Due to its important physiological role and ease of isolation, hemoglobin has become one of the most studied proteins. One of the most famous researchers of hemoglobin in the early twentieth century was Gilbert Smithson Adair (1896–1979), who published a series of six papers devoted to this protein. This review, timed to coincide with the 100th anniversary of the publication of this series, highlights Adair’s fundamental contribution to the study of the hemoglobin molecule and the mathematical description of oxygenation. The results of Adair’s experiments determined the further course of hemoglobin research, and the equation he proposed became the basis for the construction of structural and functional models of oxygenation later proposed by Pauling (PNAS 21(4):186–191, 1935) and Koshland et al (Biochemistry 5(1):365–385, 1966). This review briefly discusses the background of Adair’s experiments and theories, as well as issues related to the mathematical interpretation of this equation, its approximating properties, and the interpretation of its coefficients. © 2025 Elsevier B.V., All rights reserved.