Color constancy is an essential function in digital photography and a fundamental process for many computer vision applications. Accordingly, many methods have been proposed, and some recent ones have used deep neural networks to handle more complex scenarios. However, both the traditional and latest methods still impose strict assumptions on their target scenes in explicit or implicit ways. This paper shows that the degree of linear polarization dramatically solves the color constancy problem because it allows us to find achromatic pixels stably. Because we only rely on the physics-based polarization model, we significantly reduce the assumptions compared to existing methods. Furthermore, we captured a wide variety of scenes with ground-truth illuminations for evaluation, and the proposed approach achieved state-of-the-art performance with a low computational cost. Additionally, the proposed method can estimate illumination colors from chromatic pixels and manage multi-illumination scenes. Lastly, the evaluation scenes and codes are publicly available to encourage more development in this field.