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Mathematics and Music: Loves and Fights

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Perception, Representations, Image, Sound, Music (CMMR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12631))

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Abstract

We present different aspects of the special relationship that music has with mathematics, in particular the concepts of rigour and realism in both fields. These directions are illustrated by comments on the personal relationship of the author with Jean-Claude, together with examples taken from his own works, specially the “Duos pour un pianiste".

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Notes

  1. 1.

    The same anecdote has been also told to me with another main character in place of Chevalley.

  2. 2.

    Boucourechliev [1] claims that Stravinsky is wrong and that is possible but, actually, doesn’t give the recovered series.

  3. 3.

    Pierre Boulez comdans voluntary the third part of “Structure I for two pianos"[2] for the argument that “a computer could have composed it in a few minutes". Et alors ?.

  4. 4.

    Let us remark that, at the same period, Bourbaki’s attempt to constrict what could be called a kind of absolutely pure mathematics was offering a vision of mathematics where the only figures are commuting diagrams, which by the way are not figures but just notations.

  5. 5.

    “On dit qu’un nombre variable x a pour limite un nombre fixé a, ou tend vers a, lorsque la valeur absolue de la différence \(x-a\) finit par devenir et “rester" plus petite que n’importe quel nombre positif donné à l’avance. Lorsque \(a = 0\), le nombre x est dit “un infiniment petit“.", Gourçat [6].

  6. 6.

    The reader interested in the concept of rigour in mathematics, philosophy and music, might consult the proceedings [3] of the conference RIGUEUR held in Paris, July 2 and 3 2019, to be published by Spartacus editions (Paris).

  7. 7.

    Though wrong proofs are usaully very beautiful.

  8. 8.

    What limits the true is not the false, it is the insignificant.

  9. 9.

    Like a calisson shaped box of calissons where all calissons are replaced by ... a box of callisons where all calissons are replaced by ... a box of callisons...etc.

References

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  3. Paul, T., Schmidt, M. (eds.): RIGUEUR. Spartacus, Paris (2021). https://indico.math.cnrs.fr/event/4602/, http://ljll.math.upmc.fr/paulth//phenomath/

  4. Drouin, G.: Les deux moments de la rigueur du compositeur. In: [3]

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  5. Giavitto, J.L.: Formalisme, Exactitude, Rigueur. In: [3]

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  6. Goursat, É.: Cours d’Analyse Mathématique. Gauthier-Villars, Paris (1933)

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  7. Paul, T.: Des sons et des Quanta. In: Alunni, C., Andreatta, M., Nicolas, F. (eds.) Mathématique/Musique/Philosophie. Collection “Musique/Sciences” IRCAM-Delatour, Paris (2012)

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  10. Paul, T.: Mathematical entities without objects, on the realism in mathematics and a possible mathematization of the (non)Platonism - Does Platonism dissolve in mathematics? Eur. Rev. 29(2), 1–21 (2021)

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Acknowledgment

This work has been partially carried out thanks to the supports of the LIA AMU-CNRS-ECM- INdAM Laboratoire Ypatie des Sciences Mathématiques (LYSM).

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Author notes

  1. Thierry Paul

    Present address: Laboratoire Jacques-Louis Lions, CNRS, Sorbonne Université 4 Place Jussieu, 75005, Paris, France

Authors and Affiliations

  1. Centre de Mathématiques Laurent Schwartz, CNRS and Ecole Polytechnique, 1128, Palaiseau Cedex, France

    Thierry Paul

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  1. Thierry Paul
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Correspondence to Thierry Paul .

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Editors and Affiliations

  1. Laboratoire PRISM, CNRS-AMU, Marseille, France

    Richard Kronland-Martinet

  2. Laboratoire PRISM, CNRS-AMU, Marseille, France

    Sølvi Ystad

  3. Laboratoire PRISM, CNRS-AMU, Marseille, France

    Mitsuko Aramaki

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Paul, T. (2021). Mathematics and Music: Loves and Fights. In: Kronland-Martinet, R., Ystad, S., Aramaki, M. (eds) Perception, Representations, Image, Sound, Music. CMMR 2019. Lecture Notes in Computer Science(), vol 12631. Springer, Cham. https://doi.org/10.1007/978-3-030-70210-6_45

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  • DOI: https://doi.org/10.1007/978-3-030-70210-6_45

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  • Print ISBN: 978-3-030-70209-0

  • Online ISBN: 978-3-030-70210-6

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