Archimedes (287 - 212 BCE) is one of the most famous of all of the Greek mathematicians, contributing to the development of pure math and calculus, but also showing a great gift for using mathematics practically.
With inventions such as the Archimedes Screw and the Archimedes Claw, he showed himself to be a brilliant engineer as much as a theorist.
This was a break away from the traditions of the earlier Greeks, who felt that such pursuits were vulgar and started the process of uniting mathematics and geometry with engineering. This move possibly ties in with the practicalities of politics; Archimedes is renowned for inventing great war machines and it may have been the desire to protect his city that forced his hand.
Archimedes’ contributions to math were legion, and mostly based around his theory of exhaustion, where he would look for solutions close to the desired answer and give a range. This was the only way that the Greeks could address irrational numbers such as Pi and square roots.
For example, in his development of integration and calculus, he tried to find a value for Pi by using circumscribed and inscribed polygons, eventually using 96 sided polygons inside and outside a circle to generate a value for Pi of between 31⁄7 (approximately 3.1429) and 310⁄71 (approximately 3.1408). This range of values is extremely accurate, as the actual value is 3.1416.
|Parabolic Segment and Inscribed Triangle (Public Domain)|
Archimedes wrote a range of treatises, many of which are lost to us, but those that remain show that he truly was a mathematical genius. Modern engineers and applied mathematicians use knowledge and proofs revealed in the work of Archimedes. Some of the remaining books are
|Archimedes' Pi Approximation (Creative Commons)|
|Page Archimedes Palimpsets (Creative Commons)|
Archimedes undoubtedly made many contributions to Greek mathematics, and his works that survive show that he was one of the most influential mathematicians of all time. Strangely, he is not as well known as a mathematician as an inventor and most of the history taught about this remarkable man revolves around his war machines and the Archimedes screw.
Much of the evidence for his inventions, such as complex lever systems, including the Archimedes Claw that he used to snatch attacking Roman ships from the water, and parabolic mirrors designed to burn ships, are largely anecdotal. However, there is little doubt that he certainly had the applied mathematical ability to devise these great machines.