Hmm. I don't think so, but, feel free to expand your opinion (why do you think it should be "I am, therefore I (can) think"? Maybe you have an interesting point to make?)

Re: etymology, it's pretty much "think => exist."

Re: conceptual level: well, one of the texts where this whole concept/causal-chain is introduced is in his "Meditations on First Philosophy"[1], in particular, in Meditation 2.

Very (very) roughly (and from bad memory), the idea is that one can first start casting into doubt everything that there is (skepticism as a method) (this is Meditation 1.) When you abstract enough times, you can start doubting even the certainty of things which may seem true in themselves (this latter notion is an endless field of debate in itself; see e.g. Quine's "Two Dogmas of Empiricism"[2]) - cliche example is "2+2=4."

Say there's a deceitful daemon: each time the thought "2+2" is produced, the daemon "intercepts" the answer and produces a "5". (Yes, I'm saying that Descartes may be one of the originators of the concept of a MitM, ha!) (Also, this doesn't work so well with mathematics, since again, one could say that mathematical statements are "analytically true", and it's simply not true that one may mistake a "5" for a "4". But imagine something more mundane: each time you think if there is a god, the daemon deceives you into thinking there isn't one; whatnot.)

So now you generalize the doubt process enough to start doubting whether anything exists, what-so-ever. The point is not so much in thinking that there isn't anything, but in removing certainty from usual ontological assumptions (what (kinds of) things exist.)

So now you're not certain if there is an "I": you are able to doubt it.

But then Descartes says that this very process of certainty-removal requires an operation (he doesn't use these words, did I say this is extremely rough): namely, the "doubt" itself. "Doubts are to be had."

Or, if you will (and closer to D. (I think)): if an evil daemon can cast into doubt even the existence of your own self - it it can deceive everything, etc. - there needs to be a something to be deceived. Or at the very least, the process of deception (or: of doubt) does happen (if you want to cast everything into doubt.)

So if you doubt that anything exists and hence can not be certain of anything, then it so happens that this requires doubt "to happen." Hence "doubt exists." (He also says (I think) that, basically, "clearly since I am doubting right now, doubt does happen". A kind of phenomenological argument, which doesn't really stick with me, fwiw. He then starts using the notion of "clear and distinct perception", and that's where things go downhill imho (Meditation 3, a (kind of circular) proof of God, etc.) But I have few qualms about Meditation 2, and this includes cogito ergo sum.)

(You could say that the only thing one can be certain of is that "there are thoughts" (not an "I"). I would agree with this. "Thinking exists." And since "thinking" would be, well, thinking this thought, it is certain that "thinking exists.")

edited to include two paragraphs (this+next one): So now we (hopefully) have something that exists for certain; thoughts exist (or somesuch.) Descartes claims a bit more: this entity that does the thinking (there does need to be an agent which thinks those thoughts (is what he assumes, I guess)) - let us just say it is "I", who does the thinking/doubting - when we trace back the process by which we concluded that we are certain that it exists - involves us discovering that thinking/doubting definitely does take place. Hence "I think; I exist."

(I suppose you could have a concept of an "I" that is simply instrumental (doesn't have independent substance (oof, this is dangerous/slippery territory)): thoughts can have relations, and related thoughts can be seen as "bundles", and this process producing continuing interrelated bundles is "the I doing the thinking." But, I'm not sure of this at all. Maybe D. would say that the deceiving daemon needs to deceive something, if it does actually do any deceiving; and if this does happen, then this "something" which is being deceived is (let us call it an) "I".)

Now, to go from cogito ergo sum to proof of God and subsequent re-establishment of certainty about the whole world - that is something else. And I don't think that he does a very good job at it. (And this is "usually", "generally" agreed upon.)

[1]: https://en.wikisource.org/wiki/Meditations_on_First_Philosop... - which btw is an easier read than you might think, if you're curious enough!

[2]: http://www.ditext.com/quine/quine.html