I'm about two-thirds through the audiobook version of Daniel Kahneman's Thinking: Fast and Slow. This book is a useful corrective to Malcolm Gladwell's recent bestsellers Blink: The Power of Thinking Without Thinking and Outliers: The Story of Success. Kahneman doesn't deny the usefulness of intuition, but argues that intuition has its limits, even for experts. (For example, even the most experienced pediatrician assessing a newborn's health may be better off relying on the routine of the Apgar score than a subjective evaluation, even though that subjective evaluation is itself generally very accurate.)
Outliers popularized the 10,000-hour rule: years of deliberate practice in chess (or guitar, or corporate taxation, or...) will allow one to develop an expert's intution. Kahneman (a behavioral psycholgist, winner of the Nobel Prize in economics) doesn't discount the usefulness of the grandmaster's intuition, but in summarizing his body of research for a popular audience, he argues that such intutition is a type of "fast thinking" that is wrong far more often than experts care to admit. Chess is a concrete game, and software engines have repeatedly proved the value of colorless algorithms over romantic intuition. (Botvinnik's highest praise for his archrival was—I paraphrase— "Smyslov had a very strong algorithm in the 1950s.")
But humans play chess with a clock, and in human-vs.-human play, we don't have time to figure everything out. (We try to do that in the post-mortem, and then at home, and after that we feed our analysis to the computer to check our results.) So the intuition of a Capablanca, Kramnik, or Carlsen is a very good thing for human players to have.
How to translate these insights into studying chess and teaching chess? Algorithms are essential in pawn endings, but knowing general principles about the outside passed pawn, protected passed pawn, and the opposition are pretty darn important, too. And knowing the general principles of rook endings (defending king belongs on the short side, checking distance, recognizing the preconditions for a successful frontal defense) is important, but sometimes you gotta calculate, too.
Thinking: Fast and Slow is strongly recommended reading for folks in business and the social sciences. It might even be tangentially useful to chess players, though I'm not sure how....