Thanks for your comment.

Also, this may not be true just for math but for other areas as well.

I completely agree. I wrote about math because it's what I know best, not to suggest that the phenomenon that I allude to is true for math more than for other fields. If I incorporate this discussion board posting into a top level posting, I'll mention this.

I addressed the rest of your comment in my revised post. (I accidentally posted to the discussion area prematurely before completing the post that I was working on - still getting used to the discussion area.)