” Proceedings of the National Academy of Sciences, vol. 114, no. 47, 21 Nov. 2017, pp. 12353–12355, www.pnas.org/content/114/47/12353, 10.1073/pnas.1717950114.