No, it's just what logic and maths is. Wanky for some, but as Bertie Russell
said, it has its own severe austere beauty. Not to everyone's taste, of course.
As to that old chestnut, "useful". It's not up to logicians and mathematicians
to necessarily find something useful immediately. G.H. Hardy (a top-knotch
mathematician and the man who brought Ramanujan to Cambridge) believed that
nothing he did would be of any use to engineers or the military. He was only
interested in maths and its techniques as a creative art. Tough luck for him
that 50 years later his work found great application in cryptography and several
other fields.

EDIT: His actual quote was:
No discovery of mine has made, or is likely to make, directly or indirectly, for good
or ill, the least difference to the amenity of the world.
Of course, if you want to get a grant or funding you had better find some way of
tying it to the real world. Only arty wankers get grants for truly useless
projects.
Finding techniques and patterns within logical or mathematical systems can also
be immensely "useful" to other professions, e.g. physics, engineering and other
sciences, and they can hasten their progress. The logicians and egg-heads who
work on those problems usually do not have to have any particular science, or
field of endeavour in mind while they work. So, what is useful is not always of
interest to them. Pure research doesn't always "pay off", but it can do so in
unexpected ways and enable enormous leaps in progress. Think of the improvement
of the net, its bandwith and capability over the last 20 years. Shannon and
many others made it possible with their work 50 years ago.
Just for the record, all my work is grounded in "reality" even though the actual
objects I study (infinitely thin wings, "ideal" fluids, arrangements of
impossibly thin ships, etc) are not always buildable. Engineers were put on
this planet so eggheads like me don't cripple their typing fingers with lumps of
metal or rock.