There are loads of maths problems that look (potentially) completely trivial but which have never been solved, despite considerable effort over the years and even centuries and millennia. It's all the more amazing when one thinks of the many subtle and intricate problems that have been solved, sometimes a long while ago.
One example that comes to mind is the Union Closed Conjecture. Denote a set by curly brackets, as in python, so for example { 1, 2 } is the set comprising as its elements the integers 1 and 2. A set can also comprise other sets, such as { {3, 4}, { }, {1} } (where that example includes the empty set as an element). By definition, a set cannot contain repeated elements.
The union-closed conjecture states that for every finite set of sets, with at least one non-empty and such that the union of any pair of sets is also in the set, at least one element in the sets must be present in at least half of them.
Sounds potty, and absolutely plausible, but hasn't been proved to this day.
Good luck
One example that comes to mind is the Union Closed Conjecture. Denote a set by curly brackets, as in python, so for example { 1, 2 } is the set comprising as its elements the integers 1 and 2. A set can also comprise other sets, such as { {3, 4}, { }, {1} } (where that example includes the empty set as an element). By definition, a set cannot contain repeated elements.
The union-closed conjecture states that for every finite set of sets, with at least one non-empty and such that the union of any pair of sets is also in the set, at least one element in the sets must be present in at least half of them.
Sounds potty, and absolutely plausible, but hasn't been proved to this day.
Good luck
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