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In this paper we discuss the integrable chiral Potts model, as it clearlyrelates to how we got befriended with Vaughan Jones, whose birthday wecelebrated at the Qinhuangdao meeting. Remarkably we can also celebrate thebirthday of the model, as it has been introduced about 30 years ago as thefirst solution of the star-triangle equations parametrized in terms of highergenus functions. After introducing the most general checkerboard Yang--Baxterequation, we specialize to the star-triangle equation, also discussing itsrelation with knot theory. Then we show how the integrable chiral Potts modelleads to special identities for basic hypergeometric series in the $q$ aroot-of-unity limit. Many of the well-known summation formulae for basichypergeometric series do not work in this case. However, if we require thesummand to be periodic, then there are many summable series. For example, theintegrability condition, namely, the star-triangle equation, is a summationformula for a well-balanced ${}_4\Phi_3$ series. We finish with a few remarksabout the relation with quantum groups at roots of unity.

About 30 Years of Integrable Chiral Potts Model, Quantum Groups at Roots of Unity and Cyclic Hypergeometric Functions