Etymology of the Sanskrit word "pīḍ"
The root word of the Sanskrit words pīḍā (i.e., pain) and pīḍáyati (= pīḍ + -áyati, i.e., presses out) is pīḍ (i.e., to squeeze/press/hurt). Many linguists, such as Manfred Mayrhofer (on pages 136-137 of his book Etymologisches Wörterbuch des Altindoarischen. II.), have suggested that the Sanskrit root word pīḍ is somehow connected with the Greek word πῐέζω (pĭézō, i.e., to press/push/beset) and then made up a supposed "Proto-Indo-European" word \pisd-* to justify the suggested link. However, this is almost definitely wrong because πῐέζω (pĭézō) is connected with the word πτίσσω (ptíssō, i.e., to shell, grind grains by stamping) and because both πῐέζω (pĭézō) and πτίσσω (ptíssō) are semantically related and most likely come from the Proto-Indo-European word \peys-* (i.e., to grind/crush), which also has a descendant in Sanskrit: पिष् (piṣ, i.e., to crush, grind, pound, bruise, hurt, destroy, or injure).
It is plausible that 'to squeeze' is a derived meaning for the Greek word pĭézō that could have meant 'to press (by stamping or pushing)' and that pĭézō and ptíssō are both Greek-specific variations (descended from the Proto-Indo-European word \peys-). However, the Sanskrit word *piṣ (i.e., 'to grind' etc.) is not as similar to pīḍ (i.e., 'to squeeze' etc.), and so they likely have different roots. If the supposed Proto-Indo-European reconstruction \pisd-* were really valid, we would have seen its descendants in many Indo-European branches and languages than just Greek and Sanskrit. Moreover, 'to squeeze' is not even mentioned (and is explicitly contested) as the primary/original meaning of πῐέζω (pĭézō) in many Greek dictionaries, such as the 'Etymological Dictionary Of Greek.' Therefore, the Sanskrit root words pīḍ and piṣ most likely have different etymologies, especially given that the former is related to squeezing but the latter is related to grinding, which is not the same as squeezing, and so the Sanskrit word pīḍ does not have a Proto-Indo-European-based etymology.
Now, what could be the actual etymology of the Sanskrit root word pīḍ? To determine this, it is useful to see a list of Indo-Aryan words related to it: Punjabi word pīṛa, Gujarati word pīḍā, Hindi/Urdu word pīṛā, Marathi word pīḍā, and Bengali word piṛa, all of which mean the same thing as the Sanskrit word pīḍā (i.e., pain); as well as the Pali word pīḷeti, Magadhi Prakrit-based Magahi words peṛal, peṛāel, piṛāl, Maharastri Prakrit words pīḍaï, pīlaï, Marathi word piḷṇe, Konkani word piḷce, Sauraseni Prakrit word pīḍadi, and Old Gujarati word pīḍai, all of which mean the same thing as pīḍ (i.e., to squeeze/hurt). Therefore, variations of the root word pīḍ include pīṛ, piṛ, peṛ, pīḷ, pīl, and piḷ, and so it is possible that all (or versions) of these were variants in Old Indo-Aryan language(s)/dialects.
Furthermore, it is most likely that they were all directly borrowed from the Proto-Dravidian word \piẓ-* (i.e., to squeeze) or its plausible variant \pīẓ-* and that the sound iẓ/īẓ naturally transformed into īḍ, īṛ, iṛ, eṛ, īḷ, īl, and iḷ. This is not unlike how \piẓ-* transformed into its Dravidian descendants in multiple forms, such as piḍucu (i.e., to squeeze, wring, or press out) or piṇḍu (i.e., press/milk) in Telugu, piṛs- (i.e., to squeeze/wring) in Konda, perctre (i.e., to squash) in Malto, princing (i.e., to squeeze, squeeze out, massage, or press hard) in Brahui, pṛihpa (i.e., to squeeze out) in Kui, and piḻi (i.e., to squeeze, express, press out with hands, drip, exude, shed or pour) in Tamil and Kannada, piḻiyuka (i.e., to wring out or squeeze out) in Malayalam, and piḻẖing (i.e., to squeeze, squeeze out, massage, or press hard) in Brahui. It also not unlike how \pīẓ-* (a plausible variant of \piẓ-) transformed into its Dravidian descendants in multiple forms: *pīṅkāvuni (i.e., to press out) in Tulu, pīxnā (i.e., to press out, squeeze, or harass) in Kurux, pīnḍ- (i.e., to squeeze or milk) in Kolami and Naikri, pí(l)qe (i.e., to wring or squeeze out or milk) in Malto, and bīṛing (i.e., to milk or draw off) in Brahui.
Perhaps the original Proto-Dravidian form of \piẓ-* was \pīẓiṇḍ-, which is preserved as *bīṛing in Brahui to an extent, because most of the Dravidian descendants of the word could be explained using the transformations p > p/b/h and ī > ī/i/í/e/u and ẓ > ḻ/l/ḻẖ/lq/x/ṛ/r and ṇ > ṇ/n/ñ and ḍ > ḍ/ṭ/k/g as well as the shortenings \pīẓiṇḍ- > *pīẓi(ṇḍ)-/*p(īẓ)iṇḍ- > *pīẓi-/*piṇḍ-* and/or \piẓi-/*piṇṭ. The fact that *pi/pī variants as well as the variants pí/pe/pu exist within and across languages in distant and different branches, such as Kolami and Brahui, supports this theory. Moreover, the descendants of this Proto-Dravidian word are used very broadly for many things literally (e.g., to twist ear [to cause pain], wring out clothes, milk, squeeze a fruit to obtain juice, or press/twist/extract something with hands) and also metaphorically (e.g., to extract/extort something from someone or to harm/"squeeze" someone). Thus, this Proto-Dravidian word coincides very well semantically with the Sanskrit word pīḍ (i.e., to squeeze/press/hurt).
The true etymology of the Sanskrit root word pīḍ (i.e., to squeeze/press/hurt) and the related Indo-Aryan root words can therefore be settled without much doubt: pīḍ and its variants pīṛ, piṛ, peṛ, pīḷ, pīl, and piḷ all mostly likely come from the Proto-Dravidian word \piẓ-* (i.e., to squeeze). It is also possible that in some Indo-Aryan dialects the Old Indo-Aryan word pīḍ transformed into at least some of the Indo-Aryan variants (pīṛ, piṛ, peṛ, pīḷ, pīl, or piḷ), but it also possible that the variants pīṛ, piṛ, peṛ, pīḷ, pīl, and/or piḷ are results of some unattested similar-sounding Old Indo-Aryan words.
Etymology of the Sanskrit word "paṇḍā"
The root word of the Sanskrit word paṇḍitá (i.e., someone who can speak on a topic in an authoritative/wise manner, i.e., scholar, learned/wise person, teacher, philosopher, or a Hindu Brahmin who has memorized a substantial portion of the Vedas, along with the corresponding rhythms and melodies for chanting or singing them) is paṇḍā (i.e., knowledge, or the ability to give/deliver speeches/discourses or instructions/teachings or to speak in an authoritative/wise manner on something).
It has been speculated by some that the word paṇḍā comes from the Sanskrit word prajñā́ (i.e., wisdom, intelligence, or knowledge), which ultimately traces back to the Proto-Indo-European form \pro*-\ǵneh₃*-. However, this is likely coincidental because it is very difficult to explain the sound changes pra(jñā́) > pa(ṇḍā) and (pra)jñā́ > (pa)ṇḍā. Even the theory that prajñā́ transformed into paṇṇā in Prakrit and then further transformed into paṇḍā is problematic because the sound change ṇṇ > ṇḍ is not straightforward (even if prajñā́ transformed into paṇṇā through the sound changes pra > pa and jñā́ > ṇṇā). The Sanskrit word paṇḍā therefore most likely does not have the same ultimate Proto-Indo-European etymology of the word prajñā́.
Now, what could be the actual etymology of the Sanskrit root word paṇḍā? To determine this, it is useful to see a list of some Dravidian words with a related meaning: poṇθy- (i.e., to talk in assembly) or poṇt (i.e., speech or words in hymns/songs) in Toda, paṉṉu (i.e., to speak, say, talk, sing) or paṉuval (i.e., word or discourse) or paṇi (i.e., 'saying, word, command,' or 'to speak, say, declare, order, or command') in Tamil, paṇpini (i.e., to say, tell, inform, narrate, teach) in Tulu, panḍa (i.e., to send, or commission), pank (i.e., to send) in Naikri, pāning (i.e., to say, speak, or tell) or peṇḍavaï (i.e., sends) in Brahui, and several others. All of these words are related to the ability to speak words (or teach or command or declare) in an authoritative manner and are derived from the Proto-Dravidian word \paṇ-V-*. (In addition, as Jaroslav Vacek says in an article in Mongolica Pragensia '06, "The meaning 'to send' of some of the lexemes can be explained as a semantic extension of the meaning 'to say' > 'to command' > 'to send'.")
Most of the aforementioned Dravidian words start with pa. They then contain sounds such as ṇḍ, nḍ, ṇθ, ṇt, nk, ṉṉ, ṉ, ṇ, and n. All of these can possibly be explained as transformations or shortenings of the sound ṇḍ, which could have also had the variant ṇṇ. Thus, the Proto-Dravidian synonyms of these Dravidian words could possibly be \paṇḍ-* and \paṇṇ-. When suffixed with the Proto-Dravidian word \āḷ* (i.e., person), those forms *\paṇḍ-* and \paṇṇ-* become \paṇḍāḷ* and \paṇṇāḷ*, respectively. Both of these words could then possibly have meant 'a person with the ability to speak, teach, inform, or instruct authoritatively or the ability to sing/chant memorized hymns/songs.'
It is thus very possible that the plausible Proto-Dravidian words \paṇḍāḷ* and \paṇṇāḷ* with the same/similar meaning were directly borrowed into Old Indo-Aryan language(s)/dialects and resulted in the Sanskrit word paṇḍā and the Prakrit word paṇṇāḷ, respectively. In some dialects, prajñā́ may have also transformed into paṇṇā through the sound changes pra > pa and jñā́ > ṇṇā, and so the two suggested possibilities paṇṇāḷ > paṇṇā and prajñā́ > paṇṇā are not mutually exclusive. However, given that it is very unlikely that paṇṇā transformed into paṇḍā, the only plausible etymology for paṇḍā is based on the plausible Proto-Dravidian word paṇḍāḷ.
