Although much of Newton’s work is accessible only to specialists, some of his results can be understood and appreciated by the rest of us. In this post I will describe one such investigation – his effort to determine how the force of gravity decreases with distance from the earth. The results were very significant in a scientific sense, and the way he carried out the work shows astonishing insight and imagination.

It is unworthy of excellent men to lose hours like slaves in the labor of calculation.
Gottfried Wilhelm Leibniz

I have often told students that becoming good at math is a lot like becoming good at a sport or at playing an instrument – practice is extremely important. Hours and hours of practice.

However, there is a [...]