Visualization as an Intuitive Process in Mathematical Practice

In the field of the philosophy of mathematics, in recent years, there has been a resurgence of two processes: intuition and visualization. History has shown us that great mathematicians in their inventions have used these processes to arrive at their most brilliant proofs, theories and concepts. In...

Full description

Saved in:
Bibliographic Details
Published inConatus - journal of philosophy Vol. 9; no. 2; pp. 195 - 221
Main Author Peña-Páez, Lina María
Format Journal Article
LanguageEnglish
Published The NKUA Applied Philosophy Research Laboratory 29.12.2024
Subjects
dynamic process
intuition
mathematical practice
visualization
Online AccessGet full text
ISSN2653-9373
2459-3842
DOI10.12681/cjp.34917

Cover

Abstract In the field of the philosophy of mathematics, in recent years, there has been a resurgence of two processes: intuition and visualization. History has shown us that great mathematicians in their inventions have used these processes to arrive at their most brilliant proofs, theories and concepts. In this article, we want to defend that both intuition and visualization can be understood as processes that contribute to the development of mathematical knowledge as evidenced in the history of mathematics. Like intuition, visualization does not have a definition, and its role has become more prominent both in pure mathematics and in educational research. For us, both visualization and intuition are processes that start from the real world of those who “intuit” or “visualize,” require experience and knowledge of concepts and theories (the more expertise in the subject, the more profound the results will be) and must, in the end, be validated by the specialized academic community. In this article, we defend the importance of visualization in mathematical practice and its role in the advances of great scientists (Euclid, Euler, Galileo, Descartes, Newton, Maxwell, Riemann, Einstein, Feynman, among others) as an alternative and valuable way to symbolic thinking, which has “reigned” in the academic and scientific community.
AbstractList In the field of the philosophy of mathematics, in recent years, there has been a resurgence of two processes: intuition and visualization. History has shown us that great mathematicians in their inventions have used these processes to arrive at their most brilliant proofs, theories and concepts. In this article, we want to defend that both intuition and visualization can be understood as processes that contribute to the development of mathematical knowledge as evidenced in the history of mathematics. Like intuition, visualization does not have a definition, and its role has become more prominent both in pure mathematics and in educational research. For us, both visualization and intuition are processes that start from the real world of those who “intuit” or “visualize,” require experience and knowledge of concepts and theories (the more expertise in the subject, the more profound the results will be) and must, in the end, be validated by the specialized academic community. In this article, we defend the importance of visualization in mathematical practice and its role in the advances of great scientists (Euclid, Euler, Galileo, Descartes, Newton, Maxwell, Riemann, Einstein, Feynman, among others) as an alternative and valuable way to symbolic thinking, which has “reigned” in the academic and scientific community.
Author Peña-Páez, Lina María
Author_xml – sequence: 1
  givenname: Lina María
  orcidid: 0000-0001-7452-7014
  surname: Peña-Páez
  fullname: Peña-Páez, Lina María
BookMark eNo9kMtKAzEUhoNUsNZufIJZC1OTyW2yEaR4KVR0oW7DyU1TpjMlmQr69IZWXJ2fn8PHOd85mvRD7xG6JHhBGtGSa7vZLShTRJ6gacO4qmnLmknJgtNaUUnP0DznaDBjklLWNlN08x7zHrr4A2Mc-gpyBX216sd9HOOXr17SYH3OVeyrJxg__basWehKD7Ykf4FOA3TZz__mDL3d370uH-v188NqebuubYOlrBuuMDMeQoONY5gwBS0VyhPghlvXChmotZwEJZxgHso7gXvuHTaMKu_oDK2OXDfARu9S3EL61gNEfSiG9KEhlYM6rwXHRjoQirSSCWWNFQBggUMQ2GFZWFdHlk1DzsmHfx7B-iBSF5H6IJL-At3WZ9o
Cites_doi 10.13189/ujer.2019.070101
10.1007/BF02652763
10.1007/978-3-030-60537-7_8
10.1023/A:1024312321077
10.1017/CBO9781139136419.010
10.1007/978-94-009-2293-8
10.1007/s11245-009-9062-7
10.1007/978-94-6091-924-4_7
10.1093/philmat/nkz002
10.1007/1-4020-3335-4_8
10.1016/S0732-3123(99)00027-9
10.1007/s11858-020-01159-5
10.1016/j.cogpsych.2018.12.002
10.1007/1-4020-3335-4_2
10.2478/kjps-2019-0007
10.1007/0-306-47237-6
10.1080/10494820.2019.1683588
10.1007/s11245-009-9064-5
10.1093/acprof:oso/9780199296453.001.0001
10.1007/978-3-030-15130-0
10.15304/ag.39.2.6299
10.1007/978-94-6091-924-4
10.1007/s11245-009-9063-6
10.4013/fsu.2021.222.06
10.1007/s11245-009-9065-4
10.1007/978-94-6091-924-4_8
10.1007/978-90-481-8816-1
ContentType Journal Article
DBID AAYXX
CITATION
DOA
DOI 10.12681/cjp.34917
DatabaseName CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList CrossRef
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
DeliveryMethod fulltext_linktorsrc
EISSN 2459-3842
EndPage 221
ExternalDocumentID oai_doaj_org_article_650b7da69187469cbc6aaaca5af60d07
10_12681_cjp_34917
GroupedDBID AAYXX
ABDBF
ACUHS
ALMA_UNASSIGNED_HOLDINGS
CITATION
EN8
ESX
GROUPED_DOAJ
ID FETCH-LOGICAL-c2077-25904beaf20bd40149a8369e1a5b5cd867f3cc51f96d64ea126f5e5ed0b439ed3
IEDL.DBID DOA
ISSN 2653-9373
IngestDate Wed Aug 27 01:28:34 EDT 2025
Tue Jul 01 01:27:07 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 2
Language English
License http://creativecommons.org/licenses/by-nc/4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c2077-25904beaf20bd40149a8369e1a5b5cd867f3cc51f96d64ea126f5e5ed0b439ed3
ORCID 0000-0001-7452-7014
OpenAccessLink https://doaj.org/article/650b7da69187469cbc6aaaca5af60d07
PageCount 27
ParticipantIDs doaj_primary_oai_doaj_org_article_650b7da69187469cbc6aaaca5af60d07
crossref_primary_10_12681_cjp_34917
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2024-12-29
PublicationDateYYYYMMDD 2024-12-29
PublicationDate_xml – month: 12
  year: 2024
  text: 2024-12-29
  day: 29
PublicationDecade 2020
PublicationTitle Conatus - journal of philosophy
PublicationYear 2024
Publisher The NKUA Applied Philosophy Research Laboratory
Publisher_xml – name: The NKUA Applied Philosophy Research Laboratory
References 680461
680460
680441
680463
680440
680462
680443
680465
680442
680464
680423
680445
680467
680444
680466
680425
680447
680424
680446
680468
680427
680449
680426
680448
680429
680428
680450
680430
680452
680451
680432
680454
680431
680453
680434
680456
680433
680455
680436
680458
680435
680457
680438
680437
680459
680439
References_xml – ident: 680468
  doi: 10.13189/ujer.2019.070101
– ident: 680447
– ident: 680446
  doi: 10.1007/BF02652763
– ident: 680423
  doi: 10.1007/978-3-030-60537-7_8
– ident: 680426
– ident: 680462
– ident: 680424
  doi: 10.1023/A:1024312321077
– ident: 680433
  doi: 10.1017/CBO9781139136419.010
– ident: 680460
– ident: 680467
  doi: 10.1007/978-94-009-2293-8
– ident: 680441
– ident: 680445
  doi: 10.1007/s11245-009-9062-7
– ident: 680429
  doi: 10.1007/978-94-6091-924-4_7
– ident: 680432
  doi: 10.1093/philmat/nkz002
– ident: 680466
  doi: 10.1007/1-4020-3335-4_8
– ident: 680428
  doi: 10.1016/S0732-3123(99)00027-9
– ident: 680443
  doi: 10.1007/s11858-020-01159-5
– ident: 680455
– ident: 680459
– ident: 680444
  doi: 10.1016/j.cogpsych.2018.12.002
– ident: 680452
  doi: 10.1007/1-4020-3335-4_2
– ident: 680451
– ident: 680427
  doi: 10.2478/kjps-2019-0007
– ident: 680430
– ident: 680436
– ident: 680434
– ident: 680435
  doi: 10.1007/0-306-47237-6
– ident: 680448
  doi: 10.1080/10494820.2019.1683588
– ident: 680438
  doi: 10.1007/s11245-009-9064-5
– ident: 680453
  doi: 10.1093/acprof:oso/9780199296453.001.0001
– ident: 680463
  doi: 10.1007/978-3-030-15130-0
– ident: 680456
  doi: 10.15304/ag.39.2.6299
– ident: 680454
  doi: 10.1007/978-94-6091-924-4
– ident: 680442
– ident: 680461
– ident: 680425
– ident: 680440
– ident: 680449
  doi: 10.1007/s11245-009-9063-6
– ident: 680437
– ident: 680457
  doi: 10.4013/fsu.2021.222.06
– ident: 680439
– ident: 680465
  doi: 10.1007/s11245-009-9065-4
– ident: 680450
– ident: 680464
  doi: 10.1007/978-94-6091-924-4_8
– ident: 680431
– ident: 680458
  doi: 10.1007/978-90-481-8816-1
SSID ssib044733482
ssj0002910498
Score 2.278603
Snippet In the field of the philosophy of mathematics, in recent years, there has been a resurgence of two processes: intuition and visualization. History has shown us...
SourceID doaj
crossref
SourceType Open Website
Index Database
StartPage 195
SubjectTerms dynamic process
intuition
mathematical practice
visualization
Title Visualization as an Intuitive Process in Mathematical Practice
URI https://doaj.org/article/650b7da69187469cbc6aaaca5af60d07
Volume 9
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07SwNBEF4klY0oKsYXC9oeudvX3TaCSiQKEQsj6Y6dfUAsTjGx9bc7c3fGdDY2VyzHsDuz7DcD833D2GX0yck8hUwFDRlpYWZQmpBJqBSEygoAYiNPH81kph7mer4x6ot6wjp54M5xI8wgoAzOWBoeZ6wHb5xz3mmXTB46Hjli3kYxhTdJqVKuVVvoTRaIiqodjCuMlhlisuy1SoWpipF_xeJf2XZq2S86bYj4t2hzt8t2-jSRX3fb22NbsdlnVy-LJXEgO-Ykd0vuGn6PoNH2__C-558vGj5di7GikaeeCHXAZnfj59tJ1s8_yLzISxJQsLmC6JLIISiqZVwljY2F00CcflMm6b0ukjXBqOjwLElHHUMOmGbEIA_ZoHlr4hHjqigigRQAwnF0AtCozyFFJSNUWg3Zxc-56_dO5qKm8oC8U6N36tY7Q3ZDLln_QdLU7QIGrO4DVv8VsOP_MHLCtgVmF9RXIuwpG6w-PuMZZgcrOG8vAn6nX-NvX-W3_g
linkProvider Directory of Open Access Journals
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Visualization+as+an+Intuitive+Process+in+Mathematical+Practice&rft.jtitle=Conatus+-+journal+of+philosophy&rft.au=Pe%C3%B1a-P%C3%A1ez%2C+Lina+Mar%C3%ADa&rft.date=2024-12-29&rft.issn=2653-9373&rft.eissn=2459-3842&rft.volume=9&rft.issue=2&rft.spage=195&rft.epage=221&rft_id=info:doi/10.12681%2Fcjp.34917&rft.externalDBID=n%2Fa&rft.externalDocID=10_12681_cjp_34917
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2653-9373&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2653-9373&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2653-9373&client=summon