Christopher Smith wrote:
That is purely anecdotal. I work with a bunch of young math whiz's who are dripping with insights, and never had to memorize multiplication tables.
And you have selection bias because you are working with "whiz's". That doesn't invalidate either set of observations.
I work with a bunch of college students who can't estimate for crap because their basic arithmetic is so slow. And these are at least "above average" students because they have had at least a year of a CS degree.
Memorization of things like multiplications tables does not inherently provide insight. It is an enabler of arithmetic speed which leads to algebraic speed which leads to calculus speed.
It is the ability to calculate "with speed" that enables the ability to have insights.
Ask folks when the difference between O(n), O(n log n), and O(n^2) is perceptible on modern machines. The folks who don't use a calculator invariably finish first and give better answers.
This then dovetails into insight into "How do I trade off algorithmic complexity against algorithmic performance?" etc.
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