That involves new ideas and not just probability-guided regurgitation of data, so no.
No amount of chanting "meat computers" or citations of Blade Runner change that.
I'm not saying LLMs can't contribute to solutions with sufficient nudging and guidance from other means, but no, I don't see them on their own solving unsolved problems just by having sufficient totally-non-supersititious belief in the imminent spontaneous rise of the Singularity(tm).