automorphically
|au-to-mor-phi-cal-ly|
🇺🇸
/ˌɔtəˈmɔrfɪkli/
🇬🇧
/ˌɔːtəˈmɔːfɪkli/
(automorphic)
self-form / self-same form
Etymology
'automorphic' originates from Greek, specifically the compound 'automorphos', where 'auto-' meant 'self' and 'morphē' meant 'form'.
'automorphic' changed from New Latin/Neo-Greek constructions such as 'automorphicus'/'automorphos' used in scientific and mathematical Latin, and eventually became the modern English adjective 'automorphic' from which the adverb 'automorphically' is derived.
Initially it literally meant 'having the same form as oneself' (from the roots 'self' + 'form'), but over time it evolved into specialized mathematical usage meaning 'relating to automorphisms or self-similar/form-preserving properties', which carries into modern usage.
Meanings by Part of Speech
Adverb 1
in a manner relating to or exhibiting automorphism or self-similarity of form; in an automorphic way (often used in mathematical contexts).
The function transforms automorphically under the group action, preserving its essential structure.
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Adverb 2
in a way that is characteristic of or pertains to an automorphic form or property (used in higher mathematics, e.g., automorphic representations/forms).
Results about modular forms can often be restated automorphically in the language of automorphic representations.
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Last updated: 2025/11/27 06:54