Drawing on a variety of sources, Andreas Karachalios offers a probing account of fast-breaking developments in quantum theory that paved the way for Hückel's research. In Göttingen and later in Leipzig, Hückel interacted with leading figures not only in quantum physics and physical chemistry but also with others in nearby fields, including organic chemistry and mathematics. During his later career in Marburg, Hückel clashed with Linus Pauling over the properties of the benzine molecule. In order to appreciate this controversy, Karachalios gives a brief account of the mathematical formalism of spin invariants, with both Hückel and Pauling used in their analyses, though with different interpretations. This serves not only to clarify their differences but also to illustrate the importance of the quantum-mechanical theory of resonance for chemistry at this time.