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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
The case for supposing that logic and mathematics are revisable in the light of empirical inquiry remains, therefore, at best unproved.
At one point, we see the chip's inventor lecturing on the mathematics behind its design.
In 1846 and 1847 he was awarded mathematics scholarships at Balliol College where he became a lecturer in mathematics.
I accepted and became the first Jew to hold a tenured position in the mathematics department.
It takes quite a brainbox to possess expertise in philosophy, mathematics and drama, but John Mighton is such a man.
Adrain received a good education but this education did not include any mathematics beyond arithmetic.

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