Number & MeasureGreek → English
Isomorphism
/ˌaɪsəˈmɔrfɪzəm/noun
A correspondence between two structures that matches them part for part and can be reversed without loss.
The Greek roots
ἴσος
ísos
equal, same
μορφή
morphḗ
form, shape
Literally: “same form”
The story of the word
Eilhard Mitscherlich noticed in 1819 that chemically different salts could crystallise in identical shapes, and named the property isomorphism. Mathematics later took the word for a map that carries structure across and can be run backwards, so two objects are isomorphic when they differ in nothing but the names of their parts. Both senses hold exactly to the Greek.
- How it travelled
- Ancient Greek → German → English
- First recorded
- 19th century
The same roots elsewhere
Other languages reached for exactly the same Greek pieces.
Same family
homomorphismautomorphismisotopemetamorphosis
In a sentence
The two groups look nothing alike until you write down the isomorphism.
Isomorphism is the mathematician's way of saying the difference does not matter.