Below are my comments on the Eurasiatic data, and why I think @Anixx's forms are not Proto-Eurasiatic numerals. As I am not a specialist of Burushaski, Trans-New-Guinean, or Pama-Nyungan, I cannot weigh in meaningfully on any long-range comparisons of those language families with any others.
Notes: I use the terms Proto-Korean and Proto-Koreanic interchangeably to refer to the reconstructed ancestor of the Silla (“Old Korean”) and Baekje languages.
Micro-Altaic refers to the hypothetical genetic relationship between Turkic, Serbi-Mongolic, and Tungusic-- not accepted by all historical linguists. If I am not mistaken Juha Janhunen has suggested that Serbi-Mongolic and Tungusic may be related.
PIYU=Proto-Inuit-Yupik-Unangan also known as Proto-Eskaleut.
PSM=Proto-Serbi-Mongolic, the ancestor of Proto-Mongolic, Khitan, and other Serbi-Mongolic languages.
Below are my specific comments on each of the forms being compared to reconstruct Proto-Eurasiatic numerals. To sum up my conclusions (1) *ʔin- ‘one’ has reflexes in PIE and PC (weak). (2) *kʷat- ‘to join, meet’ has reflexes in PIE, PIYU, and maybe PU (stronger if PU is forsure) with a deverbal noun derived in PIE and maybe PU meaning ‘two, pair’. (3) *gor-/*gur- ‘three’ has reflexes in PSM and probably PFU (weak). (4a) *Proto-Micro-Altaic *dur-/dör- ‘four’ is a very tentative reconstruction, with reflexes in Proto-Turkic, Proto-Tungusic, and PSM. (4b) Silla *nəri looks sort of like PFU *neljä, maybe a loan? (5) Comparison rejected. All of the numeral stems attested in only two branches of Eurasiatic are weaker reconstructions, more likely to be due to chance or ancient borrowing than if there were other Eurasiatic cognates.
The word for ‘one’
“PIE *h₁oinom.” Looks good. Don’t forget the accent, *h₁óynom, and remember how this is derived in PIE: an accented o-grade of the root *h₁-yn- with thematic neuter sg. ending -om. Also I will add, I think there is ample evidence to suggest *h₁ was a glottal stop [ʔ] in PIE.
“Proto-Korean *hana.” hana is the Modern Korean word. Silla aka Old Korean (Silla Hyangga, 6th-9th centuries) *hatʌn ‘one’ – hana is from the Late Middle Korean /hʌ̀ná/. There is also Silla (mokgan, date I don’t know) *hatʌp ‘one’, and Baekje *katəp, suggesting a Proto-Koreanic form for this numeral like *katʌp, the initial *k- also confirmed by loans into Japanese, e.g. kata-na ‘single-blade, katana’, kata-oya ‘one parent’, kata-ude ‘one-arm’, kata-omoi ‘unreciprocated love’, etc. The semantics of ‘one’ in kata-omoi are obvious to anyone who has experienced it.
“[Proto-]Tungusian *ömen” – my notes have *əmʊ-/*ʊmə- for the Proto-Tungusic numeral for ‘one’ (using Joseph & Whitman 2013’s vowel phonemes; using Benzing’s (1955) system this would be *emu-/ume-, with *u rather than *ö. This I pulled from Wiktionary (https://en.wiktionary.org/wiki/Reconstruction:Proto-Tungusic/ume-/emu-) and I still don’t know a lot about the Tungusic family, unfortunately most of the best shit written about Proto-Tungusic remains paywalled, I intend to ask the library for a copy of The Tungusic Languages by Vovin et al. when it gets published later this month, and then I’ll be able to much better assess this. The *-m- doesn’t really correspond with *-n-, as far as I am aware, in other Eurasiatic etymologies, Proto-Tungusic *-n- corresponds with PIE *-n- usually (this in Bomhard’s (2011) proposed cognate pairs in Reconstructing Proto-Nostratic)
“Chukchi ənnen” – We need to compare the proto-form. “Itelmen qniŋ”. Fortescue (Comparative Chukotko-Kamchatkan Dictionary, 2005:241) etymologizes qniŋ from Proto-Chukotko-Kamchatkan *qun ‘one’ [or *qunæ; cf. *qonpəŋ ‘continually’ and perhaps *qul(i) ‘another or one of’ and *qu(n) ‘emphatic particle’]. The Chukchi ənnen is from Proto-Chukotian *ənnæn (Fortescue 2005:345), completely unrelated to *qun. Proto-Chukotian *ənnæn is instead compared to Proto-Chukotko-Kamchatkan *ən- ‘that (there)’ (Fortescue 2005:342).
“Ainu hine” – Proto-Ainu *sì-nɛ́ ‘one’
“North Yukaghir xuon” – Omniglot provides маархуон (maarxuon) instead as the Northern Yukaghir numeral for ‘one’. I know next to nothing about Yukaghir but a quick look at this (https://www.omniglot.com/language/numbers/yukaghirnorthern.htm) suggests that the -uon is a suffix found on every numeral (c.f. kiiuon ‘2’, jaluoń ‘3’, jalaklań ‘4’ etc.), and that the stem for ‘one’ here is something like *maarx-, not **xuon
“Burushaski hen” – besides also han, hak. Not clear which one is older to me, because I don’t know anything about Burushaski grammar & phonology.
Of these all that remains for comparison are PIE *h₁oin-om with Proto-Chukotian *ənnæn, and Burushaski hen. If Fortescue (2005) could compare this to *ən-, presumably this could be segmented like *ən-næn or *ənn-æn, yielding comparison of the Proto-Chukotian *ən(n)- with PIE *h₁in- (the zero-grade of the root), going back to a Proto-Eurasiatic *ʔin- ‘one’ (I believe that there’s plenty of evidence that PIE *h₁- was a glottal stop). This numeral reconstruction is not very strong, since it is not attested in any other branches of Eurasiatic. If Burushaski is Eurasiatic too, then hen ‘one’ maybe belongs here also.
But honestly, I do not think that the PIE *h₁oin-om is cognate with Proto-Chukotian *ənnæn, the form *ənnæn is historically weaker than PCK *qun, which appears to be the older word for ‘one’, and I think PC *ənnæn is best derived from PCK *ən- ‘that (there)’, and here we have an example of a demonstrative stem producing a numeral, much like how PDr (PZ) *ont̠- has been etymologized from the verb root PPsDr *o- ‘to be suitable, fit, join’ (so this verb root *o- would go back to PZ then). I think it is plausible also that *qun- ultimately derives from an emphatic particle, and that there may have very well been a totally different Proto-Eurasiatic numeral for ‘one’ that completely disappeared from the language over the thousands of years that Proto-Eurasiatic changed into PCK.
Okay, now the word for ‘two’:
- “PIE *du̯oe̯” - in light of metrical evidence from the Rgveda, and Proto-Balto-Slavic reconstructions, as well as Anatolian evidence, I reconstruct *h₁ phonemically as a glottal stop. The word for ‘two’ was PIE *dwóh₁ [dwóʔ]
- “Proto-Korean *dur” – this is again the Modern Korean numeral for ‘two’. Instead, Silla *tupɨl 'two' (> Mod. Korean dur), Baekje *itərɨp ‘two’. The Proto-Korean I have been unable to reconstruct, not knowing whether it was Baekje or Silla that metathesized *-p- and -l-/-r-, i.e. the Proto-Korean would be either *(i)tVpɨL or *(i)tVLɨp
- “Tungus döör” – Wiktionary provides Proto-Tungusic *dʒʊʊr ‘two’. Usually Proto-Tungusic *dʒ ~ PIE *d before PEur front vowels though, making this connection not really possible. - I would like to add, tentatively, looking at Khitan evidence from Kane (2009) of and Middle Mongol, I reconstruct Khitan *jur ‘two’ ~ Middle Mongol jir ~ jur ‘two’ < Proto-Serbi-Mongolic *jur ‘two’, which looks like a perfect match with Proto-Tungusic *dʒʊʊr ‘two’. Seeing as no other numerals between Serbi-Mongolic and Tungusic match this well, perhaps we are dealing with a loan. Or perhaps this is an inheritance from a Proto-Micro-Altaic *jūr ‘two’ ?
- “Ainu tuu” – Proto-Ainu *tuu. This, and the Proto-Ainu *trɛ ‘three’ have maybe made every historical linguist freeze in their tracks for even a few seconds, before they acknowledge the truly amazing coincidence, see the complete lack of obvious morphological or lexical correspondences otherwise between Ainu and PIE, and move on with their day. Maybe Ainu is Eurasiatic, but I think that is quite unlikely. I would rather suggest comparing Ainu with Indigenous American languages, knowing that the reconstruction of Proto-Ainu, a language spoken some 500 years ago only, won’t likely be a very useful tool for peering that far back into the past. But maybe someone can do it, I truly hope so.
- “Mongol đuirim” – Written Mongol jirin. Middle Mongol jir ~ jur, Khitan *jur < Proto-Serbi-Mongolic *jur ‘two’ (my own reconstructions—need to check the other Serbi-Mongolic languages for reflexes)
- “Old Turkic tiurem” – I believe this is supposed to represent the as-of-yet untranslated Bulgar word tvirem, which Starostin erroneously glosses as ‘two’. See Vovin (2005:85-86) for a detailed description of why this is a baseless and erroneous gloss, but to sum up- tvirem shows up in a king list full of words with uncertain or unknown meanings, and tvirem is one of them. As for attempts to translate tvirem- the word tvirem shows up in the sentence ‘his years dilom tvirem’. dilom means snake according to most scholars (c.f. Common Turkic *yïïlan ‘snake’), and in all Turkic languages, numerals come before whatever they modify, so tvirem cannot be a numeral. Moreover, the suggestion that tvirem means ‘two’ is found in no other literature, it appears to be the result of a translation of a translation-- Starostin et. al compare Bulgar tvirem with Chuvash tebər ‘other (of two)’ is glossed with its Russian translation ‘другой (второй), второй из двух’, which is then mistranslated by Starostin et. al as ‘second’. The idea that tvirem is a numeral goes back to Pritsak (1955), who offers the translation ‘nine’, but Benzing (1959) criticizes Pritsak’s proposal. But the most amazing part of this is that, we actually have a real attested Volga Bulgar word for ‘two’ which is unsurprisingly cognate with the other Turkic words for ‘two’. Volga Bulgar اَكِ (æki) ‘two’ (> Chuvash иккӗ), cf. Turkish iki, < Proto-Turkic *ek(k)i ‘two’
Of these all that remain for comparison are PIE *dwóh₁ (< *dwi- + *-oh₁ dual, for *dwi- see *(d)wí-dḱm̥ti ‘twenty’), Proto-Serbi-Mongolic *jur, Proto-Tungusic */dʒʊ:r/, Proto-Ainu *tuu, and maybe Proto-Korean *(i)tVpɨL or *(i)tVLɨp. If the Proto-Serbi-Mongolic and Proto-Tungusic words aren’t borrowings from each other, they could both go back to a Proto-Micro-Altaic *dʒuur (maybe- I think reconstructing Proto-Micro-Altaic is still very tentative, and maybe impossible, but to get there, we’d need to systematically compare Proto-Serbi-Mongolic, Proto-Tungusic, and Proto-Turkic. If I was forced to do it myself, in about 20-30 years I could probably finish this work and reconstruct Proto-Micro-Altaic if such an exercise was even possible in the first place-- more likely a consortium of scholars who already know the shit I wish I knew about all three of those language families’ diachronic evolution will produce a Proto-Micro-Altaic reconstruction within the next decade if the family is viable, but until then, the reconstruction is tentative and based loosely on Poppe’s (1955) comparison of his reconstructions of Proto-Turkic, Proto-Mongolic, and Proto-Tungusic that generated his reconstruction of Proto-Micro-Altaic (he just called it “Proto-Altaic”), but this is difficult still to compare with *dwóh₁ since the sound law some have identified by examining the personal pronouns (forms like *mi, *ti > Micro-Altaic *bi, *ci), I would expect Proto-Eurasiatic *d- > *dʒ- to be a result of palatalization due to a front vowel, like [i]. This would suggest *dʒuur < **di-uur or something, which is a bit difficult to compare with PIE *dwi- due to it requiring either PIE or Proto-Micro-Altaic undergoing metathesis of the vowels, something that isn’t really an observed sound change in Bomhard’s proposed correspondences as far as I am aware. I personally don’t think that Ainu or Proto-Korean were Eurasiatic, so I’d exclude them from comparison here, but tentatively I only see a very shitty ‘match’ in PIE *dwi- and Proto-Ainu *tuu.
Anixx also tentatively suggested parallels between Proto-Uralic *kakta/käktä ‘two’ and PIE *kʷeteh₂ ‘pair’, itself from PIE *kʷet- ‘to fit together’. Perhaps Proto-Uralic underwent the same kind of metathesis that PIE did taking *-tk- > *-kt-, and the word for two was an older **katka. I have no reason to even speculate that, except that if that were true, it enables comparison with PIE *kʷet-, < Proto-Eurasiatic *kʷat- ‘to fit together’, along with a Proto-Eurasiatic derived noun meaning ‘pair’. Proposing such a metathesis would be better motivated by other evidence from other branches of Eurasiatic besides IE and Uralic. If Proto-Inuit-Yup’ik *katət- ‘join’ can be segmented *kat-ət- (cf. PIY *katə- ‘to meet’, *kaðuɣ- ‘strike (with instrument)’, *katyuɣ- ‘’knock into or meet’, and Proto-Inuit *katuk- ‘beat drum’, also katluɣ and Atkan Aleut kasaaɣ- ‘tie (fish) together by the tails for drying’), examining all the PIY forms as well as the Atkan Aleut cognate suggests the underlying stem is Proto-Inuit-Yupik-Unangan (PIYU) *kat- ‘to meet, join’, which can also be derived from Proto-Eurasiatic *kʷat-, strengthening the reconstruction and argument for metathesis in Uralic, and suggesting the semantics of the Proto-Eurasiatic root were ‘to meet, join, fit together’. Of course, if there is a better etymology of PU *kakta/käktä that only relies on Uralic data, or if *-ka/-kä was not a derivational morpheme in PU (a huge assumption I just made right there that it was), then PU *kakta/käktä must be removed from the comparison, and this becomes a comparison between PIE and PIYU only.
Bomhard does not seem to have any Nostratic or Eurasiatic etymology for Proto-Uralic *kakta/käktä, although maybe I did not search the 3,000-page volume carefully enough. Anyone else is welcome to try. Bomhard instead connects PIY *kaðuɣ- ‘strike (with instrument)’ to PIE *gʷdʰ- ‘to strike, beat, smash’ and Proto-Dravidian *qoṭ-/*qoṭṭ- ‘to hit’ and derives them all from PN *kʷʼad- (on the inclusion of the Dravidian form, Bomhard notes that *qoṭ-/*qoṭṭ- belongs “either here or with *k’ud- ‘(vb.) to strike; (n.) stroke, blow, knock, cuff, thump’”). I think connecting the PIY * kaðuɣ- to the PIE and PDr words is not much of a better semantic connection than with the PIYU *kat- words. –
The word for ‘three’
- “Proto-Korean *ku” This one is from Starostin, Dybo, & Mudrak’s Etymological Dictionary of the Altaic Languages (2003) [henceforth EDAL], a work which is riddled with errors (see Vovin 2005). This *ku comes from Miller (1971), quoted in EDAL: Deriving Korean ilkop ‘7’ < yər ‘ten’ + *-ɣu- ‘three’ + -əp(s) ‘nonexistent’, implying a numeral stem like *-ɣu- ‘three’. I reconstructed Proto-Korean *niLkup ‘7’ (> Silla *niLkup, Baekje *nilkop) and I have no Silla or Baekje data for the numeral ‘10’. The Late Middle Korean is /jəlh ~ jərh/ ‘10’ (Note that Silla had two liquids *l₁ = *l and *l₂ = *r, and as far as I can tell, Baekje did too. These two liquids merged into one liquid in Middle Korean. In Silla and Baekje I write *L as a cover symbol for a liquid of unknown value.). Plausibly, /jəlh ~ jərh/ could’ve come from a Silla form like **nel (Silla */-l/ > LMK /-lh/ cf. Vovin 2013), cf. loss of initial n- in LMK /nìlkúp ~ nìɾkúp/ ‘7’ but that’s not the only possibility. LMK /jətɨ́lp ~ jətɨ́ɾp/ corresponds with Baekje *etərɨp ‘8’, Silla *eri ‘Japanese’ > LMK /jə̌:j/, so perhaps the Silla (or even Proto-Korean) word for ‘10’ was actually **eL. Note that LMK /jə/ < Silla */e/, not */i/. Meanwhile the Silla word for ‘7’ was *niLkup. In order to be able to compare *niLkup with **nel, an important question must be answered: Q1) did /jə/ have some kind of ‘ablaut’ type variation with /i/ in Middle Korean? If we can answer ‘yes’ to Q1 (and tentatively I think the answer is ‘no’), then plausibly /e/ ablauted with /i/ in Silla (and Proto-Korean) as well, allowing for 1) **nel > **nil- in compounds, and 2) the analysis of Proto-Korean *niLkup as such a compound, resolving the liquid as *nilkup. My next question is then: Q2) what was Miller’s -əp(s) in Silla (or Baekje, if we even have that data)? If the answer to Q2 allows for a still viable splitting of Proto-Korean *niLkup into *niL-ku-p ‘ten-three-nonexistent’, this would then allow for the reconstruction of a (pre-?)Proto-Korean numeral form *-ku- ‘3’ besides the more common Proto-Korean *saytʌp (> Silla *satʌp, Baekje *saytʌp). Note that also Silla had a numeral *səki ‘three’ (> Old Japanese loan saki, LMK inheritance /sə̌:jh/) beside *satʌp. Not implying it compares with this *-ku-, just showing that there were different coordinate terms for ‘3’. Actually, if anything, *səki perhaps establishes the stronger historical weight of a possible stem like **sa-/**sə- for ‘3’. If Miller’s etymology of ‘7’ is still valid for Proto-Koreanic, this numeral stem *-ku- ‘3’ was probably all but completely forgotten from Koreanic by the time of Proto-Korean.
- ◦Miller (1996) is also quoted as identifying a North Korean word kŏl (geol) ‘3’ in the ‘four-stick’ game. For this word I know no etymology. I don’t know which dialect of Korean this is, without consulting Miller (1996) – the Miller (1996) EDAL cites is Languages and History: Japanese, Korean, and Altaic, which I don’t have handy. And as such, I don’t know what possible Late Middle Korean form could’ve produced Miller’s kŏl, and how well it compares to *-ku-. I do know that Standard Korean -ŏ- is usually the outcome of LMK /ə/. If kŏl was inherited from an unattested LMK */kəl(h)/. If LMK had */kəl/, this could only come from Silla *kəL, while */kəlh/ < Silla *kəl. Given Silla *kəl besides *-ku- in Silla *niLkup, they don’t seem even synchronically related (I’m almost sure -ə- never had ablaut with -u- in Middle Korean)
- There are many questions that need answering before I accept Miller’s hypothesis of a Proto-Korean numeral stem *-ku- ‘3’. If we ever end up unearthing a new text in Silla and uncover the numeral for ‘10’, there’s a (maximum) 50% chance it has initial *n- to match *niLkup. On top of that, Q1 and Q2 demand answering, as well as, if we want to add additional evidence from the “North Korean kŏl”- Q3) How would we reconstruct the LMK ancestor of Miller’s kŏl ? Tentatively, I think Q1 answers ‘no’, and we can reject Miller’s etymology altogether. No “Proto-Korean *ku” then, only Proto-Korean *saytʌp ‘3’, and possibly Silla *səki ‘3’ goes back to Proto-Korean also.
- Also a note here on my transcriptions of Koreanic. I follow the reconstruction of one linguist, who argues the phoneme traditionally reconstructed *ye in Silla was actually *[e], trad. *e = *[ə], trad. *ə = *[ɨ]. This is why mine may deviate from the standard forms you see.
- “Tungus gur” – The Proto-Tungusic word for ‘3’ was *ikan. I don’t know from where this “gur” came, maybe Jurchen gorhon (see below). I tentatively reconstruct Proto-Serbi-Mongolic *gur- ‘3’ to explain Khitan <hu.ur.>- “probably [hur]” (Kane 2009) and Proto-Mongolic *gurba-n ‘3’, Written Mongol gurba, and Jurchen gorhon ‘13’ (the Jurchen numerals ‘12’ through ‘18’ were loaned from Khitan because they look clearly (para-)Mongolic and not Tungusic at all). But I still have other Serbi-Mongolic languages to check for possible cognates, which may change my Proto-Serbi-Mongolic reconstruction.
- “Chukchi kurim” – Fortescue (2005:151) provides Proto-Chukotian *kərə(mənta) ‘three-year-old male reindeer’ and offers these notes: “cf. Proto-Chukotko-Kamchatkan *kərətkən [‘top’] if not a Uralic loan word via Tungusic – note Vogul Xurym of same meaning acc. Bouda, also Evenki kōrbē ‘reindeer buck’, compare [Proto-Chukotian] *toracəmənta [‘four-year-old(male) reindeer’]”. Proto-Chukotko-Kamchatkan *ŋeroq ‘three’ (Fortescue 2005:202). Fortescue’s Comparative Chukotko-Kamchatkan Dictionary has no other roots for ‘three’ – most likely, the Proto-Chukotian *kərə(m-) is a loan from Proto-Finno-Ugric *korme ‘three’ (see below), and the native term for ‘three’ is Proto-Chukotko-Kamchatkan *ŋeroq.
- “Mongol guor” – Proto-Serbi-Mongolic *gur- ‘three’, see above bullet point on “Tungus gur”.
- “Proto-Finno-Ugric *kuurem” Uralonet Entry #341 (http://uralonet.nytud.hu/eintrag.cgi?locale=en_GB&id_eintrag=341) provides Proto-Finno-Ugric *kolme ‘three’ (Finno-Ugric only, no Samoyedic cognate; Proto-Samoyedic *nakur ‘three’ (Janhunen 1977, as cited in Wiktionary)). The -r- is found only in Hungarian and Mansi, other Ugric languages like Northeastern Khanty has xuləm matching the reflexes of *-l- found in the rest of Finno-Ugric, but Janhunen (2009) suggests that actually *korme is older-- so we are left with (pre-?)Proto-Finno-Ugric *korme ‘three’.
Of these forms, all that remain for comparison are Proto-Serbi-Mongolic *gur- ‘three’ and Proto-Finno-Ugric *korme ‘three’, and I need to prove the *-me was truly a Proto-Finno-Ugric derivational morpheme to support a derivation of both of these from a Proto-Eurasiatic *gor-/gur- ‘three’, This reconstruction is weak, only attested in two branches of Eurasiatic.
The word for ‘four’
- “Proto-Korean *nelih” – Silla *nəri
- “Tungus nol” – Proto-Tungusic *dugin ‘four’. I do not know where ‘nol’ came from.
- “Mongol nayil” – Proto-Mongolic *dörben ‘four’ cf. Khitan “possibly [dur]” (Kane 2009), Jurchen durhon ‘14’ < Khitan, all < Proto-Serbi-Mongolic *dVr- ‘four’. (If this was *dur- or *dör- in PSM, it may compare okay with Proto-Tungusic *dugin ‘four’ and Proto-Turkic *tȫrt ‘four’, tentatively < Proto-Micro-Altaic *dur-/dör- (??) ) I do not know where ‘nayil’ came from-- maybe confusion with Proto-Mongolic *nayim ‘eight’, with a Khitan cognate for whose phonetic realization “Ji Shi and Chinggeltei suggest naim ~ Mo. naima” (Kane 2009). Jurchen niyuhun ‘eighteen’, So this suggests Proto-Serbi-Mongolic *nayim ‘eight’.
- “Proto-Finno-Ugric *nelya” – Proto-Finno-Ugric *neljä (Uralonet #620)
Silla *nəri sort of looks like PFU *neljä. I will at this point admit I don’t believe that Proto-Koreanic was a Eurasiatic language (see below, after all these numerals, for more details on what exactly my views on this are). If, however, I did believe that Proto-Koreanic were Eurasiatic, I would reconstruct *nVLi- ‘four’.
The word for ‘five’
- “PIE *penkʷe” – with accent, PIE *pénkʷe.
- “PFU *peŋe” – PU *witte (Uralonet #1154), a word with Samoyedic reflexes meaning ‘ten’ and PFU reflexes meaning ‘five’. I do not know where the form **peŋe comes from. Searching on Uralonet turns up PFU *peŋe ‘circle, ring; turn (vi), spin’ (Uralonet #746), which is semantically unrelated to ‘five’.
I must finally say that it would be incomplete of an answer if I did not say that the Eurasiatic macrofamily hypothesis is definitely not supported by all historical linguists. As for me, I (at the moment) support a version of the Nostratic hypothesis that includes Afro-Asiatic, Zagrosian (Elamo-Dravidian), Kartvelian, and Eurasiatic (which includes Indo-European, Uralic, Yukaghir, Inuit-Yupik-Unangan, Chukotko-Kamchatkan, Nivkh, Turkic, Serbi-Mongolic, and Even-Manchu [those last three might belong to their own subgroup of Eurasiatic: Micro-Altaic]), and maybe Tyrsenian (Etruscan-Lemnian-Rhaetic), but not Koreanic, Japonic, or Ainu. I further think that Koreanic and Japonic are not (provably) genetically related language families. My version of Nostratic is not based on comparing a handful of numerals, but on regular sound correspondences in morphology and lexicon (Bomhard 2011, 2014, Reconstructing Proto-Nostratic, as well as everything Bomhard has written since, where he keeps updating his reconstruction in light of newer evidences and criticisms-- I too don’t agree with all of Bomhard’s proposed cognates, but I do agree with some of them.)
Below are some references:
academia.edu/6345901/The_end_of_the_Altaic_controversy - The end of the Altaic Controversy, Alexander Vovin (2005)
tinyurl.com/vx4v9fah - Lee and Ramsey, A History of the Korean Language (2011)
Serbi-Mongolic language family:
Edit: The 'join' stem is actually there as Proto-Uralo-Siberian *käte(-) 'join, joint (of hand)' in Fortescue's section of "Mid-Holocene Language Connections between Asia and North America" (Fortescue & Vajda, 2022:76). Reflexes are PFU *käti 'hand', PIY *katə- 'join', and perhaps Unangan katax- 'to beat (as with fist)'. I would need to see how (if at all) Bomhard's correspondences would be affected by Fortescue's cognate sets to be sure of a Proto-Eurasiatic root, but *kʷat-/*kʷät- would still be my reconstruction for 'to join', tentativy.
Edit #2: I am going to address your comments below.
Note, in my earlier responses I was not super clear about distinctions between different transcription schemes of various languages. Below /j/ and /dʒ/ are consistently used akin to their use in IPA.
“Proto-Kartvelian đor”: Proto-Kartvelian *jor- ‘two’ (Klimov 1964, Fähnrich 2007) [Mingrelian ž /ʒ/ < */j/-, a very normal sound change in the world’s languages. cf. Kazakh /ʒ/ < Common Turkic */j/-). Bomhard compares *ir- ‘two’ in Dravidian (in light of McAlpin’s new Zagrosian tree (2022) which sees Brahui-Elamite and Dravidian as two separate subgroups of Zagrosian, reflexes in Brahui and Dravidian for the stem make this Proto-Zagrosian *ir- ‘two’) – from Proto-Nostratic *jor- ‘two’ [Footnote 1]. Recall my earlier tentative Proto-Micro-Altaic *dʒur ‘two’ to explain Proto-Serbi-Mongolic *dʒur- (tentative) and Proto-Even-Manchu */dʒʊ:r/. Bomhard reconstructs no Proto-Nostratic phoneme whose reflexes are Proto-Mongolic */dʒ/, Proto-Tungusic */dʒ/, Proto-Kartvelian */j/ and Proto-Dravidian */j/ -- thus the Micro-Altaic *dʒur and Proto-Nostratic *jor- are entirely unrelated.
Bomhard’s comparison also is ultimately only from two language families (no Afroasiatic or Eurasiatic cognates), but it is a historically strong comparison given it is between Proto-Zagrosian and Proto-Kartvelian at the proto-stages – Proto-Zagrosian by the way doesn’t allow *yo- as far as I can tell-- PZ *i- or *e- would be a totally normal reflex of a pre-PZ *yo-.
On the reconstruction of jelan: Strahlenberg died in the 18th century, our understanding of Tungusic has developed considerably (really: begun) after that. All Tungusic languages sampled on Wiktionary (Even, Evenki, Oroqen, Negidal, Solon, Oroch, Udihe, Nanai, Orok, Ulch, Jurchen, and Manchu) have i-, except Negidal, which has elan beside ilan. The numeral has to be *ilan in Proto-Tungusic.
On the Uralic word for ‘palm’, thank you, I found it: Proto-Uralic *piŋз ‘palm, hollow of the hand’ (Uralonet #772) > Proto-Finnic *pivo. Let’s first get into PIE: PIE *pénkʷe ‘five’, *pn̥kʷ-sti-s ‘fist’, *penkʷ-ró-s ‘finger’ are clearly connected- perhaps the stem PIE *penkʷ- had primary meaning like ‘to grasp (with all five fingers)’ or maybe ‘to make a fist’ which can explain the meanings ‘five’, ‘fist’, ‘finger’. PU *piŋз ‘hollow of hand’ -- Fortescue (2022:102-103) in Mid-Holocene Language Connections between Asia and North America offers a tentative (marked with a ‘?’) Uralo-Siberian etymology, citing the form as PU *piŋi- ‘hollow hand’ (whence Proto-Samoyedic *peŋ ‘fist, flat of hand’), and comparing PIY (Proto-Inuit-Yupik) *piŋu- ‘push over’ [in West Greenlandic ‘hit with fist’], and Unangan hiŋu- ‘push’. The comparison of PIY and Unangan clearly suggests reconstructing PIYU *piŋu-. Fortescue provides the Proto-Uralo-Siberian reconstruction *piŋ(u)- ‘push with flat hand?’ No potential Proto-Chukotko-Kamchatkan cognate is given for this one (Fortescue 2022:145-46). The meaning ‘fist’ does show up secondarily in some reflexes of the Proto-Uralo-Siberian *piŋ(u)-, so it’s plausible the PIE root *penkʷ- is connected if its original meaning was ‘fist’ as Blažek (1999) suggests. Plausible semantically that is. The correspondence is not very regular phonetically, the reflex of a Proto-Eurasiatic form like *pVnkʷ- with final -kʷ- should yield a *-k- in Proto-Uralo-Siberian that is not present, not in Proto-Uralic nor in the potential (in my opinion, more likely than PIE connection) PIYU cognate.
Note also that the numeral meaning ‘five’ in PIE is a secondary derivation of unknown age (we just know that by the time the curtain comes up on PIE, *pénkʷ-e ‘five’ is there in the lexicon besides the relic of an unattested verbal stem *penkʷ-). It is possible that at some point in the past, the precursor to PIE had a separate unknown (to us) numeral for ‘five’ that was gradually replaced by *pénkʷ-e. Remember, it’s not actually that weird for numerals to be replaced within a language family- Luwian mauwa ‘four’ doesn’t even match PIE *kʷetwóres ‘four’-- but Luwian is unmistakeably Indo-European.
And this point brings me further to “Could not Bulgar tuirem mean 10, like Burushaski tóorum” – No it could not. As I mention in my answer, tuirem is not a numeral.
Edit #3: To answer your question "If the languages are not related, how these correspondences can be explained?"
As u/TKR said, coincidence. The Mbabaram word for "dog" sounds exactly like English "dog". That doesn't make them genetically related languages. We need regular correspondences to be established that can explain why the languages of that family look the way they do. That's the other key thing-- Proto-Indo-European "explains" Sanskrit, Latin, and Greek. In my view (but not everyone's) Proto-Eurasiatic "explains" PIE, and Proto-Nostratic "explains" Proto-Eurasiatic. Any precursor to Proto-Nostratic should be able to "explain" PN too.