The dhātu (dhatu; verbal-root) ‘ṛṣ‘ (rish) means ‘to go’; and it is also applied to denote śruti (hearing), satya (the truth) and tapasyā (tapasya; to practice asceticism). Those who possess such qualities and engage themselves in the thought of Brahman, are called ṛṣi (rishi)–
ṛṣityeṣu gatau dhātuḥ śrutau satye tapasyatha
etat sannirataṁ tasmin brahmaṇā sa ṛṣiḥ smṛtaḥ.
In another sense, the dhātu ‘ṛṣ’ is denotative of hiṁsā (himsa, envy or jealousy) and gati or motion (going). The second meaning ‘gati’ denotes Brahmajñāna (the perception of Brahman), truth, Vidya (knowledge), tapasyā (tapasya) and knowledge of Śāstra(s), is a ṛṣi — and above all, one who is engaged in the perception of the Brahman, is a ṛṣi —
ṛṣirhiṁsāgatau dhāturvidyā satyaṁ tapaḥ śrutam
evaṁ sannicayo yasmād brahmaṇastu tatastvaṣiḥ.

The most archetypal, general meaning of the term Ṛṣi is ‘the one who can see — see beyond the material world.’ Yāska(Yaska), the author of Nirukta, considering this very meaning, has said, one who has a visionary power to see everything– the finer truths or aspects of things, or theories perceived through insight — is a ṛṣī — ṛṣidarśanāt. Citing the name of Upamanyu, his Purvācārya (Purvacharya; predecessor-preceptor) — Yāska further says that, according to Upamanyu and his followers, those who had a vision of the mantra(s), were ṛṣi(s) —
stomān dadarśa ityaupamayavaḥ.
Going even deeper, Yāska also writes, transforming an ancient verse-line from the Svādhyāya Brāhmaṇa (Swadhyaya Brahmana) of Āraṇyaka (Aranyaka) — since the svayambhu (self-emanated) body of knowledge , in the form of Veda(s), made itself emerge in front of these ascetic Brāhmaṇa(s), engaged in tapasyā (tapasya), and contemplating on the Brahman (the Supreme Reality) — they are called ṛṣi(s). Without study, only because of their tapasyā (ascetic practice), they could visualise the Vaidika mantra(s) (hymns) in their original form(s). It is through this visionary act,that they achieved the status of ṛṣitva (rishitwa; the state of being a seer) —
tad yad enān tapasyamānān brahma svaystabhyānaryat
te ṛṣyobhavan, tad ṛṣiṇāmṛṣitvamiti vijñāyate.