If you can't prove a theorem, then it's not a theorem, it's a conjecture. Conjectures are not as useful. For example, the Shannon-Hartley theorem tells us under what circumstances it is possible to decode a radio signal. That theorem lets us design, e.g., cell phone networks.

Theorems are useful in all sorts of unexpected ways. At the turn of the 20th century group theory was considered a worthless corner of mathematics, but understanding group theory allows modern chemical instrumentation to work.

edit:

> It seems like it's the full employment act for pencil pushers

> downvoters downvote instead of providing refutation. A lot in common with fundamental religionists

You've proven the downvoters right by piling one ad hominem attack upon another.