Adam and Eve ate from the Tree of Knowledge of Good and Evil even though they weren't supposed because they couldn't stand the feeling of an available experience that they had not experienced themselves. That curiosity has survived in humanity to this day. So the importance of solving these math problems does not lie in "unravelling great mysteries" or breaking new ground in mathematical theory, or in finding new engineering applications. People solve these problems because they like the taste of apples, and no other reason. If engineers pick up the results and make something useful, that's good, but even if they don't we are left with something beautiful unto itself.
Slashdot Mirror
So pi doesn't have to contain itself, although it does contain approximations of itself. You will find a 3, 3.14, 3.142, 3.1416, etc....
roni
Adam and Eve ate from the Tree of Knowledge of Good and Evil even though they weren't supposed because they couldn't stand the feeling of an available experience that they had not experienced themselves. That curiosity has survived in humanity to this day. So the importance of solving these math problems does not lie in "unravelling great mysteries" or breaking new ground in mathematical theory, or in finding new engineering applications. People solve these problems because they like the taste of apples, and no other reason. If engineers pick up the results and make something useful, that's good, but even if they don't we are left with something beautiful unto itself.