Erik Hoel on the key ingredients for successful tutoring—
[T]he key ingredients, judged from some of the most stand-out and well-documented accounts, are
(a) the total amount of one-on-one time the child has with intellectually-engaged adults;
(b) a strong overseer who guides the education at a high level with the clear intent of producing an exceptional mind (in Mill’s case, his father, in Russell’s case, his grandmother, in Hamilton’s case, Knox, and we can look to modern examples like mathematician Terence Tao, whose parents did the same);
(c) plenty of free time, i.e., less tutoring hours in the day than traditional school;
(d) teaching that avoids the standard lecture-based system of unnecessary memorization and testing and instead encourages thinking from first principles, discussions, writing, debates, or simply overviewing the fundamentals together;
(e) in these activities, it is often best to let the student lead (e.g., writing an essay or poetry, or learning a proof);
(f) intellectual life needs to be taken abnormally seriously by either the tutors or the family at large;
(g) there is early specialization of geniuses, often into the very fields for which they would become notable (even, e.g., Hamilton’s childhood experience with logistics making him an ideal chief of staff for Washington’s war);
(g) at some point the tutoring transitions toward an apprenticeship model, often quite early, which takes the form of project-based collaboration, such as producing a scientific paper or monograph or book;
(h) a final stage of becoming pupil to another genius at the height of their powers, often as young adulthood is only beginning (Mill with the early utilitarians like the Bethams and his father, Russell with Whitehead, Hamilton with Washington).
From there, they are off and running. Earlier on in history, they often eventually became tutors themselves, as if they were an organism completing a life-cycle and returning to the place of its origins (e.g., Huygens, who was tutored by famous scientists of the day, tutoring Leibniz).