Just for the record, while Descartes may have made some notable mathematical advancements for his time period, his entire cogito philosophy and the resulting dichotomy of mind and body destroy the entire concept of self, the "I" with whose existence he was so concerned. Any philosophy that destroys the self of an individual as he/she is aware of it cannot be taken seriously, as it defies the most basic understanding by which that individual exists. Additionally, once that self is destroyed the new self (essentially some unidentifiable mind Descartes claims to use for thinking) then comes under grave suspicion, considering the fact he cannot either pinpoint this new "self" that is simply a mind not identifiable with anything else in existence and the fact if his own self, with which he claims to think, is so greatly obfuscated, then how can he hope to discern anything about anything outside of this dubious "self"?
As for solipsism, it's an assertion that is by its very nature neither capable of being proved or disproved. One has to either presume the existence of a solipsistic universe or presume the contrary in order to be able to conduct any meaningful discussion/hypothesization concerning the subject. It is impossible to create a meaningful understanding, let alone argument for or against, the notion of solipsism from any sort of point of view that even vaguely approaches an objective one. Therefore, the discussion of solipsism is futile. Should the universe indeed be solipsistic the individual actually existing could never discover that fact with any sort of verifiable proof. Likewise, no individual being could prove beyond a shadow of a doubt that the universe in which he/she exists is not solipsistic.