Ada Lovelace had a natural flair for mathematics. Being a Victorian woman, of course, she could not pursue her gift by attending a university or joining the Royal Academy. However, Lovelace was not the sort of woman to simply accept her lot in life. She employed private tutors to help her in her education. She also made the acquaintances of some of Britain's leading mathematical and scientific minds, and pursued lengthy written correspondences with them.
Unfortunately Ada's bright spark was given little opportunity to shine. She lived in a world where she was expected to fulfill the obligations of a Victorian woman, running a large household and bringing up three children. In addition, her health was poor - she died of cancer at age 36.
One of the men with whom Lovelace corresponded was the mathematician Charles Babbage. Babbage is most noted today for conceiving of and designing a mechanical universal computation device, essentially a computer, fully 100 years before the invention of the modern digital computer. Sadly, Babbage never built his 'Analytical Engine' and even his less sophisticated 'Difference Engine' only ever reached the prototype stage.
But it was regarding Babbage's entirely theoretical Analytical Engine that Ada Lovelace wrote the 1843 paper in which she described the machine in detail, including the uses it could be put to. In addition, she gave several simple examples of how it could be fed mathematical 'programs', and then described an algorithm for calculating Bernoulli numbers on the machine - and included a step-by-step 'trace' of how the machine would execute the algorithm.
Essentially, it was a program, intended to be run by a computer.
How much credit does Lovelace deserve for this remarkable achievement? The question is a complicated one. Since the Analytical Engine existed only in Babbage's head and in his notes, she corresponded with him extensively in writing her paper. How deep was their collaboration? Was Ada Lovelace merely Babbage's publicist and promoter? Or were her contributions real and original? We don't know beyond a shadow of a doubt, for instance, that she wrote the Bernoulli algorithm. however there is no specific evidence to suggest that she did not.
In a lengthy blog post, Stephen Wolfram of WolframAlpha attempts to untangle the historical significance of Ada Lovelace:
The Analytical Engine and its construction were all Babbage’s work. So what did Ada add? Ada saw herself first and foremost as an expositor. Babbage had shown her lots of plans and examples of the Analytical Engine. She wanted to explain what the overall point was—as well as relate it, as she put it, to “large, general, & metaphysical views”.
To me, there’s little doubt about what happened: Ada had an idea of what the Analytical Engine should be capable of, and was asking Babbage questions about how it could be achieved. If my own experiences with hardware designers in modern times are anything to go by, the answers will often have been very detailed. Ada’s achievement was to distill from these details a clear exposition of the abstract operation of the machine—something which Babbage never did. (In his autobiography, he basically just refers to Ada’s Notes.)
But there is more, according to Wolfram. After her paper was published, Lovelace wrote Babbage with a provocative idea: she proposed to take on oversight of the construction of the Analytical Engine. As Wolfram puts it, she would become CEO and Babbage would have been the CTO. And, amazingly, Babbage agreed to her proposal!
Alas, it wasn't to be. Within a short time Ada's health would collapse due to cancer and history would be deprived of Babbage's analytical engine as overseen by Ada Lovelace.
What if Ada’s health hadn’t failed—and she had successfully taken over the Analytical Engine project? What might have happened then?I've written more in the past. about how feasible a Victorian computer would really have been. You can check it out here.
I don’t doubt that the Analytical Engine would have been built. Maybe Babbage would have had to revise his plans a bit, but I’m sure he would have made it work. The thing would have been the size of a train locomotive, with maybe 50,000 moving parts. And no doubt it would have been able to compute mathematical tables to 30- or 50-digit precision at the rate of perhaps one result every 4 seconds.