| 词条 | Relationship between mathematics and physics |
| 释义 |
The relationship between mathematics and physics has been a subject of study of philosophers, mathematicians and physicists since Antiquity, and more recently also by historians and educators.[2] Generally considered a relationship of great intimacy,[3] mathematics has been described as "an essential tool for physics"[4] and physics has been described as "a rich source of inspiration and insight in mathematics".[5] In his work Physics, one of the topics treated by Aristotle is about how the study carried out by mathematicians differs from that carried out by physicists.[6] Considerations about mathematics being the language of nature can be found in the ideas of the Pythagoreans: the convictions that "Numbers rule the world" and "All is number",[7][8] and two millennia later were also expressed by Galileo Galilei: "The book of nature is written in the language of mathematics".[9][10] Before giving a mathematical proof for the formula for the volume of a sphere, Archimedes used physical reasoning to discover the solution (imagining the balancing of bodies on a scale).[11] From the seventeenth century, many of the most important advances in mathematics appeared motivated by the study of physics, and this continued in the following centuries (although in the nineteenth century mathematics started to become increasingly independent from physics).[12][13] The creation and development of calculus were strongly linked to the needs of physics:[14] There was a need for a new mathematical language to deal with the new dynamics that had arisen from the work of scholars such as Galileo Galilei and Isaac Newton.[15] During this period there was little distinction between physics and mathematics;[16] as an example, Newton regarded geometry as a branch of mechanics.[17] As time progressed, increasingly sophisticated mathematics started to be used in physics. The current situation is that the mathematical knowledge used in physics is becoming increasingly sophisticated, as in the case of superstring theory.[18] Philosophical problemsSome of the problems considered in the philosophy of mathematics are the following:
EducationIn recent times the two disciplines have most often been taught separately, despite all the interrelations between physics and mathematics.[29] This led some professional mathematicians who were also interested in mathematics education, such as Felix Klein, Richard Courant, Vladimir Arnold and Morris Kline, to strongly advocate teaching mathematics in a way more closely related to the physical sciences.[30][31] See also{{Col-begin}}{{Col-1-of-2}}
References1. ^{{cite book|author1=Jed Z. Buchwald|author2=Robert Fox|title=The Oxford Handbook of the History of Physics|url=https://books.google.com/books?id=1SxoAgAAQBAJ&pg=PA128|date=10 October 2013|publisher=OUP Oxford|isbn=978-0-19-151019-9|pages=128}} 2. ^{{cite journal|last1=Uhden|first1=Olaf|last2=Karam|first2=Ricardo|last3=Pietrocola|first3=Maurício|last4=Pospiech|first4=Gesche|title=Modelling Mathematical Reasoning in Physics Education|journal=Science & Education|date=20 October 2011|volume=21|issue=4|pages=485–506|doi=10.1007/s11191-011-9396-6|bibcode = 2012Sc&Ed..21..485U }} 3. ^{{cite book|author1=Francis Bailly|author2=Giuseppe Longo|title=Mathematics and the Natural Sciences: The Physical Singularity of Life|url=https://books.google.com/books?id=7-dGHyIyI-AC&pg=PA149|year=2011|publisher=World Scientific|isbn=978-1-84816-693-6|pages=149}} 4. ^{{cite book|author1=Sanjay Moreshwar Wagh|author2=Dilip Abasaheb Deshpande|title=Essentials of Physics|url=https://books.google.com/books?id=-DmfVjBUPksC&pg=PA3|date=27 September 2012|publisher=PHI Learning Pvt. Ltd.|isbn=978-81-203-4642-0|pages=3}} 5. ^{{cite conference |url=http://www.mathunion.org/ICM/ICM1990.1/Main/icm1990.1.0031.0036.ocr.pdf |title=On the Work of Edward Witten |last1=Atiyah |first1=Michael |author-link1=Michael Atiyah |year=1990 |conference=International Congress of Mathematicians |publisher= |book-title= |pages=31–35 |location=Japan |id= |deadurl=yes |archiveurl=https://web.archive.org/web/20170301004342/http://www.mathunion.org/ICM/ICM1990.1/Main/icm1990.1.0031.0036.ocr.pdf |archivedate=2017-03-01 |df= }} 6. ^{{cite book|last1=Lear|first1=Jonathan|title=Aristotle: the desire to understand|date=1990|publisher=Cambridge Univ. Press|location=Cambridge [u.a.]|isbn=9780521347624|page=232|edition=Repr.}} 7. ^{{cite book|author1=Gerard Assayag|author2=Hans G. Feichtinger|author3=José-Francisco Rodrigues|title=Mathematics and Music: A Diderot Mathematical Forum|url=https://books.google.com/books?id=bjsD8ClsFKEC&pg=PA216|date=10 July 2002|publisher=Springer|isbn=978-3-540-43727-7|pages=216}} 8. ^{{cite web|first=Ibrahim |last=Al-Rasasi |title= All is number |url=http://faculty.kfupm.edu.sa/math/irasasi/Allisnumber.pdf |publisher=King Fahd University of Petroleum and Minerals |date=21 June 2004 |accessdate=13 June 2015}} 9. ^{{cite book|author=Aharon Kantorovich|title=Scientific Discovery: Logic and Tinkering|url=https://books.google.com/books?id=vMFc43w0FfEC&pg=PA59|date=1 July 1993|publisher=SUNY Press|isbn=978-0-7914-1478-1|pages=59}} 10. ^Kyle Forinash, William Rumsey, Chris Lang, Galileo's Mathematical Language of Nature. 11. ^{{cite book|author=Arthur Mazer|title=The Ellipse: A Historical and Mathematical Journey|url=https://books.google.com/books?id=twWkDe1Y9YQC&pg=SA5-PA28|date=26 September 2011|publisher=John Wiley & Sons|isbn=978-1-118-21143-4|pages=5}} 12. ^E. J. Post, A History of Physics as an Exercise in Philosophy, p. 76. 13. ^Arkady Plotnitsky, [https://books.google.com/books?id=dmdUp97S4AYC&pg=PA177 Niels Bohr and Complementarity: An Introduction, p. 177]. 14. ^{{cite book|author=Roger G. Newton|title=The Truth of Science: Physical Theories and Reality|url=https://books.google.com/books?id=SzxsjN3t4i0C&pg=PA125|year=1997|publisher=Harvard University Press|isbn=978-0-674-91092-8|pages=125–126}} 15. ^Eoin P. O'Neill (editor), [https://books.google.com/books?id=h8TaAAAAMAAJ&redir_esc=y What Did You Do Today, Professor?: Fifteen Illuminating Responses from Trinity College Dublin, p. 62]. 16. ^{{cite book|author1=Timothy Gowers|author-link=Timothy Gowers|author2=June Barrow-Green|author3=Imre Leader|title=The Princeton Companion to Mathematics|url=https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA7|date=18 July 2010|publisher=Princeton University Press|isbn=978-1-4008-3039-8|pages=7}} 17. ^{{cite journal|author=David E. Rowe|author-link=David E. Rowe|title=Euclidean Geometry and Physical Space|journal=The Mathematical Intelligencer|year=2008|volume=28|issue=2|pages=51–59|doi=10.1007/BF02987157}} 18. ^{{cite web |url=http://www.particlecentral.com/strings_page.html |title=String theories |author= |website=Particle Central |publisher=Four Peaks Technologies |access-date=13 June 2015 }} 19. ^Albert Einstein, Geometry and Experience. 20. ^Pierre Bergé, [https://books.google.com/books?id=umFTtQAACAAJ&dq=%22Des+rythmes+au+chaos%22&hl=pt-BR&sa=X&ei=65aEU7LAKeHL8AHc74HwBg&ved=0CC4Q6AEwAA Des rythmes au chaos]. 21. ^{{cite book|author=Gary Carl Hatfield|title=The Natural and the Normative: Theories of Spatial Perception from Kant to Helmholtz|url=https://books.google.com/books?id=JikeeDbYeUQC&pg=PA223|year=1990|publisher=MIT Press|isbn=978-0-262-08086-6|page=223}} 22. ^{{cite book|author1=Gila Hanna|author2=Hans Niels Jahnke|author3=Helmut Pulte|title=Explanation and Proof in Mathematics: Philosophical and Educational Perspectives|url=https://books.google.com/books?id=3bLHye8kSAwC&pg=PA29|date=4 December 2009|publisher=Springer Science & Business Media|isbn=978-1-4419-0576-5|pages=29–30}} 23. ^{{cite web |url=http://fqxi.org/community/essay/rules |title=FQXi Community Trick or Truth: the Mysterious Connection Between Physics and Mathematics |access-date=16 April 2015}} 24. ^{{cite book|author=James Van Cleve Professor of Philosophy Brown University|title=Problems from Kant|url=https://books.google.com/books?id=6WHAgt-Mg1AC&pg=PA22|date=16 July 1999|publisher=Oxford University Press, USA|isbn=978-0-19-534701-2|pages=22}} 25. ^{{cite book|author1=Ludwig Wittgenstein|author2=R. G. Bosanquet|author3=Cora Diamond|title=Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939|url=https://books.google.com/books?id=d4YUZVq1JSEC&pg=PA96|date=15 October 1989|publisher=University of Chicago Press|isbn=978-0-226-90426-9|page=96}} 26. ^{{cite book|first=Pavel|last=Pudlák|title=Logical Foundations of Mathematics and Computational Complexity: A Gentle Introduction|url=https://books.google.com/books?id=obxDAAAAQBAJ&pg=PA659|year=2013|publisher=Springer Science & Business Media|isbn=978-3-319-00119-7|page=659}} 27. ^Stephen Hawking. "Godel and the End of the Universe" 28. ^{{Cite journal | author = Mario Livio | authorlink = Mario Livio| doi = | title = Why math works? | journal = Scientific American | volume = | pages = 80–83 | year = August 2011 | url = http://www.scientificamerican.com/article/why-math-works/| pmid = | pmc = }} 29. ^Karam; Pospiech; & Pietrocola (2010). "Mathematics in physics lessons: developing structural skills" 30. ^Stakhov "Dirac’s Principle of Mathematical Beauty, Mathematics of Harmony" 31. ^{{cite book|author1=Richard Lesh|author2=Peter L. Galbraith|author3=Christopher R. Haines|author4=Andrew Hurford|title=Modeling Students' Mathematical Modeling Competencies: ICTMA 13|url=https://books.google.com/books?id=Jj5tfi2594kC&pg=PA14|year=2009|publisher=Springer|isbn=978-1-4419-0561-1|page=14}} Further reading
External links
8 : Philosophy of physics|Philosophy of mathematics|History of science|Mathematics education|Physics education|Foundations of mathematics|History of mathematics|History of physics |
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