Exact sciences
Template:Short description Template:About
The exact sciences or quantitative sciences, sometimes called the exact mathematical sciences,<ref name = "Grant_43">Template:Citation</ref> are those sciences "which admit of absolute precision in their results"; especially the mathematical sciences.<ref>Template:Citation</ref> Examples of the exact sciences are mathematics, optics, astronomy,<ref>Template:Cite book</ref> and physics, which many philosophers from René Descartes, Gottfried Leibniz, and Immanuel Kant to the logical positivists took as paradigms of rational and objective knowledge.<ref>Template:Citation</ref> These sciences have been practiced in many cultures from antiquity<ref>Template:Citation</ref><ref>Template:Citation</ref> to modern times.<ref>Template:Citation</ref><ref>Template:Citation</ref> Given their ties to mathematics, the exact sciences are characterized by accurate quantitative expression, precise predictions and/or rigorous methods of testing hypotheses involving quantifiable predictions and measurements.<ref>Template:Cite book</ref>
The distinction between the quantitative exact sciences and those sciences that deal with the causes of things is due to Aristotle, who distinguished mathematics from natural philosophy<ref>Template:Cite book</ref> and considered the exact sciences to be the "more natural of the branches of mathematics."<ref name = "Grant_42">Template:Citation</ref> Thomas Aquinas employed this distinction when he said that astronomy explains the spherical shape of the Earth<ref>Template:Cite journal</ref> by mathematical reasoning while physics explains it by material causes.<ref>Template:Citation</ref> This distinction was widely, but not universally, accepted until the Scientific Revolution of the 17th century.<ref name = "Grant_303">Template:Citation</ref> Edward Grant has proposed that a fundamental change leading to the new sciences was the unification of the exact sciences and physics by Johannes Kepler, Isaac Newton, and others, which resulted in a quantitative investigation of the physical causes of natural phenomena.<ref name = "Grant_312">Template:Citation</ref>