= History of Euler characteristic
<Leonhard Euler>'s Elementa doctrinae solidorum, or Elements of the doctrine of solids, appeared in 1758 in volume 4 of Novi Commentarii academiae scientiarum Petropolitanae, pp. 109–140. The repository record dates its composition to 1750. Composition and publication are distinct dates here.<Elementa doctrinae solidorum by Leonhard Euler>[Repository record for E230: author, English and Latin titles, written date 1750, published date 1758 and original journal citation]{ref}
The modern <cell-count formula for Euler characteristic> puts polyhedral counting into an arbitrary-dimensional <CW complex>. It also identifies what is being counted: the <Euler characteristic of a cube boundary and its interior> distinguishes a polyhedral surface from the filled solid using the missing three-dimensional term. The modern <homology> formulation explains why this alternating arithmetic persists across different decompositions.<Algebraic Topology by Allen Hatcher>[Algebraic Topology by Allen Hatcher, §2.2, printed pp. 146–147, Theorem 2.44: alternating cell counts, homology ranks and independence from the CW structure]{ref}
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