(Not just) numbers are very old words
Common roots of some numerals like THREE, but also words like PATH or *KRSNOS (BLACK) across many language groups.
Do some words have common roots older than 10,000 years? There was a question on Quora (here) re. similarities between Proto-Indoeuropean (PIE) and Proto-Austronesian (PAN) numbers 1, 2, 3. Roughly going like this: Did anyone notice that PIE and PAN have similar numbers for one, two, three? Well, yes, I noticed, and not just in PIE and PA, and not just in the first three numbers. Not just in numbers as I want to show below.
Surprisingly, some linguists see just "coincidences" and deny this is due to common roots of language groups. Arguing that they are mostly differently shaped and lexically different now, "always" have been too far apart. Even though there are still traces of regular changes and lexical similarities across language groups in very old words, even though there is scientific work on quite some words that must be older than the present language groups and most probably have common origin, there is still fierce denial about that among part of scientists, while other part of scientist advocate their common origin. Well, did people start to speak in many places out of clear blue, or is it quite obvious that there must have been a Proto-Sapiens language before all the haplogroups and ethnic groups split and went out of Africa? If all Y-DNA haplogroups share a common Adam and all mitochondrial DNA haplogroups share a common Eve, why would languages not share a common Proto-Sapiens language? As someone who studied about 15+ languages from various language groups (to a different degree), it is quite obvious to me there are lots of words with common roots that must have preserved to this day, with more or less change. I found lots of striking similarities with identical or similar meaning in such geographically (and not just geographically) distant languages as Japanese and Basque, Japanese and Dogon, Basque and Czech, Basque and Hebrew, Japanese and Hungarian etc.
But first let's look at one, two, three in Proto-Indoeuropean and Proto-Austronesian. 
PIE: 1—*e̯oinos/*sem, 2—*du̯oe̯, 3—*trei̯es
PAN: 1—*esa, 2—*du(s)a, 3—*telu
The Proto-Indoeuropean and Proto-Austronesian numerals for one - two - three are just three examples of many many similarities in words that are certainly old, basic and must have existed tens of thousands of years ago. For example words for 1, 2, 3, 6, 7, I, my, you, woman, earth, goat, heart, head, hand and foot or food must have existed since the dawn of language. Unlike words of modern origin. These could not have existed as what they describe has not existed or people did not know it existed. Like plastic, bomb, radio or deoxyribonucleic acid. But numbers... it is a very different story. 
These must have existed tens of thousands of years ago. Not numbers for "million" that nobody needed. But one, two, three or even six, seven. Could some of them have preserved relatively unchanged or having changed little? Certainly they could, just like some other words (as documented in: Merritt Ruhlen: The Origin of Languages). One of these old words is the word for water (*akwa in many European, many Asian, many Native American and many African languages). There are quite many of them derived from *akwa actually, so coincidence with no common root is as probable as a meteorite falling from sky and shaping itself into an airplane during that flight). Not just water (akwa), but also tik (one/only/finger), pal (two, half) and more... See Merritt Ruhlen's book. But let's get back to numbers. First look at my collection of numerals in many languages of many language groups, including ancient languages. I highlighted some that probably have or could have common roots. The most of the similarities are in three, six and seven as you will probably see there.
Three, telo, thalata, ilu, hilur
Numerals are usually very very old words. I believe none of 1, 2, 3 in PA and PIE are accidentaly similar, they are probably cognates, not false cognates. 
But especially the number three is very interestingly similar in many language groups around the world. How old could possibly be a word for 3 and why would it not be possible to retain part of the original sound from Proto-Sapiens? 
Proto-Indoeuropean *treyes and Proto-Austronesian *telo. Now add to that Proto-Semitic *talát-. By the way, many Niger-Congo languages have *tat- for three, and some Na-Dene Native American languages have ta-. Possibly even Proto-Uralic *kolm- (T often changes to K or vice versa) is not far from some potential common ur-word. But also Proto-Japanese *uru-pu derived most probably from Proto-Altaic *i-lu/u-lu and who would not dare to notice its similarity with Proto-Basque *(h)ilur
If anyone doubts Proto-Basque and Proto-Altaic similarities in numerals (they are geographically too far from each other, some would say), look at one, two, three
*bade, *biga, *(h)ilur in Proto-Basque 
*biuri, *pioke, *ilu/ulu in Proto-Altaic. 
Rather clear cognates I think. If just one numeral were similar, it could be coincidence, but three? Hardly. (There are many more between Japanese and Basque - aiz and ishi for stone, toki and tokoro for place, xuri (read: shuri) and shiroi for white, etxe (read: eche) and uchi (house), txoria and tori for bird etc.). Back to number one in Proto-Altaic: *biuri and Turkic bir, English has that same word not as "one", but as "first" and Slavic languages have it as prv-, Lithuanian as pirmas meaning first.
But back to numeral THREE. My hypothesis is that there probably was some T-L- for the numeral three in some very very old proto-language like Nostratic, Eurasiatic or Proto-Sapiens and this root is very, very old (possibly 10s of thousands of years). T-L- stayed as T-L- in Austronesian and T-L-T in Proto-Semitic, while it changed to TR- in Indoeuropean. And K-LM in Proto-Uralic/Finnougric. (There is more of this change pattern from L to R between Proto-Semitic and PIE, like e.g. in the certainly old word for “heart”: K-RD in PIE, but Q-LB in Semitic.) Proto-Altaic could have lost the initial T to get i-lu from T-L-, possibly before it split with Proto-Basque which had (h)ilur. It could have been (k)ilur before, reminding of PU *kolm. And (k)ilur could have developed from tilu(r). This way we could possibly get to T-L in so many language groups or their predecessors: Proto-Indoeuropean, Proto-Semitic, Proto-Altaic, Proto-Uralic, Proto-Japanese, Proto-Basque, and possibly also Proto-Niger-Congo.
Kara, kuroi, krsnos. Path, pateo, put, bade, bide etc.
If we do not want to stay in the realm of numerals for discussion of old ur-words, let's go to the colour of black. Even words for “black” are very similar for so many language groups that they can hardly be a coincidence unless there is a too difficult case of denial: *krsnos in Proto-Indoeuropean, *kara in some Turkic languages, *karuppu in some Dravidian languages and *kuroi in Japanese. I discovered this myself coincidentally so I do not know whether professional comparative linguists know about these "black" cognates. Not coincidences to me, not false cognates, too many too similar from too far apart geographic regions. Just like we can find the same haplogroups in very distant places, we can certainly find very old cognates (or very old borrowings if not in too many language groups).
Let's add one more such word. It is path in English, Pfad in German (we are still in Germanic languages, but let's move further away). Slavic: put in Serb and Croatian and puť in Russian (and Putin, by the way, is derived from puť). In my mother tongue Czech it preserved as pouť (pilgramage, wandering), pata (=heel, foot) and verb putovat. Greek: pateoOld Persian pathi. (Also foot, pedes, pedestrian are related). But we are still in the Indoeuropean group, right? So let's move further outside our big language group and alow me to see P-T as similar to B-D (this is quite a common change). So we get to Basque and Mali Dogon and their bide and bede. Both meaning path. Hardly a coincidence, what do you think? Meaning exactly the same as path, but wide outside Indoeuropean languages in both cases. This means we just found a word that may come from the Proto-Sapiens language or any of its early descendants. Linguistic archaeology is fun.
And so we could go on and on and on... Und so weiter und so fort, as Germans say.
Links with similar words:  Japanese cognates with foreign wordsLinguistic connections between Basques and Slavs. Basque vs. Niger-Congo Basque-Ainu possible connections.  The Finnish-Japanese connection.