Analysis Situs (paper)

"Analysis Situs" is an important mathematics paper that Henri Poincaré published in 1895. Poincaré later added five more papers to this work between 1899 and 1904.

These papers changed the study of shapes forever. Poincaré used special math ideas to tell apart different kinds of spaces, creating the field of algebraic topology. He introduced important concepts like the fundamental group and simplicial homology. He also talked about the Poincaré duality theorem and the Euler–Poincaré characteristic for chain complexes.

One of his big ideas was the Poincaré conjecture, which was finally proven true much later. In this paper, Poincaré also first used the term "homeomorphism" to describe when two shapes are basically the same in a certain way. His work laid the foundation for many areas of modern mathematics.