Cogito ergo sum: Latin for 'I think therefore I am'. Briefly, the argument is also known as 'the cogito', and is an argument for one's own existence. It is due to Descartes, who believed it was certainly true.
Descartes believed the cogito is an irrefutable and certain argument for one's own existence. St Augustine, more than thousand years earlier, had a somewhat better argument, involving a similar form and same principle: "Fallor ergo sum" - if I am mistaken, then I still exist, even if I am mistaken.
Both Descartes' and St. Augustine's do not really prove more than that human beings can argue on the basis of definitions or meanings of words, and that they easily can make mistakes while doing so, especially because of wishful thinking.
This can be shown by several elementary arguments, all with the same sort of logic as used by the arguments of Descartes and St. Augustine. Thus, one may consider "I dream, therefore I am"; "I think I am an illusion, therefore I am an illusion"; "I am an illusion of something unthinkable, therefore I am not"; or "I am a computer program that cannot think but that can generate grammatical apparently valid conclusions, therefore I am a thinking genius".
And in this context here is Ambrose Bierce for the edification of the reader
"...Descartes, a famous philosopher, author of the celebrated dictum, Cogito ergo sum - whereby he was pleased to suppose he demonstrated the reality of human existence. The dictum might be improved, however, thus: Cogito cogito ergo cogito sum - 'I think that I think, therefore I think that I am'; as close an approach to certainty as any philosopher has yet made." (The Enlarged Devil's Dictionary, entry Cartesian)
As said, St. Augustine argued similarly, and did so about 1200 years earlier. He argued, more plausibly "Fallor, ergo sum" i.e. "I may be mistaken, so I am".
But in any case, such arguments do not hold, however plausible they may seem to be. For if Descartes may be misled by the devil in believing he sees a fair damsel where there is none, there is no reason to believe that the devil may not make an automaton - or some ape - that mistakenly believes itself to be the philosopher Descartes, while being no such thing, and the same may be replied to St. Augstine's more modest "If I am mistaken about what I think, then at least I think": No, at best there is some appearance that appears to say or think this: all that is logically valid in either Descartes's or Augustine's arguments is to the effect that if there is an experience of the so-and-so, there is an experience - but one may be quite mistaken about what the experience is an experience of, for there may be no so-and-so at all.
This is less fanciful or hardheaded than the reader may believe (who might incline to "Come on! I know at least that I exist, whatever you say, for whatever the explanation, there are my feelings"), because, like a symphony, the sense of self a person has may be the product of many interacting contributors none of which itself is or has a self. If so, the sense of self may still be useful and important, or it may be a useless or even - as the Buddhists and many mystics claim - a harmful illusion (not so much an optical illusion as an illusion of the I), but at least in that case what we hold to be our self is less of a unit than seems suggested by simple pronouns.
Who wants to know more about the cogito, I refer to my sections on Descartes and Russell. And whoever really desires certain knowledge, should seriously consider logic and mathematics.