<p><pre><code>   it is uncontested this is the 1st published 
   program for the Analytical Engine.
</code></pre>
Babbage constructed the AE to execute programs, so he would certainly have written some. Bernoulli numbers are old hand have been calculated since antiquity. I imagine that B. propose this program to L.<p><pre><code>   the strict gender expectations of the time, 
</code></pre>
The gender expectations today are that men ought to genuflect to women, whence your posts here.<p><pre><code>   She envisioned the engine computing music, 
   poetry and pictures, which implies creativity 
   &amp; thought , proto-A.I in idea. 
</code></pre>
It&#x27;s worth pointing out that the idea to have automata make music, and more generally for automata to be creative, predates Lovelace, Music making automata were a staple of the renaissance. For example the mathematician and astronomer Johannes Kepler, when visiting the &quot;Kunstkammer&quot; of Rudolf II in 1598, was amazed at an automaton representing a drummer who could &quot;beat his drum with greater self-assurance than a live one&quot; [1]. Incidentally, Kepler corresponded with Wilhelm Schickard on the latter&#x27;s &quot;arithmeticum organum&quot;, the first ever proper mechanical calulator (could do addition, subtraction, multiplication and division). Automating creativity was very much an idea with much currency in the renaissance. Indeed some of the key advances in mechanical automata, which later evolved into computers, where driven by the desire to automate creativity [2]. The &quot;conceptual leap&quot; that some people lazily ascribe to Lovelace, wasn&#x27;t hers!<p>Using numbers to represent syntax (what you lazily attribute to Lovelace too) is much older and can be found for example in Leibniz&#x27;s 1666 &quot;Dissertatio de arte combinatoria&quot;, where one finds a detailed exposition of a method to associate numbers with linguistic notions. I have no idea if Leibniz was the first to do this. Leibniz also built some early calculators&#x2F;computers, and is thus a cornerstone of the tradition that lead to the emergence of computers. This tradition was known in Babbage&#x27;s time, and most likely to Babbage.<p>In the light of all this, I remain convinced that Lovelace helped Babbage to write up and popularise his ideas.<p>[1] W. Zhao, Rendering the Illusion of Life: Art, Science and Politics in Automata from the Central European Princely Collections.<p>[2] D. Summers Stay, Machinamenta: The thousand year quest to build a creative machine.