I was reviewing a video of the Fermat Fest held to celebrate Andrew Wyles (sp?) solution of Fermat's Last Theorem to see if it was reasonable for my Algebra class to view (I've been doing a little with Diophantine problems so it probably is). Andrew was talking about when he was ten of trying it for the first time. I can remember when I 'tried' also (with less result :) ) and probably others can remember also. It was an accessible problem and definitely a challenge.
Some of the panel members were talking about this accessibility and the fact that some major mathematics was being done later in one's career because of the need to gain more background. I began wondering what were the new accessible challenges for our 'teens'. Are there any more accessible, easily stated, unproven mathematical statements or are those days over?