### Abstract

All physical systems in equilibrium obey the laws of thermodynamics. In other words, whatever the precise nature of the interaction between the atoms and molecules at the microscopic level, at the macroscopic level, physical systems exhibit universal behavior in the sense that they are all governed by the same laws and formulae of thermodynamics. In this paper we describe some recent history of universality ideas in physics starting with Wigner's model for the scattering of neutrons off large nuclei and show how these ideas have led mathematicians to investigate universal behavior for a variety of mathematical systems. This is true not only for systems which have a physical origin, but also for systems which arise in a purely mathematical context such as the Riemann hypothesis, and a version of the card game solitaire called patience sorting.

Original language | English (US) |
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Pages | 125-152 |

Number of pages | 28 |

State | Published - Dec 1 2006 |

Event | 25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain Duration: Aug 22 2006 → Aug 30 2006 |

### Other

Other | 25th International Congress of Mathematicians, ICM 2006 |
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Country | Spain |

City | Madrid |

Period | 8/22/06 → 8/30/06 |

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### Keywords

- Random matrices
- Riemann-hilbert problems
- Universality

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Universality for mathematical and physical systems*. 125-152. Paper presented at 25th International Congress of Mathematicians, ICM 2006, Madrid, Spain.