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How Mathematics is Rooted in Life

Published online by Cambridge University Press:  22 September 2015

Jens Erik Fenstad
Jens Erik Fenstad*
Affiliation:
University of Oslo, Oslo, Norway. E-mail: [email protected]
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Abstract

Mathematics is almost always an insider’s affair. But sometimes things happen within the mathematical community that have a relevance, and perhaps also an interest, beyond the tribe itself. The Grundlagenstreit of the 1920s is such an example. In this review essay we tell this story with a focus on the main actors involved, David Hilbert in Göttingen and L.E.J. Brouwer in Amsterdam. We shall see how fine points concerning the existence of mathematical objects, the question of the editorship of the Mathematische Annalen, and the attempts to resume normal scientific contacts between French and German scientists after the First World War led to an unusually bitter conflict within the tribe and beyond. But even if the effects of the fight were at the time negative, the long range outcome was positive. Hilbert’s work on the foundation of mathematics is still a powerful influence on current research, and Brouwer’s view on the constructive foundation of mathematics, which at the time inspired both Husserl and Wittgenstein, is today of increasing importance in the evolving science of logic and computing.

Type
Articles
Information
European Review , Volume 23 , Issue 4 , October 2015 , pp. 473 - 480
Copyright
© Academia Europaea 2015 

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References

Further Reading

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Fenstad, J. E. (2015) On what there is – infinitesimals and the nature of numbers. Inquiry, 58, pp. 57–79.CrossRefGoogle Scholar
van Heijenoort, J. (Ed). (1967) From Frege to Gödel: A Source Book in Mathematical Logic (Cambridge, MA: Harvard University Press).Google Scholar
Homotopy Type Theory, Institute for Advanced Study 2012–2013. http://homotopytypetheory.org/bookGoogle Scholar
Kleene, S. C. (1952) Introduction to Metamathematics (Amsterdam: North-Holland).Google Scholar
Martin-Löf, P. (1982) Constructive mathematics and computer programming. In: L. J. Cohen, J. Los, H. Peiffer and K. P. Podewski (Eds), Logic, Methodology and the Philosophy of Science VI (Amsterdam: North Holland).Google Scholar
Troelstra, A. S. and van Dalen, D. (1988) Constructivism in Mathematics I and II (Amsterdam: North-Holland).Google Scholar
van Atten, M. (2007) Brouwer meets Husserl. On the Phenomenology of Choice Sequences, Synthese Library 335 (Heidelberg: Springer-Verlag).CrossRefGoogle Scholar
van Dalen, D. (2013) L.E.J. Brouwer: Topologist, Intuitionist, Philosopher. How Mathematics is Rooted in Life (Heidelberg: Springer).CrossRefGoogle Scholar