The Painlevé equations and Ugh boots

I have been working on the Painlevé equations for most of my life as a mathematician. They were written down and studied by Painlevé and his students, Gambier, Garnier, and others such as Picard, R. Fuchs, in the late 1800’s and early 1900’s. For most of the time since then, they have been ignored by mathematicians. Then in the late 1970’s and early 1980’s, they were identified as reductions of soliton equations, like the Korteweg-de Vries equation, and they started being recognized as interesting. Now they are regarded as universal objects that occur in random matrix models. It occurred to me that they are like “ugh boots”, slippers and boots made out of sheepskin long seen in Australia as comfortable but not presentable objects that you might wear in your bedroom but never out. Now, as you may know, they are fashion accessories worn by Hollywood stars!

About Nalini Joshi

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