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On the Importance of Useless Mathematics

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Raising Public Awareness of Mathematics

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Abstract

It is very difficult to convey the purpose of large and important pieces of mathematics to the general public. Even college students of mathematics frequently ask, in an exasperating way: “What is this useful for?” In this short essay it is argued that in order to appropriately answer this question, one must first dispel some common-sense notions that just happen to be wrong. Fundamentally, one has to confront, head on, the question of what mathematics really is and exactly what things it deals with, which can only be satisfactorily understood within an evolutionary perspective.

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Notes

  1. 1.

    See [3–9].

  2. 2.

    I do not believe in things for which there is no real evidence for their actual existence, so I disregard beliefs in the existence of supernatural (whatever that means!) components of humans or other animals.

  3. 3.

    Nobel laureate in physics, 1965.

  4. 4.

    Available online at http://darwin-online.org.uk.

  5. 5.

    [13]. See also [14], Chaps. 3 and 4.

  6. 6.

    Although Darwin never used the term “evolution”, for good reasons, since it gives the wrong idea of a “progress”.

  7. 7.

    See [15], Chaps. 7–10.

  8. 8.

    See [16] and http://evolution.berkeley.edu/evolibrary/misconceptions_faq.php.

  9. 9.

    See [14], p. 67.

  10. 10.

    Which is, nevertheless, an amazing book, a true tour de force!

  11. 11.

    And also, it seems to me, some lack of knowledge about the theory of evolution and its consequences. In page 22, Penrose also writes something that shows that he is unaware of the evolutionary basis of moral values, namely: “Morality has a profound connection with the mental world, since it is so intimately related to the values assigned by conscious beings and, more importantly, to the very presence of consciousness itself. It is hard to see what morality might mean in the absence of sentient beings”. See, on this matter, [18, 19] and Darwin himself, in [20], Chaps. 3–5.

  12. 12.

    [17], pp. 20–21.

  13. 13.

    This is obviously simply a caricatural example.

  14. 14.

    See [22], Chap. XX, and [23], Chap. 6.

  15. 15.

    Quoted in [24], p. 101.

  16. 16.

    [10], p. 4.

  17. 17.

    See [25], Chap. 37, and §4 of Chap. 48.

  18. 18.

    See [26], p. 392.

  19. 19.

    “Fourier had the opinion that the main aim of mathematics was its public utility and the explanation of natural phenomena, but a philosopher like him should have known that the sole purpose of science is the honour of human mind, and in this regard, a question on numbers is as worthy as a question on the system of the world.”

  20. 20.

    From Chap. 64 of the Tao Te Ching.

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Acknowledgements

This work was partially supported by Fundação para a Ciência e Tecnologia (FCT) through Centro de Matemática da Universidade do Porto. Substantial parts of this paper were adapted from an article by the author, [30], published in Portuguese.

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  1. Centro de Matemática da Universidade do Porto, Porto, Portugal

    António Machiavelo

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  1. António Machiavelo
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Correspondence to António Machiavelo .

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  1. , Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 6, Berlin, 14195, Berlin, Germany

    Ehrhard Behrends

  2. Inst. Superior de Economia e Gestão, Depto. Matemática, Universidade Técnica de Lisboa, Rua Miguel Lupi 20, Lisboa, 1200, Portugal

    Nuno Crato

  3. CMAF, Universidade de Lisboa, Av. Prof. Gama Pinto 2, Lisboa, 1649-003, Portugal

    José Francisco Rodrigues

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Machiavelo, A. (2012). On the Importance of Useless Mathematics. In: Behrends, E., Crato, N., Rodrigues, J. (eds) Raising Public Awareness of Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25710-0_28

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