# Can we fairly assess Ada Lovelace's talent for mathematics?

Dorothy Stein, a biographer of Ada Lovelace, was pretty blunt in her assessment: Lovelace was a mediocre mathematician, for example see here.

I wonder if she's fair to her. The fact that Lovelace translated a printer's error "cos" (like cosine) literally as "cos" (instead of recognizing the French "cas" was meant, translating it as "case") could be just some careless mistake.

More serious is her trouble with functional equations, like the following exercise (English and notation slightly modernized):

Show that the equation $$\phi(x+y) + \phi(x-y) = 2\phi(x)\,\phi(y)$$ is satisfied by $$\phi(x)=(a^x + a^{-x})/2$$ for every value of $$a$$

So I guess that would go like this: \begin{align}2\phi(x)\,\phi(y) &= (a^x + a^{-x})(a^y + a^{-y})/2 \\&= (a^{x+y}+a^{x-y} + a^{-x+y} + a^{-x-y})/2 \\&= (a^{x+y}+ a^{-(x+y)} + a^{x-y} + a^{-(x-y)} )/2 \\&= \phi(x+y) +\phi(x-y)\,.\end{align}

Lovelace struggled with the problem and wrote:

I do not know when I have been so tantalized by anything, & should be ashamed to say how much time I have spent upon it, in vain.

Now it could be that as a beginner's mistake she misread the question, trying also to prove that this was the only solution - which would be a much, much harder mathematical problem.

These are just two examples of the controversy.

So I wonder if we can make a somewhat objective judgment about her talent for mathematics?

Wouldn't it be surprising if the evidence is compatible with both extremes:

• Ada Lovelace simply wasn't very good at math; other factors like her heritage and social connections allowed her to take the position as Charles Babbage's assistant
• she was a mathematical genius?
• We can line up the facts, as Stein apparently does, but isn't post mortem "assessment of talent" inherently subjective? To some, Ptolemy was a genius, to others he was a fraud, the facts are not in dispute. Outside the aptitude tests, "talent" is a nebulous concept, so it is hardly surprising. If someone does something deemed significant, that is, naturally, because they had the "talent". It's a perfect "explanation". Lovelace was a genius assessments are not hard to find. – Conifold Mar 17 '19 at 9:30