The Importance of Useful Mathematics: On Tools for Its Popularization, from Industry to Art

  • Jorge Buescu
  • José Francisco Rodrigues


Written popularization of mathematical sciences may have had its roots in Euler’s “Lettres à une Princesse d’Allemagne”, but have seen during the last decades an enormous increase of publications in newspapers, magazines and books. In this article we review some issues arising from our direct experience, on one hand, related to the connections of mathematics and art in the recreation of a virtual exhibition in Portugal during the WMY2000 and, on the other hand, in relation with a series of popularization articles for the magazine of the Portuguese engineering association. Concerning written popularization, we provide examples such as a natural logistic problem leading to optimization of functions without derivatives with counterintuitive results and to the use of check digit identification schemes in ID cards and in Euro banknotes, which correspond to mathematical problems with a “useful” nature or directly tangible meaning with a significant success of social communication. Illustrating the recent impact of elliptic curves in cryptography we describe the origin and the making of a recent short digital movie of mathematics and art, promoted by the “Centro Internacional de Matemática”, in collaboration with “Imaginary”.


Elliptic Curve Elliptic Curf European Central Bank Isaac Newton Institute Math Poster 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Mathematics and Industry, OECD report (2008).
  2. 2.
    ESF Forward Look on “Mathematics and Industry”, European Science Foundation, Strasbourg (2010).
  3. 3.
    Euler, L.: Lettres a une Princesse d’Allemagne sur divers sujets de Physique et de Philosophie. Petersburg, 1768, 1772, 3 vols. (a third edition of the English translation was published in Edinburgh in 1823 and is available at
  4. 4.
    Thomson (Lord Kelvin), W.: Popular Lectures and Essays, vol. II, pp. 571–592. Macmillan and Co., London (1894) Google Scholar
  5. 5.
    Reis, F.E.: Enciclopedismo – conhecimento para um público diversificado. In: Reis, F.E. (ed.) Felicidade Utilidade e Instrução - A divulgação científica no jornal enciclopédico dedicado à rainha 1779, 1788–1793; 1806. Porto Editora, Porto (2005) Google Scholar
  6. 6.
    Caraça, B.J.: Conferências e outros escritos. Lisboa (1970) Google Scholar
  7. 7.
    Caraça, B.J.: Conceitos Fundamentais da Matemática, Edições Cosmos, Lisboa, vol. I (1941); vol. 2 (1942); Re-edition, Gradiva, Lisboa (1998) Google Scholar
  8. 8.
    Aristotle, Metaphysics, XIII 3.107b Google Scholar
  9. 9.
    Livio, M.: The Golden Ratio. Broadway Books, New York (2002) zbMATHGoogle Scholar
  10. 10.
    Emmer, M. (ed.): The Visual Mind II. MIT Press, Cambridge (2005) zbMATHGoogle Scholar
  11. 11.
    Sullivan, J.: Mathematical pictures: visualization, art and outreach. In: Behrends, E., Crato, N., Rodrigues, J.F. (eds.) Raising Public Mathematical Awareness. Springer, Berlin (2011) Google Scholar
  12. 12.
    Robinson, J.: Symbolic Sculpture, the Collected Works of John Robinson.
  13. 13.
    Cipra, B.A.: The best of the 20th century: editors name top 10 algorithms. SIAM News 33(4) (2000) Google Scholar
  14. 14.
    Cannon, J.W.: Mathematics in marble and bronze: the sculpture of Helaman Rolfe Pratt Ferguson. Math. Intell. 13(1), 30–39 (1991) MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Para Além da Terceira Dimensão - Beyond the Third Dimension Catalogue of the exhibition by CMAF/Universidade de Lisboa (2000).
  16. 16.
    Banchoff, T., Cervone, D.: In and Outside the Torus (computer animated film). or
  17. 17.
    Banchoff, T.F., Cervone, D.P.: A virtual reconstruction of a virtual exhibit. In: Borwein, J., Morales, M.H., Polthier, K., Rodrigues, J.F. (eds.) Multimedia Tools for Communicating Mathematics, pp. 29–38. Springer, Berlin (2002) CrossRefGoogle Scholar
  18. 18.
    Polthier, K.: Visualizing mathematics—online. In: Bruter, C.P. (ed.) Mathematics and Art, pp. 29–42. Springer, Berlin (2002) Google Scholar
  19. 19.
    Polthier, K., et al. (eds.): MathFilm Festival 2008, a Collection of Mathematical Videos. Springer, Berlin (2008) zbMATHGoogle Scholar
  20. 20.
    Rota, G.-C.: The phenomenology of mathematical beauty. In: Palombi, F. (ed.) Indiscrete Thoughts. Birkhauser, Basel (1997). Chap. 10, republished in pp. 3–14 of The Visual Mind II. MIT Press, Cambridge (2005) Google Scholar
  21. 21.
    von Neumann, J.: The mathematician. In: Newman, J.R. (ed.) The World of Mathematics, vol. 4, pp. 2053–2063. Simon and Schuster, New York (1956) Google Scholar
  22. 22.
    Buescu, J.: O Mistério do BI e Outras Histórias. Gradiva Publicações, Lisboa (2001) Google Scholar
  23. 23.
    Buescu, J.: Da Falsificação de Euros Aos Pequenos Mundos. Gradiva Publicações, Lisboa (2003) Google Scholar
  24. 24.
    Buescu, J.: O Fim do Mundo Está Próximo? Gradiva Publicações, Lisboa (2007) Google Scholar
  25. 25.
    Buescu, J.: Casamentos e Outros Desencontros. Gradiva Publicações, Lisboa (2011) Google Scholar
  26. 26.
    Ingenium, Boletim da Ordem dos Engenheiros (Bulletin of the Portuguese Engineers Association). Available online at
  27. 27.
    Drezner, Z., Hamacher, H.W.: Facility Location: Applications and Theory. Springer, Berlin (2002) zbMATHCrossRefGoogle Scholar
  28. 28.
    Buescu, J., Casquilho, M.: A minimum distance: arithmetic and harmonic means in a geometric dispute. Int. J. Math. Educ. Sci. Technol. 142(3), 399–405 (2011) MathSciNetGoogle Scholar
  29. 29.
    Gallian, J.A.: The mathematics of identification numbers. Coll. Math. J. 22, 194–202 (1991) CrossRefGoogle Scholar
  30. 30.
    Picado, J.: A álgebra dos sistemas de identificação. Bol. SPM 44, 39–73 (2001) Google Scholar
  31. 31.
    Maths Posters in the London Underground. Isaac Newton Institute for Mathematical Sciences, University of Cambridge (2000).
  32. 32.
    Koblitz, N.: The uneasy relationship between mathematics and cryptography. Not. Am. Math. Soc. 54(8), 972–979 (2007) MathSciNetzbMATHGoogle Scholar
  33. 33.
    Hankerson, D., Menezes, A., Vanstone, S.A.: Guide to Elliptic Curve Cryptography. Springer, Berlin (2004) zbMATHGoogle Scholar
  34. 34.
    Matt, A.: IMAGINARY and the idea of an open source math exhibition platform. In: Behrends, E., Crato, N., Rodrigues, J.F. (eds.) Raising Public Awareness of Mathematics. Springer, Berlin (2012) Google Scholar
  35. 35.
    MiMa, museum for minerals and mathematics.
  36. 36.
    Rodrigues, J.F.: “LPDJLQH D VHFUHW”, a film on elliptic curves and cryptography, CIM Bulletin # 29, January 2011, pp. 27–28 Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.FCUL (Faculdade de Ciências da Universidade de Lisboa), Departamento de MatemáticaLisbonPortugal
  2. 2.FCUL/Centro de Matemática e Aplicações Fundamentais da Universidade de LisboaLisbonPortugal

Personalised recommendations