Nice to see so many math-aficionados here. So here is one question I have always found intriguing. (Note that an answer to this question has been already given long b4 most of us here were born (u will be shocked to hear the answer) but it's such a delight to hear various (unique) opinions about this that i can't help posting this stale question once again.) In our not-so-long life, we have solved or tried solving a lot of mathematical problems. For the sake of simplicity, a "mathematical problem" here will mean a problem in which we have to either prove that a certain "mathematically well-defined " statement is true or false (and nothing in between (no fuzzy here)) . And I assume there have been problems that after a lot of tinkering and contemplation still remain unsolved. If the problem is one printed in a mathematics textbook , we suppose that it has a solution but we didn't have enough wit (one can blame his patience or lack of time too) to solve it. But what if a problem remains unsolved even when attempted by all great ppl from all around the world born at all times. (eg. GoldBach's conjecture - "Every even number greater than 3 can be expressed as a sum of 2 prime numbers": remained unsolved at least till one year ago). What can we infer about such problems : can we say that the problem is unsolvable ? or should we just settle it down by assuming that the problem is solvable but nobody has yet come up with a "brilliant" idea till now. To generalize, here are two questions: 1) Can every statement be proved or disproved (disprove = to prove the converse ) mathematically ? 2) Is everything that can be proved mathematically true ? Hoping for a nice discussion.