I wonder if something analogous is true for mental training. E.g., will you improve mathematical ability faster by grinding through a bunch of relatively easy problems, or by spending a shorter amount of time mentally exhausting yourself on problems that push your limits? Anyone know of any solid evidence?

What's the basis behind HIIT? If I remember correctly, it's that the high intensity activity kicks your metabolism up a notch, continuing to burn calories / seem active for a significant period after the training is officially complete. Is there a similar mechanism for learning and memory?

There's solid evidence that spaced repetition- like in the Saxon method- is demonstrably better than doing something once and moving on with little review. In general, it seems like practice is a very important part of mathematics ability.

There are also time-based effects for learning things before going to sleep- but I'm not sure how practical using those would be.