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Explain the major subdisciplines of modern mathematics as mentioned in the text.
Explain the major subdisciplines of modern mathematics as mentioned in the text.
The major subdisciplines of modern mathematics mentioned in the text are number theory, algebra, geometry, and analysis.
What is the general nature of most mathematical activity as described in the text?
What is the general nature of most mathematical activity as described in the text?
Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them.
What do proofs in mathematics consist of, according to the text?
What do proofs in mathematics consist of, according to the text?
Proofs consist of a succession of applications of deductive rules to already established results, including previously proved theorems, axioms, and some basic properties that are considered true starting points of the theory.
What are the objects involved in modern mathematics?
What are the objects involved in modern mathematics?
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What is the lack of general consensus among mathematicians about, as mentioned in the text?
What is the lack of general consensus among mathematicians about, as mentioned in the text?
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