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When does one consider math learned ?

When you make it your own somehow. Mathematics is not a spectator sport. Nor is it about rote-learning, although some people try to get by on that.

But there's a problem, you have to integrate other thinkings, findings and concepts, it cannot only be an internal game.

When you can write a proof for every mathematical statement that is true.

What about finding creative approaches to unproven statements ?

beachbum8029 is being silly because the Godel incompleteness theorem stats that is you cannot prove all true statements.

or you can prove some false statements