Although I concede that there is some truth to the belief that the greatest conceptual breakthroughs in mathematics are made by younger mathematicians, I think it has led to the mistaken idea that older mathematicians rarely do anything significant.

I just don't think it's that uncommon for top mathematicians today to be productive after they're 50. Atiyah and Bott did great work after they were 50. It seems to me that so did Singer. Although most mathematicians slow down after they are 50, so do most non-mathematicians. But there are not a few exceptions to this.

And is any of this that different from other fields?