Galois Connections: Mathematics, Art, and Archives

Évariste Galois (1811–1832) has been increasingly recognised as an important mathematician who despite his short life developed mathematical ideas that today have led to applications in computer science (such as Galois connections) and elsewhere. Some of Galois’ mathematics can be visualised in interesting and even artistic ways, aided using software. In addition, a significant corpus of the historical documentation on Galois and his family (including his brother Alfred Galois, who was an artist), can now be accessed online as a growing number of institutional archives digitise their collections. This paper introduces some of the mathematics of Galois, ways in which it can be visualised, and also considers the issues and new opportunities with respect to visualising information on Galois and his family (including the connections between them). Although the story of Galois and his close relations can be seen as one of tragedy with lives cut short, from a historical viewpoint Évariste Galois’ contribution to humankind has been a triumph.

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Contributors

Jonathan P. Bowen: http://www.jpbowen.com

Tula Giannini: http://mysite.pratt.edu/~giannini/

Conference

Publication date: July 2015

Publication date (Print): July 2015

Pages: 176-183

Affiliations

[0001]Birmingham City University

School of Computing, Telecommunications & Networking

Birmingham, UK

[0002]Pratt Institute

School of Information & Library Science

New York, USA

Article

DOI: 10.14236/ewic/eva2015.18

SO-VID: 48e3415d-398c-4983-a16d-9f67c08df7f1

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This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Conference name: Electronic Visualisation and the Arts (EVA 2015)

Conference acronym: EVA

Conference number:

Conference location: London, UK

Conference date: 7 & 9 July 2015

Conference sponsor: Electronic Workshops in Computing (eWiC)

Conference theme: Electronic Visualisation and the Arts

History

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1477-9358 BCS Learning & Development

Self URI (article page): https://www.scienceopen.com/hosted-document?doi=10.14236/ewic/eva2015.18

Self URI (journal page): https://ewic.bcs.org/

REFERENCES

I Bakshee 1999 The Pattern of Beauty: The Art of Igor Bakshee Wolfram Media, Graphica 2 The World of Mathematica Graphics
J BalakrishnanV Venkatachalam 2014 Galois Visualizations: Program Guide Mathematical Institute, University of Oxford UK http://people.maths.ox.ac.uk/balakrishnan/galois/galois_guide.pdf 6 01 2015
H BeddardD Dodds 2009 Digital Pioneers. V&A Pattern V&A Publishing
J. P Bowen &T Giannini 2014 Digitalism: the new realism? K NgJ. P BowenS McDaid EVA London 2014: Electronic Visualisation and the Arts. British Computer Society, Electronic Workshops in Computing 324 331 10.14236/ewic/eva2014.38
J. P BowenR. J Wilson 2012 Visualising virtual communities: from Erdös to the arts S DunnJ. P BowenK Ng EVA London 2012: Electronic Visualisation and the Arts. British Computer Society, Electronic Workshops in Computingp238 244 http://ewic.bcs.org/content/ConWebDoc/46141 28 May 2015
B Kostant 1995 The graph of the truncated icosahedron and the last letter of Galois Notices of the AMS 42 9 960 968 http://www.ams.org/notices/199509/kostant.pdf 4 06 2015
J DaintithR. D Nelson 1989 The Penguin Dictionary of Mathematics Penguin Reference Books
L. C Freeman 2000 Visualizing social networks Journal of Social Structure 1 1
R GodinR MissaouiH Alaoui 1995 Incremental concept formation algorithms based on Galois (concept) lattices Computational Intelligence 11 2 246 267
C. A. R HoareJ He 1998 Unifying Theories of Programming Prentice Hall
L Le Bruyn 2008 Galois’ last letter NeB blog http://www.neverendingbooks.org/galois-last-letter 27 05 2015
R MarghoubiA BoulmakoulK Zeitouni 2006 The use of the Galois lattice for the extraction and the visualization of the spatial association rules IEEE International Symposium on Signal Processing and Information Technology 10.1109/ISSPIT.2006.270872
A MeltonD. A SchmidtG. E Strecker 1986 Galois connections and computer science applications Category Theory and Computer Programming Springer Lecture Notes in Computer Science 240 299 312 10.1007/3-540-17162-2_130
C. C Morgan 1994 The cuppest capjunctive capping, and Galois.A. W Roscoe A Classical Mind: Essays in Honour of C. A. R. Hoare, chapter 19p317 332 Prentice Hall International Series in Computer Science
S.-C MuJ. N Oliveira 2011 Programming from Galois connections Relational and Algebraic Methods in Computer Science Springer, Lecture Notes in Computer Science 6663p294 313 10.1007/978-3-642-21070-9_22
P. M Neumann 2011 The Mathematical Writings of Évariste Galois European Mathematical Society Publishing House
T Petsinis 1995 i = Galois: A Fictional Biography of the French Mathematician Évariste Galois (1811–1832) Masters thesis, Department of Humanities, Victoria University of Technology Australia
L. T Rigatelli 1996 Évariste Galois, 1811–1832 Birkhäuser
A Robinson 2010 Sudden Genius? Oxford University Press
P Stein 2012 Visualizing Galois fields. Nklein Software, 17 May http://nklein.com/2012/05/visualizing-galois-fields/ 6 01 2015
S Wolfram 2002 A New Kind of Science Wolfram Media

Comments

Comment on this article

[1] I Bakshee 1999 The Pattern of Beauty: The Art of Igor Bakshee Wolfram Media, Graphica 2 The World of Mathematica Graphics

[2] J BalakrishnanV Venkatachalam 2014 Galois Visualizations: Program Guide Mathematical Institute, University of Oxford UK http://people.maths.ox.ac.uk/balakrishnan/galois/galois_guide.pdf 6 01 2015

[3] H BeddardD Dodds 2009 Digital Pioneers. V&A Pattern V&A Publishing

[4] J. P Bowen &T Giannini 2014 Digitalism: the new realism? K NgJ. P BowenS McDaid EVA London 2014: Electronic Visualisation and the Arts. British Computer Society, Electronic Workshops in Computing 324 331 10.14236/ewic/eva2014.38

[5] J. P BowenR. J Wilson 2012 Visualising virtual communities: from Erdös to the arts S DunnJ. P BowenK Ng EVA London 2012: Electronic Visualisation and the Arts. British Computer Society, Electronic Workshops in Computingp238 244 http://ewic.bcs.org/content/ConWebDoc/46141 28 May 2015

[6] B Kostant 1995 The graph of the truncated icosahedron and the last letter of Galois Notices of the AMS 42 9 960 968 http://www.ams.org/notices/199509/kostant.pdf 4 06 2015

[7] J DaintithR. D Nelson 1989 The Penguin Dictionary of Mathematics Penguin Reference Books

[8] L. C Freeman 2000 Visualizing social networks Journal of Social Structure 1 1

[9] R GodinR MissaouiH Alaoui 1995 Incremental concept formation algorithms based on Galois (concept) lattices Computational Intelligence 11 2 246 267

[10] C. A. R HoareJ He 1998 Unifying Theories of Programming Prentice Hall

[11] L Le Bruyn 2008 Galois’ last letter NeB blog http://www.neverendingbooks.org/galois-last-letter 27 05 2015

[12] R MarghoubiA BoulmakoulK Zeitouni 2006 The use of the Galois lattice for the extraction and the visualization of the spatial association rules IEEE International Symposium on Signal Processing and Information Technology 10.1109/ISSPIT.2006.270872

[13] A MeltonD. A SchmidtG. E Strecker 1986 Galois connections and computer science applications Category Theory and Computer Programming Springer Lecture Notes in Computer Science 240 299 312 10.1007/3-540-17162-2_130

[14] C. C Morgan 1994 The cuppest capjunctive capping, and Galois.A. W Roscoe A Classical Mind: Essays in Honour of C. A. R. Hoare, chapter 19p317 332 Prentice Hall International Series in Computer Science

[15] S.-C MuJ. N Oliveira 2011 Programming from Galois connections Relational and Algebraic Methods in Computer Science Springer, Lecture Notes in Computer Science 6663p294 313 10.1007/978-3-642-21070-9_22

[16] P. M Neumann 2011 The Mathematical Writings of Évariste Galois European Mathematical Society Publishing House

[17] T Petsinis 1995 i = Galois: A Fictional Biography of the French Mathematician Évariste Galois (1811–1832) Masters thesis, Department of Humanities, Victoria University of Technology Australia

[18] L. T Rigatelli 1996 Évariste Galois, 1811–1832 Birkhäuser

[19] A Robinson 2010 Sudden Genius? Oxford University Press

[20] P Stein 2012 Visualizing Galois fields. Nklein Software, 17 May http://nklein.com/2012/05/visualizing-galois-fields/ 6 01 2015

[21] S Wolfram 2002 A New Kind of Science Wolfram Media

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