It’s usually called Euler’s Identity, after the great Swiss mathematician Leonard Euler, and several polls of mathematicians and physicists have bestowed on it titles such as “the greatest equation ever”

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 [...]

Are there an infinite number of prime numbers? Or maybe there is a largest prime number, and every number after that is composite. To get a little insight into this, we might start listing the prime numbers, beginning 2, 3, 5, 7, 11, …, to see if any pattern emerges. About all that is [...]

On the morning of August 2, 1927, a young electrical engineer named Harold Black was riding the Lakawanna Ferry across the Hudson River on his way to work in Manhattan, where he was employed by Bell Laboratories. Black was pondering an important problem that he had wrestled with for several years without making any progress. [...]