Philosophically, Descartes was concerned with the existence of reality.
i am i exist
Short answer: Descartes' doubt was like WWI - the doubt to end all doubt. Only by doubting everything could Descartes hope to find anything that was certain (even if the only certainty is that nothing else is certain!).
That he is sentient ie that he thinks.
Descartes did not invent polynomials.
Rene Descartes was a French mathematician who created coordinated geometry.
Descartes is certain that the mind and body cannot be parts of the same entity because of different functionality.
Descartes creates the evil genius in an attempt to throw everything that he thinks he knows into question. The evil genius has god-like power that he uses to deceive Descartes. Descartes cannot disprove the existence of such a creature. You cannot trust your thoughts in such a scenario, thus Descartes cannot be certain that any of the information he gets from his senses, his memories, his thoughts, or his beliefs is real.
i am i exist
Descartes uses the evil genius argument to get everything except what he can be sure is true off of the table. He asserts that there is an evil genius as powerful as God that is deceiving him about absolutely everything. He cannot be certain of any of his thoughts in such a scenario. He cannot be perfectly certain that this evil genius does not exist. As a result, it is impossible to fully trust anything in terms of senses, memories, thoughts, or beliefs.
Descartes' philosophy on reality actually shows that we cannot for sure know that we aren' dreaming. In fact, Descartes believed that we are not sure of anything, except for the fact that we exist because we use logic and reason. Sorry that this doesn't answer your question, but the point of this ideology is for others to try to show Descartes how we know FOR CERTAIN that we are not dreaming right now....harder to do than one would think.
Descartes hopes to find out what he can know for certain, without any doubt, about the world and nature.
That he is a thinking thing that exists.
Short answer: Descartes' doubt was like WWI - the doubt to end all doubt. Only by doubting everything could Descartes hope to find anything that was certain (even if the only certainty is that nothing else is certain!).
That he is sentient ie that he thinks.
Not sure what a "certain" plane is. The Cartesian plane was invented by Rene Descartes.
That the existence of God is something that we can be certain of.
Descartes believed that the truth must be indubitable because doubting leads to answers. The only thing he perceived to be certain was his own existence.