Math Blog 1
Math Blog 1: The Role of the Great Archimedes, and also a bit about Ancient Mayan mathematics.
Archimedes was not so much a collator of great mathematical ideas, but rather an innovator of them. He used the method of taking continuously thinner slices of an object to estimate the area of that object, which is very similar to integration in modern day Calculus long before Calculus was even invented! Also he computed an estimation of Pi that was pretty close to the actual value.
He also was one of the few people at the time to actually consider the concept of infinity. He thought of the infinite nature of the set of prime numbers and how there was no actual finite set of them. His favorite proof was that of the relation between the volume of sphere and a right cylinder. However, he is probably most well known for discovering that the amount of water displaced by an object correlates to its volume, which can then be used to find out the object's density!
Some of his other achievements include predicting the solstices, calculating the amount of grains of sand it would take to fill the universe, describing how levers work, creation of the Archimedes Screw, and proving the area of a parabolic section cut by a line is 4/3 of the inscribed triangle. He must have been highly respected as a scholar for people to have falsely remembered him as a person who would die over the interruption of his calculations and diagrams.
The Mayans invented an independent number system from that of Europe and Asia. They used a base 20 system, and even had the concept of zero! They used a lot of their math to help calculate astronomical positions and also to create their extremely accurate calendar. Besides accurately calculating the length of the year and also of the moon cycle, not too many of their mathematical accomplishments are known.