Evidence is building that High intensity interval training, e.g. Tabata sprints, is more effective at physical conditioning than low intensity endurance techniques. In terms of weightlifting, "low-rep, high-weight" workouts seem to be better than "high rep, low-weight" workouts.*

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?

My experience seems to reflect the latter being more effective. I spent a lot of time my last year or two of undergrad grinding through a bunch of relatively easy calculus problems in order to finish up my degrees in a reasonable amount of time. In my second year of grad school, I took a measure theoretic probability & statistics sequence that was the opposite - a small number of problems, but each one was a struggle. It was rare that I could finish more than 25% of the problems the first time I attempted them. Unsurprisingly, I felt like I improved much more in mathematical ability after taking that sequence than I improved after my undergrad calculus grind. The effect seems stronger than this though - I felt like the measure theory sequence improved my ability to do difficult yet standard calculus problems more than the calculus grind ever did even though I wasn't actually doing those types of problems during the measure theory sequence. The effect was probably mediated through improving my general mathematical/logical reasoning abilities. Now these are just my impressions - untrustworthy for the whole gamut of reasons - plus even if we take them at face value there's a ton of confounders. Nonetheless, it's Bayesian evidence. Anyone else have a similar experience?

* I'm not an expert here and could very easily be wrong. If you have evidence one way or the other to share, please allow me (and others) to update.