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To me, conjectures seem less useful than a meteorologist offering weather predictions.<p>Aside from mere intellectual entertainment, they are worthless in the practical sense. They cannot be used in proofs, nor aid in solutions of other problems. They can’t even suggest if I would take an umbrella.<p>They are little more than the type of ramblings from people who drink heavily after a day’s work.
Go tell me how many conjectures have been proven over time....<p>It's only useless to study a conjectured if their never solved, and since we can't look into the infinite future it's only solvable if we learn how to send messages back to the distant past we can never tell if it gets solved or not.<p>With that said, theirs a lot of conjectures that wouldn't help anyone if solved, so maybe pick the most useful ones at first like P=NP.