Editing Mathematical physics (section)

=== Before Newton ===
There is a tradition of mathematical analysis of nature that goes back to the ancient Greeks; examples include [[Euclid]] (''Optics''), [[Archimedes]] (''On the Equilibrium of Planes'', ''On Floating Bodies''), and [[Ptolemy]] (''Optics'', ''Harmonics'').<ref>{{Cite journal|last=Pellegrin|first=P.|title=Physics|journal=Greek Thought: A Guide to Classical Knowledge|year=2000|editor-last=Brunschwig|editor-first=J.|pages=433–451|editor-last2=Lloyd|editor-first2=G. E. R.}}</ref><ref>{{Cite journal|last=Berggren|first=J. L.|date=2008|title=The Archimedes codex|url=https://www.ams.org/notices/200808/tx080800943p.pdf|journal=Notices of the AMS|volume=55|issue=8|pages=943–947}}</ref> Later, [[Science in the medieval Islamic world|Islamic]] and [[Byzantine science|Byzantine]] scholars built on these works, and these ultimately were reintroduced or became available to the West in the [[Renaissance of the 12th century|12th century]] and during the [[History of science in the Renaissance|Renaissance]].

In the first decade of the 16th century, amateur astronomer [[Nicolaus Copernicus]] proposed [[heliocentrism]], and published a treatise on it in 1543. He retained the [[Ptolemy|Ptolemaic]] idea of [[epicycle]]s, and merely sought to simplify astronomy by constructing simpler sets of epicyclic orbits. Epicycles consist of circles upon circles. According to [[Aristotelian physics]], the circle was the perfect form of motion, and was the intrinsic motion of Aristotle's [[classical elements|fifth element]]—the quintessence or universal essence known in Greek as ''[[Aether (classical element)|aether]]'' for the English ''pure air''—that was the pure substance beyond the [[sublunary sphere]], and thus was celestial entities' pure composition. The German [[Johannes Kepler]] [1571–1630], [[Tycho Brahe]]'s assistant, modified Copernican orbits to ''[[ellipse]]s'', formalized in the equations of Kepler's [[laws of planetary motion]].

An enthusiastic atomist, [[Galileo Galilei]] in his 1623 book ''The Assayer'' asserted that the "book of nature is written in mathematics".<ref>Peter Machamer [http://plato.stanford.edu/archives/spr2010/entries/galileo "Galileo Galilei"]—sec 1 "Brief biography", in Zalta EN, ed, ''The Stanford Encyclopedia of Philosophy'', Spring 2010 edn</ref> His 1632 book, about his telescopic observations, supported heliocentrism.<ref name=Flew1984p129>Antony G Flew, ''Dictionary of Philosophy'', rev 2nd edn (New York: St Martin's Press, 1984), p [https://books.google.com/books?id=MmJHVU9Rv3YC&pg=PA129 129]</ref> Having made use of experimentation, Galileo then refuted geocentric [[cosmology]] by refuting Aristotelian physics itself. Galileo's 1638 book ''Discourse on Two New Sciences'' established the law of equal free fall as well as the principles of inertial motion, two central concepts of what today is known as [[classical mechanics]].<ref name=Flew1984p129/> By the Galilean [[law of inertia]] as well as the principle of [[Galilean invariance]], also called Galilean relativity, for any object experiencing inertia, there is empirical justification for knowing only that it is at ''relative'' rest or ''relative'' motion—rest or motion with respect to another object.

[[René Descartes]] developed a complete system of heliocentric cosmology anchored on the principle of vortex motion, [[Cartesian physics]], whose widespread acceptance helped bring the demise of Aristotelian physics. Descartes used mathematical reasoning as a model for science, and developed [[analytic geometry]], which in time allowed the plotting of locations in 3D space ([[Cartesian coordinate system|Cartesian coordinates]]) and marking their progressions along the flow of time.<ref>Antony G Flew, ''Dictionary of Philosophy'', rev 2nd edn (New York: St Martin's Press, 1984), p [https://books.google.com/books?id=MmJHVU9Rv3YC&pg=PA89&dq=mathematical+reasoning 89]</ref>

[[Christiaan Huygens]], a talented mathematician and physicist and older contemporary of Newton, was the first to successfully idealize a physical problem by a set of mathematical parameters in ''[[Horologium Oscillatorium|Horologium Oscillatorum]]'' (1673), and the first to fully mathematize a mechanistic explanation of an unobservable physical phenomenon in ''[[Treatise on Light|Traité de la Lumière]]'' (1690). He is thus considered a forerunner of [[theoretical physics]] and one of the founders of modern mathematical physics.<ref>Dijksterhuis, F. J. (2008). Stevin, Huygens and the Dutch republic. ''Nieuw archief voor wiskunde, 5,'' pp. 100–107. https://research.utwente.nl/files/6673130/Dijksterhuis_naw5-2008-09-2-100.pdf</ref><ref>Andreessen, C.D. (2005) ''Huygens: The Man Behind the Principle''. Cambridge University Press: 6</ref>