>>12500506I doubt any of the remaining ones are going to be solved soon. The only large problems which are currently receiving concentrated research efforts are ABC, twin prime, meta-mathematical work on resolving the CH, and only some paltry results on proving the RH.
Of course Physics and CS are concentrated on Yang-Mills and P=NP separately and constantly, CS is absolutely floundering with P=NP at the moment though. Yang-Mills is practically just a matter of housekeeping for physicists, it's essentially a statement about the boundedness and physical reality of certain quantum field theories, I don't know how much work has been put into it.