The '''exact sciences''', sometimes called the '''exact mathematical sciences''',<ref name = "Grant_43">{{Citation | last = Grant | first = Edward | author-link = Edward Grant | date = 2007 | title = A History of Natural Philosophy: From the Ancient World to the Nineteenth Century | publisher = Cambridge University Press | place = Cambridge | page = 43 | isbn = 9781139461092 }}</ref> are those sciences "which admit of absolute precision in their results"; especially the [[mathematical sciences]].<ref>{{ Citation | title = Oxford English Dictionary, Online version | edition = 2nd | date = June 2016 | contribution = Exact, ''adj.¹'' | publisher = Oxford University Press | place = Oxford }}</ref> Examples of the exact sciences are mathematics, [[optics]], [[astronomy]], and [[physics]], which many philosophers from [[Descartes]], [[Leibniz]], and [[Kant]] to the [[Logical positivism|logical positivists]] took as paradigms of rational and [[Objectivity (philosophy)|objective knowledge]].<ref>{{Citation | last = Friedman | first = Michael | author-link = Michael Friedman (philosopher) | editor-last = Earman | editor-first = John | editor-link = John Earman | date = 1992 | title = Inference, Explanation, and Other Frustrations: Essays in the Philosophy of Science | contribution = Philosophy and the Exact Sciences: Logical Positivism as a Case Study | series = Pittsburgh series in philosophy and history of science | volume = 14 | page = 84 | publisher = University of California Press | place = Berkeley and Los Angeles | isbn = 9780520075771}}</ref> These sciences have been practiced in many cultures from antiquity<ref>{{Citation | last = Neugebauer | first = Otto | author-link = Otto Neugebauer | date = 1962 | title = The Exact Sciences in Antiquity | publisher = Harper & Bros. | place = New York | edition = 2nd, reprint | series = The Science Library }}</ref><ref>{{Citation | last = Sarkar | first = Benoy Kumar | author-link = Benoy Kumar Sarkar | date = 1918 | title = Hindu Achievements in Exact Science: A Study in the History of Scientific Development | publisher = Longmans, Green and Company | isbn = 9780598626806 | place = London / New York | url = https://books.google.com/books?id=1CpRAAAAYAAJ }}</ref> to modern times.<ref>{{Citation | last1 = Harman | first1 = Peter M. | last2 = Shapiro | first2 = Alan E. | date = 2002 | title = The Investigation of Difficult Things: Essays on Newton and the History of the Exact Sciences in Honour of D. T. Whiteside | publisher = Cambridge University Press | place = Cambridge | isbn = 9780521892667 }}</ref><ref>{{Citation | last = Pyenson | first = Lewis | date = 1993 | title = Cultural Imperialism and Exact Sciences Revisited | journal = Isis | volume = 84 | issue = 1 | pages = 103–108 | doi = 10.1086/356376| quote = [M]any of the exact sciences… between [[Claudius Ptolemy]] and [[Tycho Brahe]] were in a common register, whether studied in the diverse parts of the Islamic world, in India, in Christian Europe, in China, or apparently in Mesoamerica. | jstor = 235556 | bibcode = 1993Isis...84..103P | s2cid = 144588820 }}</ref> Given their ties to mathematics, the exact sciences are characterized by accurate [[Quantitative research|quantitative]] expression, precise predictions and/or [[rigour|rigorous]] methods of testing [[hypothesis|hypotheses]] involving quantifiable [[prediction]]s and [[measurement]]s<ref>{{Cite book |last=Shapin |first=Steven |title=The Scientific Revolution |publisher=The University of Chicago Press |year=2018 |isbn=9780226398341 |edition=2nd |location=Chicago, IL |pages=46-47 |language=}}</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>{{Cite book |last=Principe |first=Lawrence |title=The Scientific Revolution: A Very Short Introduction |publisher=Oxford University Press |year=2011 |isbn=9780199567416 |location=New York, NY |pages=27}}</ref> and considered the exact sciences to be the "more natural of the branches of mathematics."<ref name = "Grant_42">{{Citation | last = Grant | first = Edward | author-link = Edward Grant | date = 2007 | title = A History of Natural Philosophy: From the Ancient World to the Nineteenth Century | publisher = Cambridge University Press | place = Cambridge | pages = 42–43 | isbn = 9781139461092 }}</ref> [[Thomas Aquinas]] employed this distinction when he said that astronomy explains the [[Figure of the Earth|spherical shape of the Earth]] by mathematical reasoning while physics explains it by [[material cause]]s.<ref>{{Citation | last = Aquinas | first = Thomas | author-link = Thomas Aquinas | title = Summa Theologica | at = Part I, Q. 1, Art. 1, Reply 2 | url = http://www.newadvent.org/summa/1001.htm#1 | access-date = 3 September 2016 | quote = For the astronomer and the physicist both may prove the same conclusion: that the earth, for instance, is round: the astronomer by means of mathematics (i.e. abstracting from matter), but the physicist by means of matter itself. }}</ref> This distinction was widely, but not universally, accepted until the [[scientific revolution]] of the 17th century.<ref name = "Grant_303">{{Citation | last = Grant | first = Edward | author-link = Edward Grant | date = 2007 | title = A History of Natural Philosophy: From the Ancient World to the Nineteenth Century | publisher = Cambridge University Press | place = Cambridge | pages = 303–305 | isbn = 9781139461092 }}</ref> [[Edward Grant]] has proposed that a fundamental change leading to the new sciences was the unification of the exact sciences and physics by [[Kepler]], [[Isaac Newton|Newton]], and others, which resulted in a quantitative investigation of the physical causes of natural phenomena.<ref name = "Grant_312">{{Citation | last = Grant | first = Edward | author-link = Edward Grant | date = 2007 | title = A History of Natural Philosophy: From the Ancient World to the Nineteenth Century | publisher = Cambridge University Press | place = Cambridge | pages = 303, 312–313 | isbn = 9781139461092 }}</ref>