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Ancient greek mathematics, like the culture itself, emphasized the concept of idealism... which, philosophically, means that perfection can only really be found in the ideas in our heads... Even though 'physical reality' isn't perfect, we strive to make it as perfect as possible... The Greeks tried to accomplish this in their mathematics by trying to think of mathematical objects (such as numbers and shapes) as ideal and perfect mental objects. You can see this by the kinds of problems that the Greeks worked on... They didn't work out the problem of a 'rectangular field of wheat', but just the 'rectangle' itself... They didn't worry about what the rectangle represented in real life, but considered problems about the perfect shape of a rectangle. You could say that greek mathematics was 'abstract' meaning 'separate from the real world'.

The same can be said of modern mathematics... when we work out algebraic, geometric, or really any kind of mathematical problem, we visualize it first in our heads, in a state of perfection... Then we manipulate these objects in our heads to get the answer. In essence, we think of modern mathematics as being abstract as well.

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Q: What are the similarities between ancient greek math and modern math?
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