I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future.
Mathematicians aren't satisfied because they know there are no solutions up to four million or four billion, they really want to know that there are no solutions up to infinity.
As far as I know, only a small minority of mathematicians, even of those with Platonist views, accept the idea that there may be mathematical facts which are true but unknowable.
As I say, there was this movement to try to bring philosophers and mathematicians together into an organization where they would talk to each other. An organization wasn't effective unless you had a journal. That's about all I know.
