I can doubt everything, except one thing, and that is the very fact that I doubt. Simply put - I think, therefore I am

If I found any new truths in the sciences, I can say that they follow from, or depend on, five or six principal problems which I succeeded in solving and which I regard as so many battles where the fortunes of war were on my side.

The greatest minds, as they are capable of the highest excellencies, are open likewise to the greatest aberrations; and those who travel very slowly may yet make far greater progress, provided they keep always to the straight road, than those who, while they run, forsake it.

How can you be certain that your whole life is not a dream?

Situations in life often permit no delay; and when we cannot determine the course which is certainly best, we must follow the one which is probably the best. This frame of mind freed me also from the repentance and remorse commonly felt by those vacillating individuals who are always seeking as worthwhile things which they later judge to be bad.

For how do we know that the thoughts which occur in dreaming are false rather than those others which we experience when awake, since the former are often not less vivid and distinct than the latter?

Here I beg you to observe in passing that the scruples that prevented ancient writers from using arithmetical terms in geometry, and which can only be a consequence of their inability to perceive clearly the relation between these two subjects, introduced much obscurity and confusion into their explanations.