Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.


A pariah finds a home

Pariahs are fundamental building blocks in a branch of mathematics called group theory, but seem to be unconnected from both physics and other areas of mathematics. Such a connection has now been identified.

This is a preview of subscription content

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1

    Weinberg, S. The Quantum Theory of Fields Vol. 1 (Cambridge Univ. Press, 2005).

    MATH  Google Scholar 

  2. 2

    Duncan, J. F. R., Mertens, M. H. & Ono, K. Nature Commun. 8, 670 (2017).

    ADS  Article  Google Scholar 

  3. 3

    Elwes, R. Plus Mag.; (2006).

  4. 4

    Conway, J. H. & Norton, S. P. Bull. Lond. Math. Soc. 11, 308–339 (1979).

    Article  Google Scholar 

  5. 5

    Borcherds, R. E. Invent. Math. 109, 405–444 (1992).

    ADS  MathSciNet  Article  Google Scholar 

  6. 6

    Gannon, T. Moonshine Beyond the Monster (Cambridge Univ. Press, 2006).

    Book  Google Scholar 

  7. 7

    Eguchi, T., Ooguri, H. & Tachikawa, Y. Exp. Math. 20, 91–96 (2011).

    MathSciNet  Article  Google Scholar 

  8. 8

    Duncan, J. F. R., Mertens, M. H. & Ono, K. Preprint at (2017).

  9. 9

    O'Nan, M. E. Proc. Lond. Math. Soc. 3rd Ser. 32, 421–479 (1976).

    MathSciNet  Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Terry Gannon.

Related links

Related links

Related links in Nature Research

Celestial mechanics: Fresh solutions to the four-body problem

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Gannon, T. A pariah finds a home. Nature 550, 191–192 (2017).

Download citation


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing