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Much research has been conducted to find evidence of the environmental Kuznets curve (EKC) in the relationship between air-pollutant concentration and economic development. A major focus of EKC-related research has so far been to identify the turning point illustrated by EKC theory or to predict the moment when the turning point will occur. In our research, via analyzing the relationship between an aggregate social-development-representative variable (the Socio-demographic Index or SDI) and the population-weighted concentration of PM2.5, we propose that the overall relationship takes the form of a tilted-S shape with two types of turning points rather than one. Additionally, our research shows that the EKC is highly country-specific, making it extremely difficult to predict the positions of both turning points based on the historical development or trajectories of other countries. Therefore, we conclude that EKC theory is not a useful tool to predict the location of the turning points. However, for short-term prediction of the relationship, we advocate the use of support vector regression, which can forecast the evolution, unless rapid changes are occurring. We suggest that policy makers should not anchor their hopes on predicting turning points from previous studies, but should put more effort into dealing with present particulate matter pollution.