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What is mathematics?

What is mathematics? Here are some definitions.

Noun
  1. An abstract representational system used in the study of numbers, shapes, structure, change and the relationships between these concepts.
  2. A person's ability to count, calculate, and use different systems of mathematics at differing levels.
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Examples
Einstein proceeds to describe with arcane mathematics and symbols his theory of relativity.
I accepted and became the first Jew to hold a tenured position in the mathematics department.
He won an open scholarship in mathematics and natural science to study at Trinity College, Cambridge.
Fortunately your university mathematics course has included a module on computing and you decide to try to solve this problem on a computer.
Designing good keystream sequence generators is quite difficult and some advanced mathematics is required.
Evaluating irrational and arational decisions based on our emotions with mathematics may be impossible.

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