The Mathematical Intelligencer

, Volume 35, Issue 4, pp 10–17 | Cite as

Challenges to the Assessment of Time-to-Proof of Mathematical Conjectures

Viewpoint

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Arbesman, S. and Courtland, R. (25 December 2010) 2011 preview: million-dollar mathematics problem, New Sci. 2792.Google Scholar
  2. [2]
  3. [3]
    Bolton, D. (2 Feb 2011) Time to P = NP, New Sci. 2798.Google Scholar
  4. [4]
    Eckmann, J.-P., Moses, E., and Sergi, D. (2004) Entropy of dialogues creates coherent structures in e-mail traffic, Proc. Natl. Acad. Sci. U.S.A. 101, 14333.Google Scholar
  5. [5]
    Barabasi, A.-L. (2005) The origin of bursts and heavy tails in human dynamics, Nature 435, 207.Google Scholar
  6. [6]
    Oliveira, J. G. and Barabasi, A.-L. (2005) Darwin and Einstein correspondence patterns, Nature 437, 1251.Google Scholar
  7. [7]
    Vazquez, A., Gama Oliveira, J., Dezso, Z., Goh, K. I., Kondor, I., and Barabasi, A. L. (2006) Modeling bursts and heavy tails in human dynamics, Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73, 036127.Google Scholar
  8. [8]
    Grinstein, G. and Linsker, R. (2008) Power-law and exponential tails in a stochastic priority-based model queue, Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77, 012101.Google Scholar
  9. [9]
    Saichev, A. and Sornette, D. (2009) Effects of diversity and procrastination in priority queuing theory: the different power law regimes, Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81, 016108.Google Scholar
  10. [10]
    Bouchaud, J-P., Giardina, I., and Mzard, M. (2001) On a universal mechanism for long-range volatility correlations, Quant. Financ. 1, 212–216.Google Scholar
  11. [11]
    Appel, K. and Haken, W. (1977) Every planar map is four colorable, part I. discharging, Illinois J. Math. 21, 429–490.Google Scholar
  12. [12]
    Appel, K., Haken, W., and Koch, J. (1977) Every planar map is four colorable, part II. reducibility, Illinois J. Math. 21, 491–567.Google Scholar
  13. [13]
    Appel, K. and Haken, W. (1989) Every Planar Map is Four- Colorable, Providence, RI: American Mathematical Society.Google Scholar
  14. [14]
    Maillart, M., Sornette, D., Frei, S., Duebendorfer, T., and Saichev, A. (2011) Quantification of deviations from rationality from heavy-tails in human dynamics, Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83, 056101.Google Scholar
  15. [15]
  16. [16]
    Giles, J. (2005) Internet encyclopedias go head to head, Nature 438, 900–901.Google Scholar
  17. [17]
    http://www.oakland.edu/enp/ (maintained by Jerry Grossman at Oakland University).
  18. [18]
    Daly, D. J. and Vere-Jones, D. (2003) An Introduction to the Theory of Point Processes, Vol. 1, 2nd ed., New York, Berlin, Heidelberg: Springer.Google Scholar
  19. [19]
    Laurance, A. J. (1974) Theory of interevent interval distributions for stationary point processes, Inform. Control 25, 299–316.CrossRefGoogle Scholar
  20. [20]
    Vere-Jones, D. (1970) Stochastic Models for Earthquake Occurrence, J. R. Stat. Soc. B 32, 1–62.Google Scholar
  21. [21]
  22. [22]
    Johansen, A. and Sornette, D. (2001) Finite-time Singularity in the Dynamics of the World Population and Economic Indices. Physica A 294, 465–502.Google Scholar
  23. [23]
    Bloom, D. E. (2011) 7 Billion and counting, Science 333, 562–569.Google Scholar
  24. [24]
    Huesler, A. D. and Sornette, D. (2011) Evidence for super-exponentially accelerating atmospheric carbon dioxide growth, submitted (http://arxiv.org/abs/1101.2832).

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.D-MTECETH ZurichZurichSwitzerland

Personalised recommendations