Today We Broke the Bernoulli Record: From the Analytical Engine to Mathematica
In Mathematica, a core principle is that everything should be scalable. So in my job of creating algorithms for Mathematica I have to make sure that everything I produce is scalable.
Last week I decided to test this on one particular example. The problem I chose happens to be a classic. In fact, the very first nontrivial computer program ever written—by Ada Lovelace in 1842—was solving the same problem.
The problem is to compute Bernoulli numbers.
Bernoulli numbers have a long history, dating back at least to Jakob Bernoulli’s 1713 Ars Conjectandi.
Bernoulli’s specific problem was to find formulas for sums like .
Before Bernoulli, people had just made tables of results for specific n and m. But in a Mathematica-like way, Bernoulli pointed out that there was an algorithm that could automate this.