Ada Lovelace's Calculation of Bernoulli's Numbers Ada Lovelace's Calculation of Bernoulli's Numbers Rainer Glaschick, Paderborn, Germany (
[email protected]) http://rclab.de/analyticalengine/ 2016-09-29 1. Introduction In 1843, an article with the title Sketch of the Analytical Engine… [ML1843] was published, that contains an extensive and on its level fairly complete description of Charles Babbage's plans for a fully automatic computing engine. Its name has been motivated by the aim that it should be able to numerically solve all computations in the field of mathematical analysis (p.688): … all the Operations of analysis come within the domain of the engine. The article consists of a translation of a report by L.F. Menabrea, originally written in French, and supplements designated as Note A to Note G. The author was Augusta Ada King, Countess of Lovelace, who signed the Notes not by name, only with her initials A.A.L. — for the reasons her biographies should be consulted, that are also the place to the never-ending discussion about her mathematical ability, while this article strongly supports her excellence. The closing Note G got much attention, because the corresponding table now is regarded the first fairly complex program ever. The use of machine instructions, variables and a conditional loop is easily seen; but it is instructive to look into the very details of the program — which few people might have done, not only because several typos are not widely known (the most complete and reliable source seems to be [MCK1989], in particular see p.