The binomial theorem states that for positive integers n, where are binomial coefficients.
The theorem was known for the case n = 2 by Euclid around 300 BCE, and stated in its modern form by Pascal in a posthumous pamphlet published in 1665.
Newton proved the Generalized Binomial Theorem around 1665.
I wonder if a Newton Bicentennial provided Gilbert with the idea for his lyric.
Sherlock Holmes described his nemesis, Professor Moriarty, as follows:
“He is a man of good birth and excellent education, endowed by nature with a phenomenal mathematical faculty. At the age of twenty-one he wrote a treatise upon the binomial theorem, which has had a European vogue. On the strength of it he won the mathematical chair at one of our smaller universities, and had, to all appearances, a most brilliant career before him.” (The Final Problem, 1893)I wonder if Conan Doyle had Gilbert's lyric in mind when he wrote this.
p.s. 1665-66 is known as Newton's annus mirabilis - his "wonder year". He invented calculus, discovered his laws of optics, formulated his law of universal gravitation, and discovered the laws of motion, which governed physics till Einstein. He was 24 years old. Makes you wonder why YOU are still alive, doesn't it?... what exactly have YOU accomplished?