Science

=== Classical antiquity ===
{{Main|Science in classical antiquity}}
[[File:MANNapoli 124545 plato's academy mosaic.jpg|left|thumb|[[Plato's Academy mosaic]], made between 100 BCE to 79 AD, shows many Greek philosophers and scholars|alt=Framed mosaic of philosophers gathering around and conversing]]
In [[classical antiquity]], there is no real ancient analog of a modern scientist. Instead, well-educated, usually upper-class, and almost universally male individuals performed various investigations into nature whenever they could afford the time.<ref name="Lehoux">{{cite book|last1= Lehoux|first1= Daryn|editor1-last= Shank|editor1-first= Michael|editor2-last= Numbers|editor2-first= Ronald|editor3-last= Harrison|editor3-first= Peter|title= Wrestling with Nature: From Omens to Science|date= 2011|publisher= University of Chicago Press|location= Chicago|isbn= 978-0-226-31783-0|page= 39|chapter= 2. Natural Knowledge in the Classical World}}</ref> Before the invention or discovery of the [[concept]] of ''[[phusis]]'' or nature by the [[pre-Socratic philosopher]]s, the same words tend to be used to describe the natural "way" in which a plant grows,<ref name=naddaf>An account of the pre-Socratic use of the concept of φύσις may be found in {{cite book|last=Naddaf|first=Gerard|year=2006|title=The Greek Concept of Nature|publisher=SUNY Press|postscript=,}} and in {{cite journal |last1=Ducarme |first1=Frédéric |last2=Couvet |first2=Denis |year=2020 |title=What does 'nature' mean? |journal=[[Palgrave Communications]] |volume=6 |issue=14 |publisher=[[Springer Nature]] |doi=10.1057/s41599-020-0390-y |doi-access=free |url=https://hal.science/hal-02554932/file/s41599-020-0390-y.pdf }} The word φύσις, while first used in connection with a plant in Homer, occurs early in Greek philosophy, and in several senses. Generally, these senses match rather well the current senses in which the English word ''nature'' is used, as confirmed by {{cite book|last=Guthrie|first=W.K.C.|title=Presocratic Tradition from Parmenides to Democritus|postscript=none}} (volume 2 of his ''History of Greek Philosophy''), Cambridge UP, 1965.</ref> and the "way" in which, for example, one tribe worships a particular god. For this reason, it is claimed that these men were the first philosophers in the strict sense and the first to clearly distinguish "nature" and "convention".<ref>{{Cite book |last1=Strauss |first1=Leo |url=https://books.google.com/books?id=cpx2j0TumyIC |title=An Introduction to Political Philosophy: Ten Essays by Leo Strauss |last2=Gildin |first2=Hilail |publisher=[[Wayne State University Press]] |isbn=978-0814319024 |publication-date=August 1, 1989 |chapter=Progress or Return? The Contemporary Crisis in Western Education |year=1989 |access-date=May 30, 2022 |archive-date=May 31, 2022 |archive-url=https://web.archive.org/web/20220531025640/https://books.google.com.vn/books/about/An_Introduction_to_Political_Philosophy.html?id=cpx2j0TumyIC |url-status=live|page=209}}</ref>

The early [[Ancient Greek philosophy|Greek philosophers]] of the Milesian school, which was founded by [[Thales of Miletus]] and later continued by his successors [[Anaximander]] and [[Anaximenes of Miletus|Anaximenes]], were the first to attempt to explain [[List of natural phenomena|natural phenomena]] without relying on the [[supernatural]].<ref name="O'Grady">{{cite book|last1= O'Grady|first1= Patricia F.|author-link=Patricia O'Grady|title= Thales of Miletus: The Beginnings of Western Science and Philosophy|date= 2016|publisher= Routledge|location= New York City, New York and London, England|isbn= 978-0-7546-0533-1|page= 245|url= https://books.google.com/books?id=ZTUlDwAAQBAJ&q=Thales+of+Miletus+first+scientist&pg=PA245|access-date= October 20, 2020|archive-date= March 31, 2021|archive-url= https://web.archive.org/web/20210331144842/https://books.google.com/books?id=ZTUlDwAAQBAJ&q=Thales+of+Miletus+first+scientist&pg=PA245|url-status= live}}</ref> The [[Pythagoreanism|Pythagoreans]] developed a complex number philosophy<ref name="Burkert1972">{{cite book|last= Burkert|first= Walter|author-link= Walter Burkert|date= June 1, 1972|title= Lore and Science in Ancient Pythagoreanism|url= https://books.google.com/books?id=0qqp4Vk1zG0C&q=Pythagoreanism|location= Cambridge, Massachusetts|publisher= Harvard University Press|isbn= 978-0-674-53918-1|url-status=live|archive-url= https://web.archive.org/web/20180129145253/https://books.google.com/books?id=0qqp4Vk1zG0C&printsec=frontcover&dq=Pythagoreanism&hl=en&sa=X&ved=0ahUKEwiX4Y3W9bfXAhXBeSYKHfBxCG4Q6AEIMTAC#v=onepage&q=Pythagoreanism&f=false|archive-date= January 29, 2018}}</ref>{{rp|467–68}} and contributed significantly to the development of mathematical science.<ref name="Burkert1972" />{{rp|465}} The [[atomism|theory of atoms]] was developed by the Greek philosopher [[Leucippus]] and his student [[Democritus]].<ref>{{Cite book|last1= Pullman|first1= Bernard|title= The Atom in the History of Human Thought|date= 1998|isbn= 978-0-19-515040-7|pages= 31–33|publisher= Oxford University Press|url= https://books.google.com/books?id=IQs5hur-BpgC&q=Leucippus+Democritus+atom&pg=PA56|bibcode= 1998ahht.book.....P|access-date= October 20, 2020|archive-date= February 5, 2021|archive-url= https://web.archive.org/web/20210205165029/https://books.google.com/books?id=IQs5hur-BpgC&q=Leucippus+Democritus+atom&pg=PA56|url-status= live}}</ref><ref>{{cite book|editor1-last= Cohen|editor1-first= Henri|editor2-last= Lefebvre|editor2-first= Claire|title= Handbook of Categorization in Cognitive Science|date= 2017|publisher= Elsevier|location= Amsterdam, the Netherlands|isbn= 978-0-08-101107-2|page= 427|edition= 2nd|url= https://books.google.com/books?id=zIrCDQAAQBAJ&q=Leucippus+Democritus+atom&pg=PA427|access-date= October 20, 2020|archive-date= February 5, 2021|archive-url= https://web.archive.org/web/20210205162707/https://books.google.com/books?id=zIrCDQAAQBAJ&q=Leucippus+Democritus+atom&pg=PA427|url-status= live}}</ref> Later, [[Epicurus]] would develop a full natural cosmology based on atomism, and would adopt a "canon" (ruler, standard) which established physical criteria or standards of scientific truth.<ref name=canon >[[Lucretius]] (fl. 1st c. BCE) ''[[De rerum natura]]''</ref> The Greek doctor [[Hippocrates]] established the tradition of systematic medical science<ref>{{cite book|last= Margotta|first= Roberto|date= 1968|title= The Story of Medicine|url= https://books.google.com/books?id=vFZrAAAAMAAJ|location= New York City, New York|publisher= [[Golden Press]]|access-date= November 18, 2020|archive-date= February 5, 2021|archive-url= https://web.archive.org/web/20210205161915/https://books.google.com/books?id=vFZrAAAAMAAJ|url-status= live}}</ref><ref name="Touwaide2005">{{cite book|last1= Touwaide|first1= Alain|title= Medieval Science, Technology, and Medicine: An Encyclopedia|date= 2005|editor1-last= Glick|editor1-first= Thomas F.|editor2-last= Livesey|editor2-first= Steven|editor3-last= Wallis|editor3-first= Faith|publisher= Routledge|location= New York City, New York and London, England|isbn= 978-0-415-96930-7|page= 224|url= https://books.google.com/books?id=77y2AgAAQBAJ&q=Hippocrates+medical+science&pg=PA224|access-date= October 20, 2020|archive-date= February 6, 2021|archive-url= https://web.archive.org/web/20210206081848/https://books.google.com/books?id=77y2AgAAQBAJ&q=Hippocrates+medical+science&pg=PA224|url-status= live}}</ref> and is known as "[[List of persons considered father or mother of a scientific field#Medicine and physiology|The Father of Medicine]]".<ref>{{cite book|last1= Leff|first1= Samuel|last2= Leff|first2= Vera|date= 1956|title= From Witchcraft to World Health|url= https://books.google.com/books?id=HjNrAAAAMAAJ|location= London, England|publisher= [[Macmillan Publishers|Macmillan]]|access-date= August 23, 2020|archive-date= February 5, 2021|archive-url= https://web.archive.org/web/20210205162709/https://books.google.com/books?id=HjNrAAAAMAAJ|url-status= live}}</ref>

A turning point in the history of early philosophical science was [[Socrates]]' example of applying philosophy to the study of human matters, including human nature, the nature of political communities, and human knowledge itself. The [[Socratic method]] as documented by [[Plato]]'s dialogues is a [[dialectic]] method of hypothesis elimination: better hypotheses are found by steadily identifying and eliminating those that lead to contradictions. The Socratic method searches for general commonly-held truths that shape beliefs and scrutinizes them for consistency.<ref>{{cite web |url= https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0170%3Atext%3DApol.%3Apage%3D17 |title= Plato, Apology| page= 17 |access-date= November 1, 2017 |url-status=live |archive-url= https://web.archive.org/web/20180129145253/http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0170%3Atext%3DApol.%3Apage%3D17 |archive-date= January 29, 2018 }}</ref> Socrates criticized the older type of study of physics as too purely speculative and lacking in [[self-criticism]].<ref>{{cite web |url= https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0170%3Atext%3DApol.%3Apage%3D27 |title= Plato, Apology| page = 27 |access-date= November 1, 2017 |url-status=live |archive-url= https://web.archive.org/web/20180129145253/http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0170%3Atext%3DApol.%3Apage%3D27 |archive-date= January 29, 2018 }}</ref>

[[Aristotle]] in the 4th century BCE created a systematic program of [[teleological]] philosophy.<ref>{{cite book|author1= Aristotle|title= Nicomachean Ethics|edition= H. Rackham|url= https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0054%3Abekker%20page%3D1139b|url-status= live|archive-url= https://web.archive.org/web/20120317140402/http://www.perseus.tufts.edu/hopper/text?doc=|archive-date= March 17, 2012|access-date= September 22, 2010|at=1139b}}</ref> In the 3rd century BCE, Greek astronomer [[Aristarchus of Samos]] was the first to propose a [[Heliocentrism|heliocentric model]] of the universe, with the [[Sun]] at the center and all the planets orbiting it.<ref name="McClellan2015">{{cite book|last1= McClellan III|first1= James E.|last2= Dorn|first2= Harold|title= Science and Technology in World History: An Introduction|date= 2015|publisher= Johns Hopkins University Press|location= Baltimore, Maryland|isbn= 978-1-4214-1776-9|pages= 99–100|url= https://books.google.com/books?id=ah1ECwAAQBAJ&q=Aristarchus+heliocentrism&pg=PA99|access-date= October 20, 2020|archive-date= February 6, 2021|archive-url= https://web.archive.org/web/20210206081851/https://books.google.com/books?id=ah1ECwAAQBAJ&q=Aristarchus+heliocentrism&pg=PA99|url-status= live}}</ref> Aristarchus's model was widely rejected because it was believed to violate the laws of physics,<ref name="McClellan2015" /> while Ptolemy's ''[[Almagest]]'', which contains a geocentric description of the [[Solar System]], was accepted through the early Renaissance instead.<ref name="Graßhoff">{{Cite book|last=Graßhoff|first=Gerd|url=http://link.springer.com/10.1007/978-1-4612-4468-4|title=The History of Ptolemy's Star Catalogue|date=1990|publisher=Springer New York|isbn=978-1-4612-8788-9|series=Studies in the History of Mathematics and Physical Sciences|volume=14|location=New York, NY|doi=10.1007/978-1-4612-4468-4|access-date=May 27, 2022|archive-date=May 30, 2022|archive-url=https://web.archive.org/web/20220530023947/https://link.springer.com/book/10.1007/978-1-4612-4468-4|url-status=live}}</ref><ref name=Hoffmann>{{Cite book|last=Hoffmann|first=Susanne M.|url=http://link.springer.com/10.1007/978-3-658-18683-8|title=Hipparchs Himmelsglobus|date=2017|publisher=Springer Fachmedien Wiesbaden|isbn=978-3-658-18682-1|location=Wiesbaden|language=de|doi=10.1007/978-3-658-18683-8|bibcode=2017hihi.book.....H |access-date=May 27, 2022|archive-date=May 30, 2022|archive-url=https://web.archive.org/web/20220530023947/https://link.springer.com/book/10.1007/978-3-658-18683-8|url-status=live}}</ref> The inventor and mathematician [[Archimedes|Archimedes of Syracuse]] made major contributions to the beginnings of [[calculus]].<ref name="Edwards1979">{{cite book|last1= Edwards|first1= C.H. Jr.|title= The Historical Development of the Calculus|date= 1979|publisher= Springer-Verlag|location= New York City, New York|isbn= 978-0-387-94313-8|page= 75|edition= |url= https://books.google.com/books?id=ilrlBwAAQBAJ&q=Archimedes+calculus&pg=PA75|access-date= October 20, 2020|archive-date= February 5, 2021|archive-url= https://web.archive.org/web/20210205165030/https://books.google.com/books?id=ilrlBwAAQBAJ&q=Archimedes+calculus&pg=PA75|url-status= live}}</ref> [[Pliny the Elder]] was a Roman writer and polymath, who wrote the seminal encyclopedia ''[[Natural History (Pliny)|Natural History]]''.<ref name="Lawson2004">{{cite book|last1= Lawson|first1= Russell M.|title= Science in the Ancient World: An Encyclopedia|date= 2004|publisher= ABC-CLIO|location= Santa Barbara, California|isbn= 978-1-85109-539-1|pages= 190–91|url= https://books.google.com/books?id=1AY1ALzh9V0C&q=Pliny+the+Elder+encyclopedia&pg=PA190|access-date= October 20, 2020|archive-date= February 5, 2021|archive-url= https://web.archive.org/web/20210205165032/https://books.google.com/books?id=1AY1ALzh9V0C&q=Pliny+the+Elder+encyclopedia&pg=PA190|url-status= live}}</ref><ref>{{cite book|last1= Murphy|first1= Trevor Morgan|title= Pliny the Elder's Natural History: The Empire in the Encyclopedia|date= 2004|publisher= Oxford University Press|location= Oxford, England|isbn= 978-0-19-926288-5|page= 1|url= https://books.google.com/books?id=6NC_T_tG9lQC&q=Pliny+the+Elder+encyclopedia|access-date= October 20, 2020|archive-date= February 6, 2021|archive-url= https://web.archive.org/web/20210206081849/https://books.google.com/books?id=6NC_T_tG9lQC&q=Pliny+the+Elder+encyclopedia|url-status= live}}</ref><ref>{{cite book|last1= Doody|first1= Aude|title= Pliny's Encyclopedia: The Reception of the Natural History|date= 2010|publisher= Cambridge University Press|location= Cambridge, England|isbn= 978-1-139-48453-4|page= 1|url= https://books.google.com/books?id=YoEhAwAAQBAJ&q=Pliny+the+Elder+encyclopedia|access-date= October 20, 2020|archive-date= March 31, 2021|archive-url= https://web.archive.org/web/20210331144844/https://books.google.com/books?id=YoEhAwAAQBAJ&q=Pliny+the+Elder+encyclopedia|url-status= live}}</ref>

[[Positional notation]] for representing numbers likely emerged between the 3rd and 5th centuries CE along Indian trade routes. This numeral system made efficient [[arithmetic]] operations more accessible and would eventually become standard for mathematics worldwide.<ref>{{Cite book |last=Conner |first=Clifford D. |title=A People's History of Science: Miners, Midwives, and "Low Mechanicks" |date=2005 |publisher=Nation Books |isbn=1-56025-748-2 |location=New York |oclc=62164511 |pages=72–74}}</ref>