Compare 2 folders, copy uncommon to a new folder

Hello folks, I have a task of sorting 3120 pdf files into various folders depending on their topic. These are all research papers I have downloaded over the period of last 12 years. Was using a bilbiographic application to keep them in check, but after a decade, it failed. Now I have 3120 pdfs in One folder. These files relate to 6 different projects I work/worked on. I need to sort them to...