The most general and colloquial division is into “hard” and “soft” sciences, the former comprising disciplines that deal in quantifiable numbers, such as mathematics, chemistry, astronomy, and physics, the latter referring to fields like psychology, sociology, and health science.
Another way to categorize the various branches is outlined in the Wikipedia page below: natural science, formal science, social science, and applied science, each with its own various subcategories and offshoots.
There also are many interdisciplinary branches of science, such as Atmospheric Sciences, Earth and Space Sciences, Climate Sciences, and Biogeochemistry.
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