Mathematics, while not a science, is closely allied to the sciences because of their extensive use of it.
The physical sciences include physics, chemistry, and astronomy; the earth sciences (sometimes considered a part of the physical sciences) include geology, paleontology, oceanography, and meteorology; and the life sciences include all the branches of biology such as botany, zoology, genetics, and medicine.
Science, in the modern sense of the term, came into being in the 16th and 17th cent., with the merging of the craft tradition with scientific theory and the evolution of the scientific method.
Science is practiced in universities and other scientific institutes as well as in the field; as such it is a solid vocation in academia, but is also practiced by amateurs, who typically engage in the observational part of science.
Studies of anthropology, history, psychology, and sociology are sometimes called "soft sciences." Proponents of this division use the arguments that the "soft sciences" do not use the scientific method, admit anecdotal evidence, or are not mathematical, all adding up to a "lack of rigor" in their methods.
The term "science" is sometimes pressed into service for new and interdisciplinary fields that make use of scientific methods at least in part, and which in any case aspire to be systematic and careful explorations of their subjects, including computer science, library and information science, and environmental science.