It’s all about what “new” means. It is possible to prove something in a very tedious way using preexisting techniques. There have many times in history been new ideas which are not just very impressive applications of old techniques. I’m still not aware of any famous problem in mathematics being solved by an unambiguous introduction of a genuinely new idea or semantic concept in this sense, as the candidates I previously had in mind have fallen into question by new findings of non-cited work; i.e. many if not all it seems have been impressive applications using ideas from known frameworks. I don’t know if this will continue into the future or not, but I think it’s important to try to make an honest assessment of reality at all times.
Of course in isolation it is a strict positive to have a verified truth value to any particular statement. Mathematicians currently are advocating for the idea that human understanding greater than this also be prioritized. There are in fact utilitarian arguments for this but I won’t go into everything here.
Of course in isolation it is a strict positive to have a verified truth value to any particular statement. Mathematicians currently are advocating for the idea that human understanding greater than this also be prioritized. There are in fact utilitarian arguments for this but I won’t go into everything here.