Mistakes are always a part of the process and are one way to learn. However I don't think we would have had Ramanujan if he were left to rediscover all of math

Mistakes are always a part of the process and are one way to learn. However I don't think we would have had Ramanujan if he were left to rediscover all of mathematics on his own. Having an expert validate your insights or point you in the right direction can speed up the learning process a lot.