From Pythagoras to Archimedes

Abstract

In the history of mathematics, there are a lot of famous names, and much can be said about them. This paper is dedicated to some outstanding Ancient Greek mathematicians: Thales of Miletus, Pythagoras and Archimedes. Thales of Miletus can be considered the father of today's mathematics. His main achievement in mathematics was his idea about mathematical proof. Today, mathematics is not imaginable without proofs.
Today's mathematics has undoubtedly taken a lot from Pythagoras of Samos Island. There are many interesting facts in the biography of Pythagoras. Pythagoras gathered around himself a group of young people, who started doing scientific research in philosophy and mathematics. This group was later named the School of Pythagoras. Under Pythagoras leadership, mathematics became the science in the meaning we understand it today, that is, mathematics started working with abstract numbers and geometrical figures. Here are some of Pythagorean achievements: they strengthened the idea of mathematical proof; they researched relationships between numbers and came to the concept of irrational numbers, without which today's mathematics is impossible; established the base for the regular polygon theory. Archimedes of Syracuse is another great mathematician of the ancient world.
Archimedes devoted all his life to science and protecting his home town from attacks of the Roman fleet. Thanks to Archimedes, Syracuse was considered an inaccessible city for a long time. Archimedes discovered the lever law, invented the block system, screws and polyplastics to lift great weigh. He built war throwing machines that were able to throw huge stones to a great distance. Archimedes was not only a great mathematician, but also the greatest technician of the ancient world, under the leadership of whom a small group of people in a long period of time could resist the power of thousands of armed men.