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Does anyone know who was the first person to invent the term homology and what their motivation was?

All I could find was that Emmie Noether is accredited with inventing the homology group, and that Poincare made essential contributions to the nascent concept. Although I thought Poincare called topology "analysis situs", so I doubt he coined the term "homology".

Most of the results relating to the etymology of "homology" were regarding its application in biology (even after trying to explicitly filter those results).

Also I am not certain if I should ask this question here or English language or usage, so if this question should be migrated then please do so.

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    $\begingroup$ the order may not be what you think. Topology terms can often be traced to earlier use in biology and botany in particular. You might be able to find the first use in English, hard to say. You may find a path from Latin to, say, French and German, finally to what you want in English. $\endgroup$ – Will Jagy Aug 1 '16 at 3:15
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    $\begingroup$ en.wikipedia.org/wiki/Plant_morphology and en.wikipedia.org/wiki/… says about 1656 $\endgroup$ – Will Jagy Aug 1 '16 at 3:17
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    $\begingroup$ This may be a great question for HSM. $\endgroup$ – Willie Wong Aug 1 '16 at 3:22
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According to Weibel's History of Homological Algebra this term was first used by Poincaré in his 1895 paper Analysis Situs, building off of ideas of Riemann and Betti. You can confirm that he uses this term by reading this translation by John Stillwell.

"Homologous" in general is just a word that means "similar or corresponding in some way," so it's not a particularly unusual choice of word for an equivalence relation. Poincaré's notion of what it meant for things to be homologous is closer to what we would now call (co)bordism, though.

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