AUMathTutor, most of those unsolved problems are well-known (the OP asked for ones which are little known), and furthermore I believe that the last three are ill-posed (since english has no formal grammar and angels and woodchucks are afaik undefined).
Actually, the P=NP problem is quite poorly known, if you look at how many people in the world have ever heard of it and divide by the number of people in the world.
Far more poorly known if you look at how many people understand what the question is actually asking.
And I think the English sentence one is actually not so ill-posed. You might have to make certain stipulations, but you do that all the time in any mathematical problem.
- Does an odd perfect number(s) exist?
- Prove the abc conjecture.
- Explain the role of modulus in Parrondo paradox.
- What is the probability that an infinitely small object would become finitely big?(well "big bang" theory :)...no comment..
- Prove the Riemann hypothesis.
I can give you many more - but those are OK for now :). The problem about the probability is more than obvious(0 probability for such thing to happen regardless of the fairytales about "singularity"!...) - it's interesting how it objects the big bang funny hypothesis of singularity. I believe in the bang - just don't believe in the idiotic religious assumptions about creation. Religion and dogmatic science(why not every science???:) should be forbidden by law...including present day big bang assumptions.
Anyway... :)
The problems above can be formulated without a single differential equation and believe it or not - many people haven't heard of the Riemann hypothesis - including many math teachers in economically developed countries.
