Writer Benjamin Woolley would say that while Ada's mathematical abilities have been contested, she can claim "some contribution": "Note A, the first she wrote and the one over which Babbage had the least influence, contains a sophisticated analysis of the idea and implications of mechanical computation." And that this discussion of the implications of Babbage's invention was the most important aspect of her work. According to Woolley, her notes were "detailed and thorough [a]nd still... metaphysical, meaningfully so"; they were able to explain how the machine worked and "[rose] above the technical minutiae of Babbage's extraordinary invention to reveal its true grandeur."It would be only a slight exaggeration to say that Babbage wrote the 'Notes' to Menabrea's paper, but for reasons of his own encouraged the illusion in the minds of Ada and the public that they were authored by her. It is no exaggeration to say that she was a manic depressive with the most amazing delusions about her own talents, and a rather shallow understanding of both Charles Babbage and the Analytical Engine... To me, [correspondence between Ada and Babbage] seems to make obvious once again that Ada was as mad as a hatter, and contributed little more to the 'Notes' than trouble.
Babbage published the following on Ada's contribution, in his Passages from the Life of a Philosopher (1864):
The "algebraic working out" Babbage describes is the derivation of the mathematical equations 1 through 9 in Note G, not the Table & Diagram in Note G showing punch card flow. The table, not the equations, is considered the first computer program. In Ada's and Babbage's letters to each other in 1843, the only contemporary documentation, Ada mentions finding and correcting errors in "our first edition of a Table & Diagram" (Ada frequently used "our" when discussing the Notes in letters with Babbage).I then suggested that she add some notes to Menabrea's memoir, an idea which was immediately adopted. We discussed together the various illustrations that might be introduced: I suggested several but the selection was entirely her own. So also was the algebraic working out of the different problems, except, indeed, that relating to the numbers of Bernoulli, which I had offered to do to save Lady Lovelace the trouble. This she sent back to me for an amendment, having detected a grave mistake which I had made in the process.
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