WAS MATHETMATICS DISCOVERED OR CREATED?

Pythagoras (571-496 B.C.), a mathematician (perhaps best known for his "Pythagorean theorem") and philosopher born in Samos, Greece, believed that the answer to the big question "What is reality made of?" lay in mathematics. Pythagoras is famously quoted as having said "All is number." He even went as far as to declare that justice was the number 4 as it was a square number.

1. What do you think Pythagoras meant by "All is number."?
2. Do you agree with him? To what extent is it possible to explain the concept of reality through mathematics?


While most of us would find it difficult to entirely agree with Pythagoras, there is little doubt that mathematics has played a large role in our understanding of the world around us, and those we have yet to discover and explore.

When trying to define mathematics, several questions are raised. The big question concerning math, as far as ToK is concerned, is whether mathematics is a natural phenomenon or merely a game of logic invented by the human mind.

3. What is your "gut reaction" to this question? Was mathematics discovered or invented?

While Pythagoras believed that mathematics held all the answers,, PLATO,another Greek philosopher and mathematician whom we've discussed before (remember K=JTB?), held the belief that numbers held some kind of mystical existence, separate to the rest of the world.

Read the brief biography of Plato paying particular attention to the section on mathematics. In it you're reminded that Plato founded "The Academy" (an institution devoted to research and instruction in philosophy and the sciences) over which he presided from 387 BC until his death in 347 BC. Over the door of the Academy was written:

"Let no one unversed in geometry enter here."


4. What does this quotation reveal to us about Plato's view of mathematics? Summarize his belief about mathematics.
5. Why were so many of Plato's friends and students significant contributors to the field of mathematics despite the fact that Plato, himself, made no important mathematical discoveries?