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Raman Sundström, Manya

Open this publication in new window or tab >>Mathematical fit: a case study### Raman-Sundström, Manya

### Öhman, Lars-Daniel

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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Available from: 2016-07-21 Created: 2016-07-21 Last updated: 2018-11-01Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

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.

Open this publication in new window or tab >>Young children's aesthetic development in the context of mathematical explanation### Levenson, Esther

### Raman Sundström, Manya

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 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]

##### 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
#####

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Available from: 2019-09-23 Created: 2019-09-23 Last updated: 2019-09-23Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.

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.

Open this publication in new window or tab >>An Exercise on Limits### Raman Sundström, Manya

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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##### Note

Umeå University, Faculty of Science and Technology.

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

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 approvedOpen this publication in new window or tab >>The Nature and Experience of Mathematical Beauty### Raman-Sundström, Manya

### Öhman, Lars-Daniel

### Sinclair, Nathalie

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 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 ()
#####

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##### Projects

Karriärbidrag
Available from: 2016-02-01 Created: 2016-02-01 Last updated: 2018-06-07Bibliographically approved

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Faculty of Education, Simon Fraser University, CANADA.

Open this publication in new window or tab >>The Notion of Fit as a Mathematical Value### Raman Sundström, Manya

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 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]

##### 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:

#####

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Available from: 2016-08-23 Created: 2016-08-23 Last updated: 2018-06-07Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.

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.

Open this publication in new window or tab >>The Notion of Fit as a Mathematical Value### Raman-Sundström, Manya

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 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
#####

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Available from: 2017-08-31 Created: 2017-08-31 Last updated: 2018-06-09Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.

Open this publication in new window or tab >>A pedagogical history of compactness### Raman-Sundström, Manya

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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Available from: 2015-08-03 Created: 2015-08-03 Last updated: 2018-06-07Bibliographically approved

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).

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.

Open this publication in new window or tab >>Mathematical fit: A first approximation### Raman Sundström, Manya

### Öhman, Lars-Daniel

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 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]

##### 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.
#####

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Available from: 2019-09-18 Created: 2019-09-18 Last updated: 2019-09-18Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

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.

Open this publication in new window or tab >>Seduced by the beauty of mathematics### Sundstrom, Manya Raman

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 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 ()
#####

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Available from: 2015-03-18 Created: 2015-03-16 Last updated: 2018-06-07Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education.

Open this publication in new window or tab >>Beauty as fit: A metaphor in mathematics?### Raman Sundström, Manya

### Öhman, Lars-Daniel

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2013 (English)In: Research in Mathematics Education, Vol. 15, no 2, p. 199-200Article in journal (Refereed) Published
##### Abstract [en]

##### 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)
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##### Projects

Karriärbidrag on Beauty in Mathematics, Umeå University
Available from: 2015-01-15 Created: 2015-01-15 Last updated: 2018-06-07Bibliographically approved

Umeå University, Faculty of Science and Technology.

Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

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.