Editing Mathematics (section)

==== Social sciences ====
{{Further|Mathematical economics|Historical dynamics}}
Areas of mathematics used in the social sciences include probability/statistics and differential equations. These are used in linguistics, [[economics]], [[sociology]],<ref>{{Cite journal |last=Edling |first=Christofer R. |year=2002 |title=Mathematics in Sociology |url=https://www.annualreviews.org/doi/10.1146/annurev.soc.28.110601.140942 |journal=Annual Review of Sociology |language=en |volume=28 |issue=1 |pages=197–220 |doi=10.1146/annurev.soc.28.110601.140942 |issn=0360-0572 |archive-date=November 15, 2021 |access-date=September 30, 2023 |archive-url=https://web.archive.org/web/20211115130943/https://www.annualreviews.org/doi/10.1146/annurev.soc.28.110601.140942 |url-status=live }}</ref> and [[psychology]].<ref>{{Citation |last=Batchelder |first=William H. |title=Mathematical Psychology: History |date=January 1, 2015 |url=https://www.sciencedirect.com/science/article/pii/B978008097086843059X |encyclopedia=International Encyclopedia of the Social & Behavioral Sciences (Second Edition) |pages=808–815 |editor-last=Wright |editor-first=James D. |access-date=September 30, 2023 |place=Oxford |publisher=Elsevier |isbn=978-0-08-097087-5 |archive-date=February 17, 2023 |archive-url=https://web.archive.org/web/20230217140558/https://www.sciencedirect.com/science/article/pii/B978008097086843059X |url-status=live }}</ref>
[[File:Supply-demand-equilibrium.svg|thumb|[[Supply and demand]] curves, like this one, are a staple of mathematical economics.|class=skin-invert-image]]
Often the fundamental postulate of mathematical economics is that of the rational individual actor – ''[[Homo economicus]]'' ({{Literal translation|economic man}}).<ref name=":3">{{Cite book |last=Zak |first=Paul J. |url={{GBurl|id=6QrvmNo2qD4C|p=158}} |title=Moral Markets: The Critical Role of Values in the Economy |date=2010 |page=158 |publisher=Princeton University Press |isbn=978-1-4008-3736-6 |language=en |access-date=January 3, 2023 }}</ref> In this model, the individual seeks to maximize their [[rational choice theory|self-interest]],<ref name=":3" /> and always makes optimal choices using [[perfect information]].<ref>{{cite book |url=https://web.stanford.edu/~jdlevin/Econ%20202/Choice%20Theory.pdf |title=Introduction to Choice Theory |first1=Jonathan |last1=Levin |first2=Paul |last2=Milgrom |date=September 2004}}</ref> This atomistic view of economics allows it to relatively easily mathematize its thinking, because individual [[calculations]] are transposed into mathematical calculations. Such mathematical modeling allows one to probe economic mechanisms. Some reject or criticise the concept of ''Homo economicus''. Economists note that real people have limited information, make poor choices, and care about fairness and altruism, not just personal gain.<ref>{{cite book |author1=Kremer, Michael |author2=Rao, Gautam |author3=Schilbach, Frank |url=https://economics.mit.edu/sites/default/files/2022-09/behavioral-development-economics.pdf |title=Handbook of Behavioral Economics: Applications and Foundations |chapter=Chapter 5 Behavioral development economics |year=2019 |volume=2 |archive-date=June 2, 2024 |access-date=June 2, 2024 |archive-url=https://web.archive.org/web/20240602215911/https://economics.mit.edu/sites/default/files/2022-09/behavioral-development-economics.pdf |url-status=live }}</ref>

Without mathematical modeling, it is hard to go beyond statistical observations or untestable speculation. Mathematical modeling allows economists to create structured frameworks to test hypotheses and analyze complex interactions. Models provide clarity and precision, enabling the translation of theoretical concepts into quantifiable predictions that can be tested against real-world data.<ref>{{Cite web|url=https://www.mdpi.com/journal/mathematics/special_issues/Mathematical_Modeling_Economics_Ecology_Environment|title=Mathematics|website=mdpi.com}}</ref>

At the start of the 20th century, there was a development to express historical movements in formulas. In 1922, [[Nikolai Kondratiev]] discerned the ~50-year-long [[Kondratiev cycle]], which explains phases of economic growth or crisis.<ref>{{Cite web |title=Kondratiev, Nikolai Dmitrievich {{!}} Encyclopedia.com |url=https://www.encyclopedia.com/history/encyclopedias-almanacs-transcripts-and-maps/kondratiev-nikolai-dmitrievich |access-date=December 29, 2022 |website=www.encyclopedia.com |archive-date=July 1, 2016 |archive-url=https://web.archive.org/web/20160701224009/http://www.encyclopedia.com/doc/1G2-3404100667.html |url-status=live }}</ref> Towards the end of the 19th century, mathematicians extended their analysis into [[geopolitics]].<ref>{{Cite web|url=https://onlinebooks.library.upenn.edu/webbin/book/lookupid?key=ha010090244#:~:text=|title=Mathématique de l'histoire-géometrie et cinématique. Lois de Brück. Chronologie géodésique de la Bible., by Charles LAGRANGE et al. &#124; The Online Books Page|website=onlinebooks.library.upenn.edu|access-date=January 3, 2024|archive-date=January 3, 2024|archive-url=https://web.archive.org/web/20240103142807/https://onlinebooks.library.upenn.edu/webbin/book/lookupid?key=ha010090244#:~:text=|url-status=live}}</ref> [[Peter Turchin]] developed [[cliodynamics]] in the 1990s.<ref>{{Cite web |title=Cliodynamics: a science for predicting the future |url=https://www.zdnet.com/article/cliodynamics-a-science-for-predicting-the-future/ |access-date=December 29, 2022 |publisher=ZDNet |language=en |archive-date=December 29, 2022 |archive-url=https://web.archive.org/web/20221229204104/https://www.zdnet.com/article/cliodynamics-a-science-for-predicting-the-future/ |url-status=live }}</ref>

Mathematization of the social sciences is not without risk. In the controversial book ''[[Fashionable Nonsense]]'' (1997), [[Alan Sokal|Sokal]] and [[Jean Bricmont|Bricmont]] denounced the unfounded or abusive use of scientific terminology, particularly from mathematics or physics, in the social sciences.<ref>{{cite book|last=Sokal|first=Alan|url=https://archive.org/details/fashionablenonse00soka|title=Fashionable Nonsense|author2=Jean Bricmont|publisher=Picador|year=1998|isbn=978-0-312-19545-8|location=New York|oclc=39605994|author-link=Alan Sokal|author2-link=Jean Bricmont}}</ref> The study of [[complex systems]] (evolution of unemployment, business capital, demographic evolution of a population, etc.) uses mathematical knowledge. However, the choice of counting criteria, particularly for unemployment, or of models, can be subject to controversy.<ref>{{Cite web|url=https://www.factcheck.org/2023/01/bidens-misleading-unemployment-statistic/|title=Biden's Misleading Unemployment Statistic – FactCheck.org|date=January 27, 2023 |access-date=June 2, 2024|archive-date=June 2, 2024|archive-url=https://web.archive.org/web/20240602215913/https://www.factcheck.org/2023/01/bidens-misleading-unemployment-statistic/|url-status=live}}</ref><ref>{{Cite web|url=https://www.minneapolisfed.org/article/2010/modern-macroeconomic-models-as-tools-for-economic-policy|title=Modern Macroeconomic Models as Tools for Economic Policy &#124; Federal Reserve Bank of Minneapolis|website=minneapolisfed.org|access-date=June 2, 2024|archive-date=August 3, 2024|archive-url=https://web.archive.org/web/20240803124409/https://www.minneapolisfed.org/article/2010/modern-macroeconomic-models-as-tools-for-economic-policy|url-status=live}}</ref>