The mathematical infinity

Infinity: New Research Frontiers

Volumn , Issue , 2011, Pages 55-75

  Bombieri, Enrico ^a  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

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EID: 84865967151     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511762000.004     Document Type: Chapter

References (21)

1. Ax, J., and Kochen, S. 1965. Diophantine problems over local fields. I. American Journal of Mathematics 87: 605–30.
2. Bartocci, U., and Vipera, M.C. 2004. Variazioni sul problema dei buoi di Archimede, ovvero, alla ricerca di soluzioni “possibili”… http://www.cartesio-episteme.net/mat/cattle-engl.htm.
3. Busard, H. L. L. 2001. Johannes de Tinemue’s Redaction of Euclid’s Elements, the So-called Adelard III version. vol. 1. Stuttgart: Franz Steiner Verlag.
4. Cohen, P. J. 1969. Decision procedures for real and p-adic fields. Communications on Pure and Applied Mathematics 22: 131–51.
5. Cook, S. 1971. The complexity of theorem proving procedures. In Proceedings, Third Annual ACM Symposium on the Theory of Computing, ACM, New York, pp. 151–58.
6. Correspondence d’Hermite et de Stieltjes. 1905. T.II. Paris: Gauthier-Villars.
7. Dante Alighieri. 1966–1967. La Commedia secondo l’antica vulgata a cura di Giorgio Petrocchi. Edizione Nazionale a cura della Societa Dantesca Italiana. Milano: Arnoldo Mondadori Editore.
8. Davis, M. (ed.) 1965. The Undecidable. Hewlett, NY: Raven Press. http://cs.nyu.edu/pipermail/fom/2007-October/012156.html. http://forum.wolframscience.com/showthread.php?s=&threadid=1472.
9. Dickson, L. E. 1952. History of the Theory of Numbers, vol. 2. Reprint New York: Chelsea.
10. De Morgan, A. 1872. A Budget of Paradoxes. London: Longmans, Green.
11. Gamow, G. 1947. One, Two, Three… Infinity: Facts and Speculations of Science. Illustrated by author. Rev. ed. 1961. London: Macmillan.
12. Gardner, M. 1975. Mathematical Carnival. New York: Borzoi Books, Alfred A. Knopf. p. 264. http://www-groups.dcs.st-and.ac.uk/∼history/Mathematicians.
13. Geymonat, M. 2006. Il grande Archimede. 2nd ed. Roma: Sandro Teti Editore.
14. Netz, R., Saito, K., and Tchernetska, N. 2001. A new reading of Method Proposition 14: Preliminary evidence from the Archimedes palimpsest. I. Source and Commentaries in Exact Sciences 2: 9–29.
15. Nygren, A. 2001. A simple solution to Archimedes’ cattle problem. University of Oulu, Linnanmaa, Oulu, Finland. Acta Universitatis, Ouluensis, Scientiae Rerum Naturalium. http://herkules.oulu.fi/isbn9514259327/index.html?tulosta=yes.
16. Paris, J., and Harrington, L. 1977. A mathematical incompleteness in Peano arithmetic. In Proof Theory and Constructive Mathematics, with contributions by C. Smorynski, Helmut Schwichtenberg, Richard Statman, et al. Handbook of Mathematical Logic, part D, pp. 819–1142. Studies in Logic and the Foundations of Math, vol. 90. Amsterdam: North-Holland.
17. Rado, T. 1962. On non-computable functions. Bell System Technical Journal 41: 877–84.
18. Lin, S., and Radó, T. 1965. Computer studies of Turing machine problems. Journal of the Association of Computing Machinery 12: 196–212.
19. Shor, P. W. 1994. Algorithms for quantum computation: Discrete logarithms and factoring. In 35th Annual Symposium on Foundations of Computer Science, Santa Fe, New Mexico, pp. 124–34. Los Alamitos, CA: IEEE Computer Society Press.
20. Terjanian, G. 1966. Un contre-example à une conjecture d’Artin. Compte Rendus de L’Académie des Sciences Paris Séries A-B 262: A612.
21. Vardi, I. 1998. Archimedes’ cattle problem. American Mathematical Monthly 105: 305–19.