Ok
Descartes
Buddha
Formal logic uses variables and usually these variables take on a constant as a value. Formalism is a surefire way of getting your point across because the structure of the argument is clearly visible. Think of it as an X-ray of arguments. They’re meant to clarify and are employed to expose bad arguments and linguistic sleight of hand or deceptive footwork. 
Not sure making a statement like (y=x) suddenly without explaining what y is, and how and where (y=x) came from, makes sense. Does it mean y is identical to x? or same value as x?
Because being identical has different categories.
Clearly visible with ambiguity on what it implies and what it is claiming under what ground and reasons.
We can introduce a variable as and when necessary. Identical, yes. Like in math we say, t = 0.123456.... Same for formal logic.
Ambiguity arises when you don’t restrict the domain. For example if I don’t limit the domain of discourse to fruits and I say, “there’s a big apple on the chair”, you might get confused and think I’m saying, “there’s NY on the chair.” 
Ok, let’s look at Cogito first. My concern here is that, it seems missing the links between Cogito and Sum.
Does Cogito entails logical consequence of Sum? It seems it is missing the ground for Sum. What entails Sum from Cogito?
Because “I think” statement is unclear. It is missing information what “I” is thinking about.
Thinking is always about something. You cannot just think and don’t know what you are thinking about.
It could be,
I think about tomorrow.
I think about my weekend.
I think about that I am existing.
I think about that I might not existing.
I think about that I don’t exist.
If it is the last example, then Cogito Ergo Sum seems a contradiction.
You’ll have to read The Meditations for that. People say reading is time well-spent. You can come back and post once you’re done. Hopefully they won’t penalize you for zombifying a dead thread. 
It sounds low effort / insufficient engagement, which is not argument for the point of discussion at all.
Please let us know if the any point is unclear to you, or if there is part that you don’t quite understand, then will try to explain.
I’d like to list the main players in this little I game
No problems. I find it a bit difficult to understand, for anyone to have opened a very interesting OP (Cogito and No-Self), but then refuse to keep discussing until we learn something on the topic or clarify on the concepts.
Asking questions on the unclear or obscure part of the arguments or statements is just part of philosophizing. If you cannot accept that, and find no point to even trying to think about the points and reply on them, then it is a shame.
What was the point for opening any OP, if that is the main methodology for discussions? But never mind. All the best & good luck.
It seems you want to help me see the puppeteer behind the puppets.
Not at all. I just thought you don’t understand my points, and if you specifically point out what part of my point you don’t understand, then I was going to try explain in different way.
I am not here to help. I am here to learn philosophizing by sharing ideas and views with others.
Not sure what you are even talking about now. Why talk about puppets suddenly?
Well, we have the dyads (Descartes, sum) and (Buddha, non sum). These dyads are further representable as (cogito, sum) and (dependent origination, non sum). These are consonant dyads but from them we get the dissonant dyad (sum, non sum).
As for the reference to puppets I might’ve meant (puppet, non sum) or (puppetmaster, sum).
Sometimes the effort and engagement are just not worth it.
Good luck with philosophizing. I’m surprised you didn’t intend to assist me. You sounded so helpful, so patient and understanding.
Is the I not important? Concerns of most people are about themselves. We need food, water, shelter, etc.. This leads us to the Buddhist obsession with ego, ultimately negating it (ego-death, aka anatta). Contrast this with Descartes having unequivocally proven to himself that he is (re the cogito). As some have said this apparent disagreement is likely a result of a simplistic reading of Cartesianism and Buddhism. However to say this is the case doesn’t quite scratch that itch. Of the many variables that are at play is Christianity, firmly planted in the minds of 17th century folks, philosophers included. Was Descartes like Newton?
The doctrine of sunyata also needs to be considered in this equation. It is easily mistaken for nihilism and hence the panic it triggers among Buddhists, who vehemently assert that Buddhism isn’t a religion of 0.
I’ve already brought up for discussion 3 of the 6 heretical teachers, which I’ll repeat here for ease of recall: Pakudah Kaccayana (eternalism: earth, fire, water, air, soul, suffering, pleasure are eternal), Ajita Kesakambali (no karma, no soul, materialism, death is annihilation, hedonism) and Sanjaya Belathiputta (the eel-wriggler ).
A little must be said about dependent origination. The canonical analog is the horse chariot. A horse chariot is a composite: Horse Chariot = Horse + Wheels + Carriage + Canopy + Charioteer. Viewed this way we see why a chariot lacks inherent existence. So the self/atman/soul must be like a chariot and hence it too is existentially compromised.
Descartes, on the other hand, proves the existence of the self in an elegant, and beautiful way: Cogito, ergo sum.
Well, this is true: I can decide when to (try to) think. What I should have said was I don’t decide on whether it is thinking, e.g. “now that’s a thought”, or “you’re not even thinking you’re just saying whatever comes to your mind”, “If you would just think about it, you’d see.”
I agree, but this “thinking” is not passive, but an activity.
A thing that thinks. What is that? A thing that…
doubts almost everything,
understands some things,
affirms this one thing – namely, that I exist and think,
denies everything else,
wants to know more,
refuses to be deceived,
imagines many things involuntarily, and
is aware of others that seem to come from the senses?
…These activities are all aspects of my thinking, and are all inseparable from myself. 2nd Med.
And so not a constant; not our nature that just happens, but something that is done.
But this is an imposed sense of “existing”, as in: here, instead of: not here.
Thanks to all the contributors for keeping the fire going.
There are issues with comparing the Buddha and Descarte. As Wayfarer opined, they’re from different times.
Questions arise, and though they’re ultimately apropos they’re not that helpful to the matter at hand, which is to find out how Descartes and the Buddha are similar or different.