archimedes!
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He made his 'discoveries' by studying and compiling the works of other mathematicians who lived many years before him.
pytagoras made one that i know of and that is the pythagorean therom
He spent years calculating and decalculating until he created the pythagoream theorem
Many significant discoveries have been made from errors. Cereal was one such discovery. It was accidently left out and became stale before it was cut up and found to be delicious. The microwave oven also came to be because of an error.
paranesia was his father