>If you ask a current PhD student how hard things are and then wait 10 years and ask how hard their PhD was you will get totally different answers. I'm not sur

>If you ask a current PhD student how hard things are and then wait 10 years and ask how hard their PhD was you will get totally different answers. I'm not sure this is true. From my own experience studying math, I often heard people remark upon how hard it must be and how only a small subset of people would ever be able to understand the concepts in a graduate level math course. I don't agree with this at all. In my opinion, the reality is that learning is incremental, and everything new builds upon something that you've previously learned (hopefully). This is particularly true with math. I don't think that I had to work any harder to learn linear algebra in undergrad than I did to learn differential calc in highschool. I think the delta in difficulty between geometry and algebra, pre-calc and calc 1, diff eq and real analysis, is basically the same. But that is only true if you have a solid understanding of whatever came before. This is of course a minor nitpick with your last point, because I agree with your overall point that k-8 learning is important. I think it's important precisely because of the reasons I mentioned before: you need to have a strong foundation in 'last years' concepts if you are going to succeed in learning this years.