Abstract Enumeration of alkanes and monosubstituted alkanes with given carbon contents has been investigated by chemists and mathematicians over 130 years and solved recently by the present author in agreement with stereochemical and mathematical requirements. In the present account, the advances of the methodologies for solving the problem are discussed from an interdisciplinary point of view between chemistry and mathematics. Historical backgrounds of the interdisciplinary problem are introduced by emphasizing three epochs, i.e., the first epoch marked by Cayley, a mathematician (the 1870s), the second epoch by Pólya, a mathematician (the 1930s), and the third epoch by Fujita, an organic chemist (the first decade of this century). Among them, the accomplishments of the second epoch and those of the third epoch are compared in detail, where graphs (trees, rooted trees, or planted trees) and three-dimensional (3D) objects as mathematical terms are correlated to constitutions (two-dimensional structures) and 3D structures as chemical terms. After an introduction to terminology on isomerism and stereoisomerism, alkanes and monosubstituted alkanes are enumerated as graphs or constitutional isomers by Pólya’s theorem, while they are alternatively enumerated as 3D objects or 3D-structural isomers by Fujita’s proligand method. The present account of the long-standing problem would provide readers with a hint or a motivation for pursuing a concrete route to “the Heavens of Fujita,” which have caricatured stereochemical and mathematical barriers lying in wait for them.