Here is the link to the Wikipedia article on this topic.
The Wikipedia article makes no distinction between levels of activity, for example, idle amusement versus study, nor does it bring in the effect of inertia to the discussion. Choosing idle amusement over study not only means loss of that amount of intellectual development, but also brings an increase in the propensity to make a similar choice in the future. (Hence the advice, “Don’t have any fun until you’re fifty.”, and the advice, “Lead simple lives, so that you may do complicated mathematics.”)
Here is the link to the Wikipedia article on this.
Here is the link.
a quote from the article:
“I define subjective rationalism as the practice of deductive reasoning, while attending to matters of probability and personal preference.”
— Gary A. Wenger
(suggested new terminology)
I would like to suggest the term ‘Wengerism’ for ‘the practice of deductive reasoning, while attending to matters of probability and personal preference’.
Note: The document downloads automatically, so I’m not giving any url for it.
(Also: There is also a related book available on Amazon.)
Pascal's Triangle: A Scaffolded Approach
Here is the link.
“The human mind is so constructed that it must see every perception in a time-relation—in an order—and every perception of an object in a space-relation—as outside or beside our perceiving selves. These necessary time-relations are reducible to Number, and they are studied in the theory of number, arithmetic and algebra. These necessary space-relations are reducible to Position and Form, and they are studied in geometry. Mathematics, therefore, studies an aspect of all knowing, and reveals to us the universe as it presents itself, in one form, to mind. To apprehend this and to be conversant with the higher developments of mathematical reasoning, are to have at hand the means of vitalizing all teaching of elementary mathematics.”
— Nicholas Murry Butler
“Nothing is of greater importance than the early instruction of youth.”
— Peter Stuyvesant