Relationship between mathematics and physics (English Wikipedia)

MICHAEL ATIYAH ET AL. "RESPONSES TO THEORETICAL MATHEMATICS: TOWARD A CULTURAL SYNTHESIS OF MATHEMATICS AND THEORETICAL PHYSICS, BY A. JAFFE AND F. QUINN. https://www.ams.org/journals/bull/1994-30-02/S0273-0979-1994-00503-8/S0273-0979-1994-00503-8.pdf"

archive.org

Lear, Jonathan (1990). Aristotle: the desire to understand (Repr. ed.). Cambridge [u.a.]: Cambridge Univ. Press. p. 232. ISBN 9780521347624.
Roger G. Newton (1997). The Truth of Science: Physical Theories and Reality. Harvard University Press. pp. 125–126. ISBN 978-0-674-91092-8.

books.google.com

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.
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.
Sanjay Moreshwar Wagh; Dilip Abasaheb Deshpande (27 September 2012). Essentials of Physics. PHI Learning Pvt. Ltd. p. 3. ISBN 978-81-203-4642-0.
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.
Aharon Kantorovich (1 July 1993). Scientific Discovery: Logic and Tinkering. SUNY Press. p. 59. ISBN 978-0-7914-1478-1.
Arthur Mazer (26 September 2011). The Ellipse: A Historical and Mathematical Journey. John Wiley & Sons. p. 5. Bibcode:2010ehmj.book.....M. ISBN 978-1-118-21143-4.
Arkady Plotnitsky, Niels Bohr and Complementarity: An Introduction, p. 177.
Eoin P. O'Neill (editor), What Did You Do Today, Professor?: Fifteen Illuminating Responses from Trinity College Dublin, p. 62.
Timothy Gowers; June Barrow-Green; Imre Leader (18 July 2010). The Princeton Companion to Mathematics. Princeton University Press. p. 7. ISBN 978-1-4008-3039-8.
Zeidler, Eberhard (2008-09-03). Quantum Field Theory II: Quantum Electrodynamics: A Bridge between Mathematicians and Physicists. Springer Science & Business Media. ISBN 978-3-540-85377-0.
Pierre Bergé, Des rythmes au chaos.
Gary Carl Hatfield (1990). The Natural and the Normative: Theories of Spatial Perception from Kant to Helmholtz. MIT Press. p. 223. ISBN 978-0-262-08086-6.
Gila Hanna; Hans Niels Jahnke; Helmut Pulte (4 December 2009). Explanation and Proof in Mathematics: Philosophical and Educational Perspectives. Springer Science & Business Media. pp. 29–30. ISBN 978-1-4419-0576-5.
James Van Cleve Professor of Philosophy Brown University (16 July 1999). Problems from Kant. Oxford University Press, USA. p. 22. ISBN 978-0-19-534701-2.
Ludwig Wittgenstein; R. G. Bosanquet; Cora Diamond (15 October 1989). Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939. University of Chicago Press. p. 96. ISBN 978-0-226-90426-9.
Pudlák, Pavel (2013). Logical Foundations of Mathematics and Computational Complexity: A Gentle Introduction. Springer Science & Business Media. p. 659. ISBN 978-3-319-00119-7.
Richard Lesh; Peter L. Galbraith; Christopher R. Haines; Andrew Hurford (2009). Modeling Students' Mathematical Modeling Competencies: ICTMA 13. Springer. p. 14. ISBN 978-1-4419-0561-1.

caltech.edu

feynmanlectures.caltech.edu

Feynman, Richard P. (2011). "Characteristics of Force". The Feynman lectures on physics. Volume 1: Mainly mechanics, radiation, and heat (The new millennium edition, paperback first published ed.). New York: Basic Books. ISBN 978-0-465-02493-3.

doi.org

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.
Rédei, M. "On the Tension Between Physics and Mathematics". J Gen Philos Sci 51, pp. 411–425 (2020). https://doi.org/10.1007/s10838-019-09496-0
David E. Rowe (2008). "Euclidean Geometry and Physical Space". The Mathematical Intelligencer. 28 (2): 51–59. doi:10.1007/BF02987157. S2CID 56161170.
Gorban, A. N. (2018-04-28). "Hilbert's sixth problem: the endless road to rigour". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 376 (2118): 20170238. doi:10.1098/rsta.2017.0238. ISSN 1364-503X. PMC 5869544. PMID 29555808.
Redish, Edward F.; Kuo, Eric (2015-07-01). "Language of Physics, Language of Math: Disciplinary Culture and Dynamic Epistemology". Science & Education. 24 (5): 561–590. doi:10.1007/s11191-015-9749-7. ISSN 1573-1901.
P.W. Bridgman (1959), "How Much Rigor is Possible in Physics?" https://doi.org/10.1016/S0049-237X(09)70030-8

fqxi.org

"FQXi Community Trick or Truth: the Mysterious Connection Between Physics and Mathematics". Archived from the original on 14 December 2021. Retrieved 16 April 2015.

harvard.edu

ui.adsabs.harvard.edu

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.
Arthur Mazer (26 September 2011). The Ellipse: A Historical and Mathematical Journey. John Wiley & Sons. p. 5. Bibcode:2010ehmj.book.....M. ISBN 978-1-118-21143-4.

hawking.org.uk

"Stephen Hawking. "Godel and the End of the Universe"". Archived from the original on 2020-05-29. Retrieved 2015-06-12.

ius.edu

homepages.ius.edu

Kyle Forinash, William Rumsey, Chris Lang, Galileo's Mathematical Language of Nature Archived 2013-09-27 at the Wayback Machine.

jstor.org

Kevin Davey. "Is Mathematical Rigor Necessary in Physics?", The British Journal for the Philosophy of Science, Vol. 54, No. 3 (Sep., 2003), pp. 439–463 https://www.jstor.org/stable/3541794

kfupm.edu.sa

faculty.kfupm.edu.sa

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.

mathunion.org

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.

nih.gov

ncbi.nlm.nih.gov

Gorban, A. N. (2018-04-28). "Hilbert's sixth problem: the endless road to rigour". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 376 (2118): 20170238. doi:10.1098/rsta.2017.0238. ISSN 1364-503X. PMC 5869544. PMID 29555808.

pubmed.ncbi.nlm.nih.gov

Gorban, A. N. (2018-04-28). "Hilbert's sixth problem: the endless road to rigour". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 376 (2118): 20170238. doi:10.1098/rsta.2017.0238. ISSN 1364-503X. PMC 5869544. PMID 29555808.

oregonstate.edu

bridge.math.oregonstate.edu

https://bridge.math.oregonstate.edu/papers/ampere.pdf

pair.com

www22.pair.com

E. J. Post, A History of Physics as an Exercise in Philosophy, p. 76.

particlecentral.com

"String theories". Particle Central. Four Peaks Technologies. Retrieved 13 June 2015.

sanfordlab.org

"The coevolution of physics and math", Symmetry Magazine, April 24, 2018

scientificamerican.com

Mario Livio (August 2011). "Why math works?". Scientific American: 80–83.

semanticscholar.org

api.semanticscholar.org

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.
David E. Rowe (2008). "Euclidean Geometry and Physical Space". The Mathematical Intelligencer. 28 (2): 51–59. doi:10.1007/BF02987157. S2CID 56161170.

st-andrews.ac.uk

mathshistory.st-andrews.ac.uk

Albert Einstein, Geometry and Experience.

stanford.edu

plato.stanford.edu

Shields, Christopher (2023), "Aristotle", in Zalta, Edward N.; Nodelman, Uri (eds.), The Stanford Encyclopedia of Philosophy (Winter 2023 ed.), Metaphysics Research Lab, Stanford University, retrieved 2024-11-11
Bourdeau, Michel (2023), "Auguste Comte", in Zalta, Edward N.; Nodelman, Uri (eds.), The Stanford Encyclopedia of Philosophy (Spring 2023 ed.), Metaphysics Research Lab, Stanford University, retrieved 2024-11-08

taylorfrancis.com

Mark Steiner (1992), "Mathematical Rigor in Physics". https://www.taylorfrancis.com/chapters/edit/10.4324/9780203979105-13/mathematical-rigor-physics-mark-steiner

univ-reims.fr

Karam; Pospiech; & Pietrocola (2010). "Mathematics in physics lessons: developing structural skills"

unlp.edu.ar

www2.fisica.unlp.edu.ar

Stakhov "Dirac’s Principle of Mathematical Beauty, Mathematics of Harmony"

web.archive.org

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.
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.
Kyle Forinash, William Rumsey, Chris Lang, Galileo's Mathematical Language of Nature Archived 2013-09-27 at the Wayback Machine.
"FQXi Community Trick or Truth: the Mysterious Connection Between Physics and Mathematics". Archived from the original on 14 December 2021. Retrieved 16 April 2015.
"Stephen Hawking. "Godel and the End of the Universe"". Archived from the original on 2020-05-29. Retrieved 2015-06-12.

worldcat.org

search.worldcat.org

Gorban, A. N. (2018-04-28). "Hilbert's sixth problem: the endless road to rigour". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 376 (2118): 20170238. doi:10.1098/rsta.2017.0238. ISSN 1364-503X. PMC 5869544. PMID 29555808.
Redish, Edward F.; Kuo, Eric (2015-07-01). "Language of Physics, Language of Math: Disciplinary Culture and Dynamic Epistemology". Science & Education. 24 (5): 561–590. doi:10.1007/s11191-015-9749-7. ISSN 1573-1901.