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.
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