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Complexity and diversity indices based on fundamental mathematical entities (topological invariants) are used to calculate the changes that take place during synthetic reactions, such as the Aldol, Diels–Alder, Wittig, Reppe–Vollhardt, Pauson–Khand and House–Whitesides reactions. Such calculations provide a way to compare the power of various reactions to increase molecular complexity, and they furnish a ‘yardstick’ to gauge the state of the art of synthetic chemistry. Retrosynthetic transforms and disconnections are also evaluated, and in the latter case, topological simplification principles are derived. In this way we may reveal the ‘unseen hand’ of synthesis.

Complexity and diversity indices can be used to evaluate the structural changes that take place during the course of a synthesis. From the generalized ‘complexity versus step’ plot and the definition of the ‘ideal synthesis’ we derive the concept of excess complexity and the heuristic, minimization of excess complexity. Molecular complexity and synthetic complexity are differentiated by identifying them with intrinsic and extrinsic complexity, respectively, and the effect of chirality on each is clarified. The role of symmetry in synthetic analysis is delineated by considering symmetry in molecules, their molecular graphs and the synthesis digraphs for their preparation, which leads to the concept of reflexivity and the heuristic, maximization of reflexivity. Vulnerability and robustness are introduced in connection with linear and convergent syntheses, which are also considered in relation to reflexivity.