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Relationship between mathematics and physics

A cycloidal pendulum is isochronous, a fact discovered and proved by Christiaan Huygens under certain mathematical assumptions.[1]
Mathematics was developed by the Ancient Civilizations for intellectual challenge and pleasure. Surprisingly, many of their discoveries later played prominent roles in physical theories, as in the case of the conic sections in celestial mechanics.

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]

  1. ^ Jed Z. Buchwald; Robert Fox (10 October 2013). The Oxford Handbook of the History of Physics. OUP Oxford. p. 128. ISBN 978-0-19-151019-9.
  2. ^ Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche (20 October 2011). "Modelling Mathematical Reasoning in Physics Education". Science & Education. 21 (4): 485–506. Bibcode:2012Sc&Ed..21..485U. doi:10.1007/s11191-011-9396-6. S2CID 122869677.
  3. ^ Francis Bailly; Giuseppe Longo (2011). Mathematics and the Natural Sciences: The Physical Singularity of Life. World Scientific. p. 149. ISBN 978-1-84816-693-6.
  4. ^ Sanjay Moreshwar Wagh; Dilip Abasaheb Deshpande (27 September 2012). Essentials of Physics. PHI Learning Pvt. Ltd. p. 3. ISBN 978-81-203-4642-0.
  5. ^ Atiyah, Michael (1990). On the Work of Edward Witten (PDF). International Congress of Mathematicians. Japan. pp. 31–35. Archived from the original (PDF) on 2017-03-01.
  6. ^ Lear, Jonathan (1990). Aristotle: the desire to understand (Repr. ed.). Cambridge [u.a.]: Cambridge Univ. Press. p. 232. ISBN 9780521347624.
  7. ^ Gerard Assayag; Hans G. Feichtinger; José-Francisco Rodrigues (10 July 2002). Mathematics and Music: A Diderot Mathematical Forum. Springer. p. 216. ISBN 978-3-540-43727-7.
  8. ^ Al-Rasasi, Ibrahim (21 June 2004). "All is number" (PDF). King Fahd University of Petroleum and Minerals. Archived from the original (PDF) on 28 December 2014. Retrieved 13 June 2015.
  9. ^ Aharon Kantorovich (1 July 1993). Scientific Discovery: Logic and Tinkering. SUNY Press. p. 59. ISBN 978-0-7914-1478-1.
  10. ^ Kyle Forinash, William Rumsey, Chris Lang, Galileo's Mathematical Language of Nature Archived 2013-09-27 at the Wayback Machine.

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