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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
In 1846 and 1847 he was awarded mathematics scholarships at Balliol College where he became a lecturer in mathematics.
Designing good keystream sequence generators is quite difficult and some advanced mathematics is required.
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.
In 1751 he went to the University of Utrecht to lecture on mathematics and astronomy.
At one point, we see the chip's inventor lecturing on the mathematics behind its design.

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