umu.sePublications
Change search
Link to record
Permanent link

Direct link
BETA
Raman Sundström, Manya
Alternative names
Publications (10 of 25) Show all publications
Raman-Sundström, M. & Öhman, L.-D. (2018). Mathematical fit: a case study. Philosophia mathematica, 26(2), 184-210
Open this publication in new window or tab >>Mathematical fit: a case study
2018 (English)In: Philosophia mathematica, ISSN 0031-8019, E-ISSN 1744-6406, Vol. 26, no 2, p. 184-210Article in journal (Refereed) Published
Abstract [en]

Mathematicians routinely pass judgments on mathematical proofs. A proof might be elegant, cumbersome, beautiful, or awkward. Perhaps the highest praise is that a proof is right, that is that the proof fits the theoremin an optimal way. It is also common to judge that a proof fits better than another, or that a proof does not fit a theorem at all. This paper attempts to clarify the notion of mathematical fit. We suggest six criteria that distinguish proofs as being more or less fitting, and provide examples from several different mathematical fields.

Place, publisher, year, edition, pages
Cary: Oxford University Press, 2018
Keywords
Fit, aesthetics, explanation
National Category
Philosophy Mathematics
Research subject
Aesthetics; Mathematics
Identifiers
urn:nbn:se:umu:diva-124162 (URN)10.1093/philmat/nkw015 (DOI)000439703300003 ()2-s2.0-85053033011 (Scopus ID)
Available from: 2016-07-21 Created: 2016-07-21 Last updated: 2018-11-01Bibliographically approved
diva2:1353546
Open this publication in new window or tab >>Young children's aesthetic development in the context of mathematical explanation
2017 (English)In: Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10) / [ed] Dooley, T Gueudet, G, Dublin: Dublin City University , 2017, p. 1861-1868Conference paper, Published paper (Refereed)
Abstract [en]

Mathematicians routinely report that beauty is both a reward and a motivation for the work they do. However, how and to what extent children can appreciate mathematical beauty is an open question. This exploratory study looks at young children (ages 6-12, with a focus on the younger years) as they evaluate different explanations of claims about even numbers and triangular numbers. While our results are fairly speculative, we provide case studies which illustrate possible kinds of aesthetic reactions, and some of the factors which might impact on those reactions.

Place, publisher, year, edition, pages
Dublin: Dublin City University, 2017
Keywords
Aesthetics, explanation, even numbers, triangular numbers, affect
National Category
Learning
Identifiers
urn:nbn:se:umu:diva-163254 (URN)000467053302067 ()978-1-873769-73-7 (ISBN)
Conference
10th Congress of European Research in Mathematics Education, Dublin, February 1-5, 2017
Available from: 2019-09-23 Created: 2019-09-23 Last updated: 2019-09-23Bibliographically approved
diva2:953291
Open this publication in new window or tab >>An Exercise on Limits
2016 (English)In: Journal of Humanistic Mathematics, ISSN 2159-8118, E-ISSN 2159-8118, Vol. 6, no 2, p. 1Article in journal (Other (popular science, discussion, etc.)) [Artistic work] Published
Abstract [en]

A poem about different kinds of limits, not all mathematical.

Publisher
p. 1
National Category
Other Mathematics Literary Composition
Research subject
Aesthetics
Identifiers
urn:nbn:se:umu:diva-124591 (URN)10.5642/jhummath.201602.20 (DOI)
Note

DOI för artikeln felaktigt angiven som 10.5642/jhummath.201602.10. Korrekt DOI är 10.5642/jhummath.201602.20

Available from: 2016-08-17 Created: 2016-08-17 Last updated: 2018-06-07Bibliographically approved
Raman-Sundström, M., Öhman, L.-D. & Sinclair, N. (2016). The Nature and Experience of Mathematical Beauty (1ed.). Journal of Humanistic Mathematics, 6(1), 3-7
Open this publication in new window or tab >>The Nature and Experience of Mathematical Beauty
2016 (English)In: Journal of Humanistic Mathematics, ISSN 2159-8118, E-ISSN 2159-8118, Vol. 6, no 1, p. 3-7Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Claremont, CA, USA: , 2016 Edition: 1
National Category
Philosophy Other Mathematics
Research subject
Mathematics; Aesthetics
Identifiers
urn:nbn:se:umu:diva-115217 (URN)10.5642/jhummath.201601.03 (DOI)000388610000002 ()
Projects
Karriärbidrag
Available from: 2016-02-01 Created: 2016-02-01 Last updated: 2018-06-07Bibliographically approved
diva2:954671
Open this publication in new window or tab >>The Notion of Fit as a Mathematical Value
2016 (English)In: Mathematical Cultures: The London Meetings 2012-2014 / [ed] Brendan Larvor, Basel: Birkhäuser Verlag, 2016, p. 271-285Chapter in book (Refereed)
Abstract [en]

Fit, or the lack of it, might occur in a large number of different settings, from visual art, to music, to relationships between people, and so on. This paper explores the metaphor of beauty as fit as it occurs in mathematics. The central claim is that, be it instantiated in the relationship of a type of tree to its natural shape or of a particular proof to a theorem, fit is what brings about the feeling that that tree or that theorem is beautiful. The greater the degree of fit, the greater our sense of beauty (given that we have the requisite understanding to appreciate the fit.) This claim will not be fully defended, but we will set up some ground work for doing so. In particular, the paper will illustrate two distinct types of fit in mathematics via contrasting examples of proofs typically held to be beautiful or not beautiful.

Place, publisher, year, edition, pages
Basel: Birkhäuser Verlag, 2016
Series
Trends in the History of Science, ISSN 2297-2951
National Category
Mathematics
Research subject
Aesthetics
Identifiers
urn:nbn:se:umu:diva-124742 (URN)10.1007/978-3-319-28582-5 (DOI)978-3-319-28582-5 (ISBN)
External cooperation:
Available from: 2016-08-23 Created: 2016-08-23 Last updated: 2018-06-07Bibliographically approved
Raman-Sundström, M. (2016). The Notion of Fit as a Mathematical Value. In: Larvor, B (Ed.), MATHEMATICAL CULTURES: . Paper presented at 2nd Meeting on Mathematical Cultures, SEP 17-19, 2013, London, ENGLAND (pp. 271-285). BIRKHAUSER VERLAG AG
Open this publication in new window or tab >>The Notion of Fit as a Mathematical Value
2016 (English)In: MATHEMATICAL CULTURES / [ed] Larvor, B, BIRKHAUSER VERLAG AG , 2016, p. 271-285Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
BIRKHAUSER VERLAG AG, 2016
Series
Trends in the History of Science, ISSN 2297-2951
National Category
Other Mathematics
Identifiers
urn:nbn:se:umu:diva-138635 (URN)10.1007/978-3-319-28582-5_16 (DOI)000391223500016 ()978-3-319-28582-5 (ISBN)978-3-319-28580-1 (ISBN)
Conference
2nd Meeting on Mathematical Cultures, SEP 17-19, 2013, London, ENGLAND
Available from: 2017-08-31 Created: 2017-08-31 Last updated: 2018-06-09Bibliographically approved
Raman-Sundström, M. (2015). A pedagogical history of compactness. The American mathematical monthly, 122(7), 619-635
Open this publication in new window or tab >>A pedagogical history of compactness
2015 (English)In: The American mathematical monthly, ISSN 0002-9890, E-ISSN 1930-0972, Vol. 122, no 7, p. 619-635Article in journal (Refereed) Published
Abstract [en]

Compactness is a central notion in advanced mathematics, but we often teach the concept without much historical motivation.  This paper fills in many of the gaps left by the standard textbook treatment, including what motivated the definition, how did the definition evolve, and how can compactness be expressed in terms of nets and filters.

Keywords
Compact, Compactness, History of Analysis, History of Topology
National Category
Other Mathematics
Research subject
Mathematics; didactics of mathematics; History Of Sciences and Ideas
Identifiers
urn:nbn:se:umu:diva-106686 (URN)10.4169/amer.math.monthly.122.7.619 (DOI)000370068500001 ()
Available from: 2015-08-03 Created: 2015-08-03 Last updated: 2018-06-07Bibliographically approved
Raman Sundström, M. & Öhman, L.-D. (2015). Mathematical fit: A first approximation. In: Krainer, K Vondrova, N (Ed.), Proceedings of the ninth conference of the Euorpean Society for research in Mathermatics education (CERME9): . Paper presented at 9th Congress of European Research in Mathematics Education, Prague, February 4-8, 2015. (pp. 185-191). Prague: Charles University
Open this publication in new window or tab >>Mathematical fit: A first approximation
2015 (English)In: Proceedings of the ninth conference of the Euorpean Society for research in Mathermatics education (CERME9) / [ed] Krainer, K Vondrova, N, Prague: Charles University , 2015, p. 185-191Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

We discuss here the notion of mathematical fit, a concept that might relate to mathematical explanation and mathematical beauty. We specify two kinds of fit a proof can have, intrinsic and extrinsic, and provide characteristics that help distinguish different proofs of the same theorem.

Place, publisher, year, edition, pages
Prague: Charles University, 2015
Keywords
Proof, fit, explanation, beauty, aesthetics
National Category
Mathematics Learning
Identifiers
urn:nbn:se:umu:diva-163260 (URN)000466853900021 ()978-80-7290-844-8 (ISBN)
Conference
9th Congress of European Research in Mathematics Education, Prague, February 4-8, 2015.
Available from: 2019-09-18 Created: 2019-09-18 Last updated: 2019-09-18Bibliographically approved
Sundstrom, M. R. (2015). Seduced by the beauty of mathematics. New scientist (1971), 225(3006), 26-27
Open this publication in new window or tab >>Seduced by the beauty of mathematics
2015 (English)In: New scientist (1971), ISSN 0262-4079, Vol. 225, no 3006, p. 26-27Article in journal, Editorial material (Other academic) Published
National Category
Mathematics
Identifiers
urn:nbn:se:umu:diva-100969 (URN)000349517800017 ()
Available from: 2015-03-18 Created: 2015-03-16 Last updated: 2018-06-07Bibliographically approved
Raman Sundström, M. & Öhman, L.-D. (2013). Beauty as fit: A metaphor in mathematics?. Research in Mathematics Education, 15(2), 199-200
Open this publication in new window or tab >>Beauty as fit: A metaphor in mathematics?
2013 (English)In: Research in Mathematics Education, Vol. 15, no 2, p. 199-200Article in journal (Refereed) Published
Abstract [en]

Beauty, which plays a central role in the practice of mathematics, is almost absent in discussions of school mathematics. This is problematic, because students will decide whether or not to continue their studies inmathematics without having an accurate picture of what the subject is about. In order to have a discussion about how to introduce beauty into the school mathematicscurriculum, we need to have a clear idea about what beauty means. That is the aim ofthis study, with a focus on characterising beauty in mathematical proof.

Keywords
Beauty, aesthetics, mathematics
National Category
Other Mathematics Philosophy
Research subject
Aesthetics
Identifiers
urn:nbn:se:umu:diva-98062 (URN)10.1080/14794802.2013.797740 (DOI)
Projects
Karriärbidrag on Beauty in Mathematics, Umeå University
Available from: 2015-01-15 Created: 2015-01-15 Last updated: 2018-06-07Bibliographically approved
Organisations

Search in DiVA

Show all publications