One major way that I personally see important that we acquired from Greek mathematicians is the use of the Pythagorean theorem. When we learn this formula we often learn it out of context and just as another formula to memorize pertaining to right triangles. But this theorem has done a lot for our very industrialized world, such as aiding in construction of buildings and findings of unknown distances. Formulas mean nothing unless they are given a context for which they should or are most likely used. In math classes today we see that push toward bridging the gap between a given formula and the context for which it belongs. I think that it is so beneficial to students to see the why and how because then instead of memorizing they are more likely to recall from the context why it works. By providing them with that we are really giving them the tools they need to be successful when working with the theorem.

Democritus, a Greek mathematician was most famous for his prescient ideas about all matter being composed of tiny atoms, was also a pioneer of mathematics and geometry and he produced works with titles like "On Numbers", "On Geometrics", "On Tangencies", "On Mapping" and "On Irrationals”. These works are important but the fact that Democritus was recording his work in writing is more interesting to me. Not many mathematicians of this time period were recording their work and were being published. Without publication of new findings these new discoveries were relayed via word of mouth and we all know what can happen to information that way. Having the original document that was written by whomever discovered it is valuable and at this point in time, that was recognized. Think of all the resources we would be missing out on without documentation. Many of us going into teaching would have to have photographic memories to try to recall the information we are expected to teach. This documenting development did a lot for our future society.

Even though these were only two instances in Greek mathematics it is very apparent of the imperative role they played in how we use and do mathematics in every day life. Math is a tool and in order to use that tool we have to know what kinds of problems the tool fixes, just as the Greeks knew when coming up with the Pythagorean theorem. Once we know that important information the rest is more bearable.