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Explain the major subdisciplines of modern mathematics mentioned in the text.
Explain the major subdisciplines of modern mathematics mentioned in the text.
The major subdisciplines of modern mathematics mentioned in the text are number theory, algebra, geometry, and analysis.
What does most mathematical activity involve, according to the text?
What does most mathematical activity involve, according to the text?
Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them.
What does a proof in mathematics consist of, according to the text?
What does a proof in mathematics consist of, according to the text?
A proof consists of a succession of applications of deductive rules to already established results, including previously proved theorems, axioms, and basic properties.
How is mathematics essential in various fields, as mentioned in the text?
How is mathematics essential in various fields, as mentioned in the text?
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What distinguishes the fundamental truths of mathematics from scientific experimentation, according to the text?
What distinguishes the fundamental truths of mathematics from scientific experimentation, according to the text?
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