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Mathematics is the study of abstractions of concrete objects, attempting to deal with such abstractions in as logical a manner as possible. To the ancient Greeks, mathematics meant geometry, the study of abstract lines (which can extend infinitely), planes and solids that represent concrete things on Earth. To the modern lay person, mathematics means mostly the study of numbers, which represent quantities of concrete things; this includes arithmetic, statistics, algebra and calculus. And to some modern mathematicians, mathematics can involve so many levels of abstraction that any connection to concrete objects is rather tenuous.