Philosophy of mathematics (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Philosophy of mathematics" in English language version.

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academia.edu

Dorato, Mauro (2005). "Why are laws mathematical?" (PDF). The Software of the Universe, An Introduction to the History and Philosophy of Laws of Nature. Ashgate. pp. 31–66. ISBN 978-0-7546-3994-7. Archived (PDF) from the original on August 17, 2023. Retrieved December 5, 2022.

archive.org

Ayer, Alfred Jules (1952). Language, Truth, & Logic. New York: Dover Publications, Inc. p. 74 ff. ISBN 978-0-486-20010-1.
Popper, Karl R. (1995). "On knowledge". In Search of a Better World: Lectures and Essays from Thirty Years. New York: Routledge. p. 56. Bibcode:1992sbwl.book.....P. ISBN 978-0-415-13548-1.

arxiv.org

Tegmark, Max (February 2008). "The Mathematical Universe". Foundations of Physics. 38 (2): 101–150. arXiv:0704.0646. Bibcode:2008FoPh...38..101T. doi:10.1007/s10701-007-9186-9. S2CID 9890455.

berkeley.edu

undsci.berkeley.edu

"The science checklist applied: Mathematics". Understanding Science. University of California, Berkeley. Archived from the original on October 27, 2019. Retrieved October 27, 2019.

books.google.com

Bellomo, Nicola; Preziosi, Luigi (December 22, 1994). Modelling Mathematical Methods and Scientific Computation. Mathematical Modeling. Vol. 1. CRC Press. p. 1. ISBN 978-0-8493-8331-1. Retrieved November 16, 2022.
Stewart, Ian (2018). "Mathematics, Maps, and Models". In Wuppuluri, Shyam; Doria, Francisco Antonio (eds.). The Map and the Territory: Exploring the Foundations of Science, Thought and Reality. The Frontiers Collection. Springer. pp. 345–356. doi:10.1007/978-3-319-72478-2_18. ISBN 978-3-319-72478-2. Retrieved November 17, 2022.
Mackay, A. L. (1991). Dictionary of Scientific Quotations. London: Taylor & Francis. p. 100. ISBN 978-0-7503-0106-0. Retrieved March 19, 2023.
Bishop, Alan (1991). "Environmental activities and mathematical culture". Mathematical Enculturation: A Cultural Perspective on Mathematics Education. Norwell, Massachusetts: Kluwer Academic Publishers. pp. 20–59. ISBN 978-0-7923-1270-3. Retrieved April 5, 2020.

c2.com

Review Archived 2011-05-14 at the Wayback Machine of The Emperor's New Mind.

dartmouth.edu

math.dartmouth.edu

Wigner, Eugene (1960). "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". Communications on Pure and Applied Mathematics. 13 (1): 1–14. Bibcode:1960CPAM...13....1W. doi:10.1002/cpa.3160130102. S2CID 6112252. Archived from the original on February 28, 2011.

doi.org

Borel, Armand (1983). "Mathematics: Art and Science". The Mathematical Intelligencer. 5 (4). Springer: 9–17. doi:10.4171/news/103/8. ISSN 1027-488X.
See White, L. (1947). "The locus of mathematical reality: An anthropological footnote". Philosophy of Science. 14 (4): 289–303. doi:10.1086/286957. S2CID 119887253. 189303; also in Newman, J. R. (1956). The World of Mathematics. Vol. 4. New York: Simon and Schuster. pp. 2348–2364.
Hamami, Yacin (June 2022). "Mathematical Rigor and Proof" (PDF). The Review of Symbolic Logic. 15 (2): 409–449. doi:10.1017/S1755020319000443. S2CID 209980693. Archived (PDF) from the original on December 5, 2022. Retrieved November 21, 2022.
Ferreirós, José (2001). "The Road to Modern Logic—An Interpretation" (PDF). Bulletin of Symbolic Logic. 7 (4): 441–484. doi:10.2307/2687794. hdl:11441/38373. JSTOR 2687794. S2CID 43258676. Archived (PDF) from the original on February 2, 2023. Retrieved November 11, 2022.
Davis, Jon D.; McDuffie, Amy Roth; Drake, Corey; Seiwell, Amanda L. (2019). "Teachers' perceptions of the official curriculum: Problem solving and rigor". International Journal of Educational Research. 93: 91–100. doi:10.1016/j.ijer.2018.10.002. S2CID 149753721.
Hennig, Christian (2010). "Mathematical Models and Reality: A Constructivist Perspective". Foundations of Science. 15: 29–48. doi:10.1007/s10699-009-9167-x. S2CID 6229200. Retrieved November 17, 2022.
Stewart, Ian (2018). "Mathematics, Maps, and Models". In Wuppuluri, Shyam; Doria, Francisco Antonio (eds.). The Map and the Territory: Exploring the Foundations of Science, Thought and Reality. The Frontiers Collection. Springer. pp. 345–356. doi:10.1007/978-3-319-72478-2_18. ISBN 978-3-319-72478-2. Retrieved November 17, 2022.
Wigner, Eugene (1960). "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". Communications on Pure and Applied Mathematics. 13 (1): 1–14. Bibcode:1960CPAM...13....1W. doi:10.1002/cpa.3160130102. S2CID 6112252. Archived from the original on February 28, 2011.
Wilson, Edwin B.; Lewis, Gilbert N. (November 1912). "The Space-Time Manifold of Relativity. The Non-Euclidean Geometry of Mechanics and Electromagnetics". Proceedings of the American Academy of Arts and Sciences. 48 (11): 389–507. doi:10.2307/20022840. JSTOR 20022840.
Borel, Armand (1983). "Mathematics: Art and Science". The Mathematical Intelligencer. 5 (4). Springer: 9–17. doi:10.4171/news/103/8. ISSN 1027-488X.
Hanson, Norwood Russell (November 1961). "Discovering the Positron (I)". The British Journal for the Philosophy of Science. 12 (47). The University of Chicago Press: 194–214. doi:10.1093/bjps/xiii.49.54. JSTOR 685207.
Ginammi, Michele (February 2016). "Avoiding reification: Heuristic effectiveness of mathematics and the prediction of the Ω^– particle". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 53: 20–27. Bibcode:2016SHPMP..53...20G. doi:10.1016/j.shpsb.2015.12.001.
S, F. (January 1941). "A Mathematician's Apology". Nature. 147 (3714): 3–5. Bibcode:1941Natur.147....3S. doi:10.1038/147003a0. S2CID 4212863.
Tegmark, Max (February 2008). "The Mathematical Universe". Foundations of Physics. 38 (2): 101–150. arXiv:0704.0646. Bibcode:2008FoPh...38..101T. doi:10.1007/s10701-007-9186-9. S2CID 9890455.
Franklin, James (2022). "Mathematics as a science of non-abstract reality: Aristotelian realist philosophies of mathematics". Foundations of Science. 27 (2): 327–344. doi:10.1007/s10699-021-09786-1. S2CID 233658181. Retrieved 30 June 2021.
Ganesalingam, Mohan (2013). The Language of Mathematics: A Linguistic and Philosophical Investigation. Lecture Notes in Computer Science. Vol. 7805. Springer. doi:10.1007/978-3-642-37012-0. ISBN 978-3-642-37011-3. S2CID 14260721.

edge.org

Hersh, Reuben (February 10, 1997). "What Kind of a Thing is a Number?" (Interview). Interviewed by John Brockman. Edge Foundation. Archived from the original on May 16, 2008. Retrieved 2008-12-26.

ex.ac.uk

people.ex.ac.uk

Ernest, Paul. "Is Mathematics Discovered or Invented?". University of Exeter. Archived from the original on 2008-04-05. Retrieved 2008-12-26.

exeter.ac.uk

socialsciences.exeter.ac.uk

"Is mathematics discovered or invented?". University of Exeter. Archived from the original on 27 July 2018. Retrieved 28 March 2018.

goodreads.com

"A Mathematician's Apology Quotes by G.H. Hardy". Archived from the original on 2021-05-08. Retrieved 2020-07-20.

handle.net

hdl.handle.net

Ferreirós, José (2001). "The Road to Modern Logic—An Interpretation" (PDF). Bulletin of Symbolic Logic. 7 (4): 441–484. doi:10.2307/2687794. hdl:11441/38373. JSTOR 2687794. S2CID 43258676. Archived (PDF) from the original on February 2, 2023. Retrieved November 11, 2022.

harvard.edu

ui.adsabs.harvard.edu

Wigner, Eugene (1960). "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". Communications on Pure and Applied Mathematics. 13 (1): 1–14. Bibcode:1960CPAM...13....1W. doi:10.1002/cpa.3160130102. S2CID 6112252. Archived from the original on February 28, 2011.
Ginammi, Michele (February 2016). "Avoiding reification: Heuristic effectiveness of mathematics and the prediction of the Ω^– particle". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 53: 20–27. Bibcode:2016SHPMP..53...20G. doi:10.1016/j.shpsb.2015.12.001.
S, F. (January 1941). "A Mathematician's Apology". Nature. 147 (3714): 3–5. Bibcode:1941Natur.147....3S. doi:10.1038/147003a0. S2CID 4212863.
Tegmark, Max (February 2008). "The Mathematical Universe". Foundations of Physics. 38 (2): 101–150. arXiv:0704.0646. Bibcode:2008FoPh...38..101T. doi:10.1007/s10701-007-9186-9. S2CID 9890455.
Popper, Karl R. (1995). "On knowledge". In Search of a Better World: Lectures and Essays from Thirty Years. New York: Routledge. p. 56. Bibcode:1992sbwl.book.....P. ISBN 978-0-415-13548-1.

jstor.org

Ferreirós, José (2001). "The Road to Modern Logic—An Interpretation" (PDF). Bulletin of Symbolic Logic. 7 (4): 441–484. doi:10.2307/2687794. hdl:11441/38373. JSTOR 2687794. S2CID 43258676. Archived (PDF) from the original on February 2, 2023. Retrieved November 11, 2022.
Sarukkai, Sundar (February 10, 2005). "Revisiting the 'unreasonable effectiveness' of mathematics". Current Science. 88 (3): 415–423. JSTOR 24110208.
Wilson, Edwin B.; Lewis, Gilbert N. (November 1912). "The Space-Time Manifold of Relativity. The Non-Euclidean Geometry of Mechanics and Electromagnetics". Proceedings of the American Academy of Arts and Sciences. 48 (11): 389–507. doi:10.2307/20022840. JSTOR 20022840.
Hanson, Norwood Russell (November 1961). "Discovering the Positron (I)". The British Journal for the Philosophy of Science. 12 (47). The University of Chicago Press: 194–214. doi:10.1093/bjps/xiii.49.54. JSTOR 685207.

mathforum.org

"Humanism and Mathematics Education". Math Forum. Humanistic Mathematics Network Journal. Archived from the original on 2008-07-24. Retrieved 2008-12-26.

mit.edu

Yablo, S. (November 8, 1998). "A Paradox of Existence". Archived from the original on January 7, 2020. Retrieved August 26, 2019.

nyu.edu

cs.nyu.edu

From an 1886 lecture at the 'Berliner Naturforscher-Versammlung', according to H. M. Weber's memorial article, as quoted and translated in Gonzalez Cabillon, Julio (2000-02-03). "FOM: What were Kronecker's f.o.m.?". Archived from the original on 2007-10-09. Retrieved 2008-07-19. Gonzalez gives as the sources for the memorial article, the following: Weber, H: "Leopold Kronecker", Jahresberichte der Deutschen Mathematiker Vereinigung, vol ii (1893), pp. 5-31. Cf. page 19. See also Mathematische Annalen vol. xliii (1893), pp. 1-25.

pbs.org

"Math: Discovered, Invented, or Both?". pbs.org. 13 April 2015. Archived from the original on 28 March 2018. Retrieved 28 March 2018.

philosophynow.org

Pigliucci, Massimo (2014). "Are There 'Other' Ways of Knowing?". Philosophy Now. Archived from the original on May 13, 2020. Retrieved April 6, 2020.
"Philosophy Now: "Mathematical Knowledge: A dilemma"". Archived from the original on February 7, 2011.

purdue.edu

cs.purdue.edu

Wagstaff, Samuel S. Jr. (2021). "History of Integer Factoring" (PDF). In Bos, Joppe W.; Stam, Martijn (eds.). Computational Cryptography, Algorithmic Aspects of Cryptography, A Tribute to AKL. London Mathematical Society Lecture Notes Series 469. Cambridge University Press. pp. 41–77. Archived (PDF) from the original on November 20, 2022. Retrieved November 20, 2022.

rdcu.be

Franklin, James (2022). "Mathematics as a science of non-abstract reality: Aristotelian realist philosophies of mathematics". Foundations of Science. 27 (2): 327–344. doi:10.1007/s10699-021-09786-1. S2CID 233658181. Retrieved 30 June 2021.

researchgate.net

Hennig, Christian (2010). "Mathematical Models and Reality: A Constructivist Perspective". Foundations of Science. 15: 29–48. doi:10.1007/s10699-009-9167-x. S2CID 6229200. Retrieved November 17, 2022.

semanticscholar.org

api.semanticscholar.org

See White, L. (1947). "The locus of mathematical reality: An anthropological footnote". Philosophy of Science. 14 (4): 289–303. doi:10.1086/286957. S2CID 119887253. 189303; also in Newman, J. R. (1956). The World of Mathematics. Vol. 4. New York: Simon and Schuster. pp. 2348–2364.
Hamami, Yacin (June 2022). "Mathematical Rigor and Proof" (PDF). The Review of Symbolic Logic. 15 (2): 409–449. doi:10.1017/S1755020319000443. S2CID 209980693. Archived (PDF) from the original on December 5, 2022. Retrieved November 21, 2022.
Ferreirós, José (2001). "The Road to Modern Logic—An Interpretation" (PDF). Bulletin of Symbolic Logic. 7 (4): 441–484. doi:10.2307/2687794. hdl:11441/38373. JSTOR 2687794. S2CID 43258676. Archived (PDF) from the original on February 2, 2023. Retrieved November 11, 2022.
Davis, Jon D.; McDuffie, Amy Roth; Drake, Corey; Seiwell, Amanda L. (2019). "Teachers' perceptions of the official curriculum: Problem solving and rigor". International Journal of Educational Research. 93: 91–100. doi:10.1016/j.ijer.2018.10.002. S2CID 149753721.
Hennig, Christian (2010). "Mathematical Models and Reality: A Constructivist Perspective". Foundations of Science. 15: 29–48. doi:10.1007/s10699-009-9167-x. S2CID 6229200. Retrieved November 17, 2022.
Wigner, Eugene (1960). "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". Communications on Pure and Applied Mathematics. 13 (1): 1–14. Bibcode:1960CPAM...13....1W. doi:10.1002/cpa.3160130102. S2CID 6112252. Archived from the original on February 28, 2011.
S, F. (January 1941). "A Mathematician's Apology". Nature. 147 (3714): 3–5. Bibcode:1941Natur.147....3S. doi:10.1038/147003a0. S2CID 4212863.
Tegmark, Max (February 2008). "The Mathematical Universe". Foundations of Physics. 38 (2): 101–150. arXiv:0704.0646. Bibcode:2008FoPh...38..101T. doi:10.1007/s10701-007-9186-9. S2CID 9890455.
Franklin, James (2022). "Mathematics as a science of non-abstract reality: Aristotelian realist philosophies of mathematics". Foundations of Science. 27 (2): 327–344. doi:10.1007/s10699-021-09786-1. S2CID 233658181. Retrieved 30 June 2021.
Ganesalingam, Mohan (2013). The Language of Mathematics: A Linguistic and Philosophical Investigation. Lecture Notes in Computer Science. Vol. 7805. Springer. doi:10.1007/978-3-642-37012-0. ISBN 978-3-642-37011-3. S2CID 14260721.

st-andrews.ac.uk

mathshistory.st-andrews.ac.uk

"Curves: Ellipse". MacTutor. School of Mathematics and Statistics, University of St Andrews, Scotland. Archived from the original on October 14, 2022. Retrieved November 20, 2022.

stanford.edu

plato.stanford.edu

Horsten, Leon. "Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)". Stanford Encyclopedia of Philosophy. Stanford University.
Balaguer, Mark (2016). "Platonism in Metaphysics". In Zalta, Edward N. (ed.). The Stanford Encyclopedia of Philosophy (Spring 2016 ed.). Metaphysics Research Lab, Stanford University. Archived from the original on January 30, 2022. Retrieved April 2, 2022.
Alexander Paseau; Fabian Pregel (2023). Deductivism in the Philosophy of Mathematics. Metaphysics Research Lab, Stanford University.
Zach, Richard (2019), "Hilbert's Program", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Summer 2019 ed.), Metaphysics Research Lab, Stanford University, archived from the original on 2022-02-08, retrieved 2019-05-25
"Platonism in the Philosophy of Mathematics". Standard Encyclopaedia of Philosophy. Metaphysics Research Lab, Stanford University. 2018. Archived from the original on 2010-12-04. Retrieved 2011-02-13.

thewire.in

Mukunth, Vasudevan (September 10, 2015). "Beyond the Surface of Einstein's Relativity Lay a Chimerical Geometry". The Wire. Archived from the original on November 20, 2022. Retrieved November 20, 2022.

unsw.edu.au

web.maths.unsw.edu.au

Franklin, James (2014). An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure (PDF). Palgrave Macmillan. ISBN 9781137400727.

us.es

idus.us.es

Ferreirós, José (2001). "The Road to Modern Logic—An Interpretation" (PDF). Bulletin of Symbolic Logic. 7 (4): 441–484. doi:10.2307/2687794. hdl:11441/38373. JSTOR 2687794. S2CID 43258676. Archived (PDF) from the original on February 2, 2023. Retrieved November 11, 2022.

uva.nl

seop.illc.uva.nl

Frigg, Roman; Hartmann, Stephan (February 4, 2020). "Models in Science". Stanford Encyclopedia of Philosophy. Archived from the original on November 17, 2022. Retrieved November 17, 2022.

web.archive.org

Balaguer, Mark (2016). "Platonism in Metaphysics". In Zalta, Edward N. (ed.). The Stanford Encyclopedia of Philosophy (Spring 2016 ed.). Metaphysics Research Lab, Stanford University. Archived from the original on January 30, 2022. Retrieved April 2, 2022.
Dorato, Mauro (2005). "Why are laws mathematical?" (PDF). The Software of the Universe, An Introduction to the History and Philosophy of Laws of Nature. Ashgate. pp. 31–66. ISBN 978-0-7546-3994-7. Archived (PDF) from the original on August 17, 2023. Retrieved December 5, 2022.
Hamami, Yacin (June 2022). "Mathematical Rigor and Proof" (PDF). The Review of Symbolic Logic. 15 (2): 409–449. doi:10.1017/S1755020319000443. S2CID 209980693. Archived (PDF) from the original on December 5, 2022. Retrieved November 21, 2022.
Ferreirós, José (2001). "The Road to Modern Logic—An Interpretation" (PDF). Bulletin of Symbolic Logic. 7 (4): 441–484. doi:10.2307/2687794. hdl:11441/38373. JSTOR 2687794. S2CID 43258676. Archived (PDF) from the original on February 2, 2023. Retrieved November 11, 2022.
Frigg, Roman; Hartmann, Stephan (February 4, 2020). "Models in Science". Stanford Encyclopedia of Philosophy. Archived from the original on November 17, 2022. Retrieved November 17, 2022.
"The science checklist applied: Mathematics". Understanding Science. University of California, Berkeley. Archived from the original on October 27, 2019. Retrieved October 27, 2019.
Pigliucci, Massimo (2014). "Are There 'Other' Ways of Knowing?". Philosophy Now. Archived from the original on May 13, 2020. Retrieved April 6, 2020.
Wigner, Eugene (1960). "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". Communications on Pure and Applied Mathematics. 13 (1): 1–14. Bibcode:1960CPAM...13....1W. doi:10.1002/cpa.3160130102. S2CID 6112252. Archived from the original on February 28, 2011.
Wagstaff, Samuel S. Jr. (2021). "History of Integer Factoring" (PDF). In Bos, Joppe W.; Stam, Martijn (eds.). Computational Cryptography, Algorithmic Aspects of Cryptography, A Tribute to AKL. London Mathematical Society Lecture Notes Series 469. Cambridge University Press. pp. 41–77. Archived (PDF) from the original on November 20, 2022. Retrieved November 20, 2022.
"Curves: Ellipse". MacTutor. School of Mathematics and Statistics, University of St Andrews, Scotland. Archived from the original on October 14, 2022. Retrieved November 20, 2022.
Mukunth, Vasudevan (September 10, 2015). "Beyond the Surface of Einstein's Relativity Lay a Chimerical Geometry". The Wire. Archived from the original on November 20, 2022. Retrieved November 20, 2022.
"Is mathematics discovered or invented?". University of Exeter. Archived from the original on 27 July 2018. Retrieved 28 March 2018.
"Math: Discovered, Invented, or Both?". pbs.org. 13 April 2015. Archived from the original on 28 March 2018. Retrieved 28 March 2018.
"A Mathematician's Apology Quotes by G.H. Hardy". Archived from the original on 2021-05-08. Retrieved 2020-07-20.
Zach, Richard (2019), "Hilbert's Program", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Summer 2019 ed.), Metaphysics Research Lab, Stanford University, archived from the original on 2022-02-08, retrieved 2019-05-25
From an 1886 lecture at the 'Berliner Naturforscher-Versammlung', according to H. M. Weber's memorial article, as quoted and translated in Gonzalez Cabillon, Julio (2000-02-03). "FOM: What were Kronecker's f.o.m.?". Archived from the original on 2007-10-09. Retrieved 2008-07-19. Gonzalez gives as the sources for the memorial article, the following: Weber, H: "Leopold Kronecker", Jahresberichte der Deutschen Mathematiker Vereinigung, vol ii (1893), pp. 5-31. Cf. page 19. See also Mathematische Annalen vol. xliii (1893), pp. 1-25.
Ernest, Paul. "Is Mathematics Discovered or Invented?". University of Exeter. Archived from the original on 2008-04-05. Retrieved 2008-12-26.
Hersh, Reuben (February 10, 1997). "What Kind of a Thing is a Number?" (Interview). Interviewed by John Brockman. Edge Foundation. Archived from the original on May 16, 2008. Retrieved 2008-12-26.
"Humanism and Mathematics Education". Math Forum. Humanistic Mathematics Network Journal. Archived from the original on 2008-07-24. Retrieved 2008-12-26.
Yablo, S. (November 8, 1998). "A Paradox of Existence". Archived from the original on January 7, 2020. Retrieved August 26, 2019.
"Philosophy Now: "Mathematical Knowledge: A dilemma"". Archived from the original on February 7, 2011.
"Platonism in the Philosophy of Mathematics". Standard Encyclopaedia of Philosophy. Metaphysics Research Lab, Stanford University. 2018. Archived from the original on 2010-12-04. Retrieved 2011-02-13.
Review Archived 2011-05-14 at the Wayback Machine of The Emperor's New Mind.

wikisource.org

en.wikisource.org

Gregory, Frank Hutson (1996) "Arithmetic and Reality: A Development of Popper's Ideas". City University of Hong Kong. Republished in Philosophy of Mathematics Education Journal No. 26 (December 2011)

worldcat.org

search.worldcat.org

Borel, Armand (1983). "Mathematics: Art and Science". The Mathematical Intelligencer. 5 (4). Springer: 9–17. doi:10.4171/news/103/8. ISSN 1027-488X.
Borel, Armand (1983). "Mathematics: Art and Science". The Mathematical Intelligencer. 5 (4). Springer: 9–17. doi:10.4171/news/103/8. ISSN 1027-488X.

yacinhamami.com

Hamami, Yacin (June 2022). "Mathematical Rigor and Proof" (PDF). The Review of Symbolic Logic. 15 (2): 409–449. doi:10.1017/S1755020319000443. S2CID 209980693. Archived (PDF) from the original on December 5, 2022. Retrieved November 21, 2022.