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Logical Probability and the Strength of Mathematical Conjectures

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References

  1. S. Arbesman and R. Courtland, 2011 Preview: Million-dollar mathematics problem, New Scientist 2972 (25 Dec 2010), 24.

  2. D. H. Bailey, J. M. Borwein, C. S. Calude, M. J. Dinneen, M. Dumitrescu, and A. Yee, An empirical approach to the normality of π, Experimental Mathematics 21 (2014), 375–384.

  3. A. Baker, Is there a problem of induction for mathematics?, in Mathematical Knowledge, M. Leng, A. Paseau, and M. D. Potter, eds. (Oxford University Press, Oxford, 2007), 59–73.

  4. A. Baker, Non-deductive methods in mathematics, Stanford Encyclopedia of Philosophy (2009); http://plato.standord.edu/ entries/mathematics-nondeductive.

  5. J. Berger, The case for objective Bayesian analysis, Bayesian Analysis 1 (2006), 385–402.

  6. J. M. Borwein and D. Bailey, Mathematics by Experiment: Plausible reasoning in the 21st century (A. K. Peters, Natick, MA, 2004).

  7. A. Eagle, Chance versus randomness, Stanford Encyclopedia of Philosophy (2010/2012); http://plato.stanford.edu/entries/ chance-randomness/.

  8. H. M. Edwards, Riemann’s Zeta Function (Academic, New York, 1974).

  9. L. Fortnow, The status of the P versus NP problem, Communications of the ACM 52 (9) (2009), 78–86.

  10. J. Franklin, Resurrecting logical probability, Erkenntnis 55 (2001), 277–305.

  11. J. Franklin, The objective Bayesian conceptualisation of proof and reference class problems, Sydney Law Review 33 (2011), 545–561.

  12. J. Franklin, Non-deductive logic in mathematics: The probability of conjectures, in A. Aberdein and I. Dove, eds. The Argument of Mathematics (Springer, Dordrecht, 2013), 11–29.

  13. R. E. Ganz, The decimal expansion of π is not statistically random, Experimental Mathematics 23 (2014), 99–104.

  14. W. I. Gasarch, The second P=?NP poll, ACM SIGACT News 43 (2) (June 2012), 53–77.

  15. A. Gelman and C. R. Shalizi, Philosophy and the practice of Bayesian statistics, British of Mathematical and Statistical Psychology 66 (2013), 8–38.

  16. Goldbach conjecture verification; http://sweet.ua.pt/tos/ goldbach.html.

  17. X. Gourdon, The 1013 first zeros of the Riemann Zeta Function, and zeros computation at very large height, 2004; http:// numbers.computation.free.fr/Constants/Miscellaneous/zetazeros 1e13-1e24.pdf.

  18. R. Hisano and D. Sornette, Challenges to the distribution of time-to-proof of mathematical conjectures, Mathematical Intelligencer 35 (4) (Dec 2013), 10–17.

  19. E. T. Jaynes, Probability Theory: The Logic of Science (Cambridge University Press, Cambridge, 2003).

  20. J. M. Keynes, Treatise on Probability (Macmillan, London, 1921).

  21. G. Marsaglia, On the randomness of pi and other decimal expansions, Interstat 5, 2005; http://www.yaroslavvb. com/papers/marsaglia-on.pdf.

  22. B. Mazur, Is it plausible? Mathematical Intelligencer 36 (1) (Feb 2014), 25–33.

  23. J. Neyman, Silver jubilee of my dispute with Fisher, Journal of the Operations Research Society of Japan 3 (1961), 145–154.

  24. G. Pólya, Mathematics and Plausible Reasoning (vol. I, Induction and Analogy in Mathematics, and vol. II, Patterns of Plausible Inference, Princeton University Press, Princeton, 1954).

  25. P. Rothman and J. Rothman, Festina lente, Mathematical Intelligencer 20 (3) (1998), 17–18.

  26. E. W. Weisstein, Pólya Conjecture, Wolfram Mathworld; http://mathworld.wolfram.com/PolyaConjecture.html.

  27. J. Williamson, In Defence of Objective Bayesianism (Oxford University Press, Oxford, 2010).

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Franklin, J. Logical Probability and the Strength of Mathematical Conjectures. Math Intelligencer 38, 14–19 (2016). https://doi.org/10.1007/s00283-015-9612-3

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