You Can't Teach an Old Dog New Tricks

As someone looking to enter the field of mathematics, I am often told how most mathematicians do all their best work by the age of 30. And then of course after that, you have little chance of making any significant contribution to the field. The standard explanation for this is that people hit their creative peak in their early 20's and it decreases from there. (Yes, mathematics is a very creative field!) However, I am starting to see this in a different way.

Instead of viewing the young mathematician's success as a matter of creativity, I think it might be a matter of stupidity. Well, maybe not actual stupidity, but a lack of mathematical knowledge. I believe that what hinders older mathematicians is their massive amount of knowledge. This may sound odd, but after so much exposure and experience it becomes habit to look at problems through the lense of what you know and using the same methods repeatedly rather than considering problems from new angles and approaches. This is the advantage of the young mathematician for he/she looks at a problem with a blank slate and is willing to consider approaches the veterans might not. It seems to me that a young talented student's lack of knowledge is what spawns their creativity. As the saying goes, you can't teach an old dog new tricks.