REFERENCES
Atiyah, M. et. al.: 1994, 'Responses to “Theoretical Mathematics”', Bull. Amer. Math. Soc. 30, 178–207.
Hirsch, M. W.: 1994, 'Theoretical, Speculative and Nonrigorous Mathematics', pp. 186-190, in (Atiyah 1994).
Horgan, J.: 1993, 'The Death of Proof', Scientific American Oct. 1993, pp. 93ff.
Jaffe, A. and Quinn, F.: 1993, '“Theoretical Mathematics”: Toward a Cultural Synthesis of Mathematics and Theoretical Physics', Bull. Amer. Math. Soc. 29, 1–13.
Kolata, G.: 1992, 'New Short Cut Found for Long Math Proofs', New York Times, Tuesday, April 7, 1992, 135–139.
Mandelbrodt, B. B.: 1994, pp. 193–196 in (Atiyah 1994).
Mac Lane, S.: 1963, 'Natural Associativity and Commutativity', Rice University Studies 49, 28–46.
Mac Lane, S.: 1979, 'Abgekurzte Beweise im Logikkalkul', pp. 1–63 in Saunders Mac Lane, Selected papers, edited by I. Kaplansky, Springer-Verlag, New York.
Mac Lane, S.: 1992, 'Coherence Theorems and Conformal Field Theory', in Canadian Math. Society, AMS Conferences Proceedings 13, 32l–8.
Mac Lane, S.: 1994, 'Real Mathematics Will Not Synthesize with Physics', pp. 190–193 in (Atiyah, 1994).
Mac Lane, S.: 1992, “The Protean Character of Mathematics', in The Space of Mathematics (edited by J. Echeverra, A. Ibarra and J. Mormann), de Gruyter, Berlin/New York, pp. 3–12.
Mac Lane, S.: 1996, 'Categorical Foundations of the Protean Character of Mathematics', in Philosophy of Mathematics Today, Evandro Agazzi (ed.), Episteme 22 Kluwer Academic Press, Dordrecht, p. 5.
Moore, G. and Seiberg, N.: 1989, 'Classical and Quantum Field Theory', Comm. Math. Phys. 123, 177–259.
Quine, W. V.: 1994, Pursuit of Truth, Harvard University Press, Cambridge, MA.
Schütte, K.: 1960, Beweistheorie, Springer-Verlag, Berlin.
Sommaruga-Rosolemos, G.: 1995, 'History and Philosophy of Constructive Type Theory', Habilitations Schrift. Phil. Faculty, Universitat Freiburg, Switzerland.
Stasheff, J. D.: 1963, 'Homotopy Associativity of H-Spaces I', Trans. Amer. Math. Soc. 108, 275–92.
Thurston, W. P.: 1994, 'On Proof and Progress in Mathematics', Bull. AMS. 30, 161–77.
Zariski, O.: 1951, 'Review of L. Derwidué: Le probléme de la reduction des singularities d'une variété algébrique', Math Reviews 13, 67–70. Math Ann. 123, 302-33.
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MAC LANE, S. DESPITE PYHSICISTS, PROOF IS ESSENTIAL IN MATHEMATICS. Synthese 111, 147–154 (1997). https://doi.org/10.1023/A:1004918402670
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DOI: https://doi.org/10.1023/A:1004918402670