Charles Babbage, Ada Lovelace, and the Bernoulli Numbers

TL;DR

This paper revises the historical view of Ada Lovelace, highlighting her mathematical contributions and her role in developing an algorithm for Bernoulli numbers alongside Charles Babbage, emphasizing their collaborative efforts.

Contribution

It provides new evidence of Lovelace's mathematical sophistication and clarifies her role in creating an algorithm for Bernoulli numbers, challenging negative scholarly perceptions.

Findings

Lovelace had a strong mathematical background through correspondence with notable mathematicians.

Lovelace and Babbage collaborated on the Bernoulli numbers in their notes.

Lovelace created an algorithm for computing Bernoulli numbers.

Abstract

This chapter makes needed corrections to an unduly negative scholarly view of Ada Lovelace. Credit between Lovelace and Babbage is not a zero-sum game, where any credit added to Lovelace somehow detracts from Babbage. Ample evidence indicates Babbage and Lovelace each had important contributions to the famous 1843 Sketch of Babbage's Analytical Engine and the accompanying Notes. Further, Lovelace's correspondence with two highly accomplished figures in 19th century mathematics, Charles Babbage and Augustus De Morgan, establish her mathematical background and sophistication. Babbage and Lovelace's treatment of the Bernoulli numbers in Note 'G' spotlights this aspect of their collaboration. Finally, while acknowledging significant definitional problems in calling Lovelace the world's "first computer programmer," I affirm that Lovelace created an elemental sequence of instructions -- that is, an algorithm -- for computing the series of Bernoulli numbers.