The long friendship between Charles Babbage and Ada Lovelace created one of the most exciting and mysterious of collaborations ever to have resulted in a technological breakthrough. The fireworks that created by the collision of two prodigious mathematical and creative talents resulted in an invention, the Analytical Engine, which went on to change society fundamentally. However, beyond that, we just don't know what the bulk of their collaborative work was about:;  it was done in strictest secrecy. Even the known outcome of their friendship, the first programmable computer, was shrouded in mystery. At the time, nobody, except close friends and family, had any idea of Ada Byron's contribution to the invention of the ‘Engine’, and how to program it. Her great insight was published in August 1843, under the initials AAL, standing for Ada Augusta Lovelace, her title then being the Countess of Lovelace. It was contained in a lengthy ‘note’ to her translation of a publication that remains the best description of Babbage's amazing Analytical Engine. The secret identity of the person behind those enigmatic initials was finally revealed by Prince de Polignac who, seventy years later, wrote to Ada's daughter to seek confirmation that her mother had, indeed, been the author of the brilliant sentences that described so accurately how Babbage's mechanical computer could be programmed with punch-cards. L.F. Menabrea's paper on the Analytical Engine first appeared in the 'Bibliotheque Universelle de Geneve' in October 1842, and Ada translated it anonymously for Taylor's 'Scientific Memoirs'. Charles Babbage was surprised that she had not written an original paper as she already knew a surprising amount about the way the machine worked. He persuaded her to at least write some explanatory notes. These notes ended up extending to four times the length of the original article and represented the first published account of how a machine could be programmed to perform any calculation. Her example of programming the Bernoulli sequence would have worked on the Analytical engine had the device’s construction been completed, and gave Ada an unassailable claim to have invented the art of programming. What was the reason for Ada's secrecy? She was the only legitimate child of Lord Byron, who was probably the best known celebrity of the age, so she was already famous. She was a senior aristocrat, with titles, a fortune in money and vast estates in the Midlands. She had political influence, and was the cousin of Lord Melbourne, who was the Prime Minister at that time. She was friendly with the young Queen Victoria. Her mathematical activities were a pastime, and not one that would be considered by others to be in keeping with her roles and responsibilities. You wouldn't dare to dream up a fictional heroine like Ada. She was dazzlingly beautiful and talented. She could speak several languages fluently, and play some musical instruments with professional skill. Contemporary accounts refer to her being 'accomplished in science, art and literature'. On top of that, she was a brilliant mathematician, a talent inherited from her mother, Annabella Milbanke. In her mother's circle of literary and scientific friends was Charles Babbage, and Ada's friendship with him dates from her teenage zest for Mathematics. She was one of the first people he'd ever met who understood what he had attempted to achieve with the 'Difference Engine', and with whom he could converse as intellectual equals. He arranged for her to have an education from the most talented academics in the country. Ada melted the heart of the cantankerous genius to the point that he became a faithful and loyal father-figure to her. She was one of the very few who could grasp the principles of the later, and very different, ‘Analytical Engine’ which was designed from the start to tackle a variety of tasks. Sadly, Ada Byron's life ended less than a decade after completing the work that assured her long-term fame, in November 1852. She was dying of cancer, her gambling habits had caused her to run up huge debts, she'd had more than one affairs, and she was being blackmailed. Her brilliant but unempathic mother was nursing her in her final illness, destroying her personal letters and records, and repaying her debts. Her husband was distraught but helpless. Charles Babbage, however, maintained his steadfast paternalistic friendship to the end. She appointed her loyal friend to be her executor. For years, she and Babbage had been working together on a secret project, known only as 'The Book'. We have a clue to what it was in a letter written by her nine years earlier, on 11th August 1843. It was a joint project by herself and Lord Lovelace, her husband, and was intended to involve Babbage's 'undivided energies'. It involved 'consulting your Engine' (it required Babbage’s computer). The letter gives no hint about the project except for the high-minded nature of its purpose, and its highly mathematical nature.  From then on, the surviving correspondence between the two gives only veiled references to 'The Book'. There isn't much, since Babbage later destroyed any letters that could have damaged her reputation within the Establishment. 'I cannot spare the book today, which I am very sorry for. At the moment I want it for constant reference, but I think you can have it tomorrow' (Oct 1844)  And 'I will send you the book directly, and you can say, when you receive it, how long you will want to keep it'. (Nov 1844)  The two of them were obviously intent on the work: She writes, four years later, 'I have an engagement for Wednesday which will prevent me from attending to your wishes about the book' (Dec 1848). This was something that they both needed to work on, but could not do in parallel: 'I will send the book on Tuesday, and it can be left with you till Friday' (11 Feb 1849). After six years work, it had been so well-handled that it was beginning to fall apart: 'Don't forget the new cover you promised for the book. The poor book is very shabby and wants one' (20 Sept 1849). So what was going on? The word 'book' was not a code-word: it was a real book, probably a 'printer's blank', plain paper, but properly bound so printers and publishers could show off how the published work might look. The hints from the correspondence are of advanced mathematics. It is obvious that the book was travelling between them, back and forth, each one working on it for less than a week before passing it back. Ada and her husband were certainly involved in gambling large sums of money on the horses, and so most biographers have concluded that the three of them were trying to calculate the mathematical odds on the horses. This theory has three large problems. Firstly, Ada's original letter proposing the project refers to its high-minded nature. Babbage was temperamentally opposed to gambling and would scarcely have given so much time to the project, even though he was devoted to Ada. Secondly, Babbage would have very soon have realized the hopelessness of trying to beat the bookies. This sort of betting never attracts his type of intellectual background. The third problem is that any work on calculating the odds on horses would not need a well-thumbed book to pass back and forth between them; they would have not had to work in series. The original project was instigated by Ada, along with her husband, William King-Noel, 1st Earl of Lovelace. Charles Babbage was invited to join the project after the couple had come up with the idea. What could William have contributed? One might assume that William was a Bertie Wooster character, addicted only to the joys of the turf, but this was far from the truth. He was a scientist, a Cambridge graduate who was later elected to be a Fellow of the Royal Society. After Eton, he went to Trinity College, Cambridge. On graduation, he entered the diplomatic service and acted as secretary under Lord Nugent, who was Lord Commissioner of the Ionian Islands. William was very friendly with Babbage too, able to discuss scientific matters on equal terms. He was a capable engineer who invented a process for bending large timbers by the application of steam heat. He delivered a paper to the Institution of Civil Engineers in 1849, and received praise from the great engineer, Isambard Kingdom Brunel. As well as being Lord Lieutenant of the County of Surrey for most of Victoria's reign, he had time for a string of scientific and engineering achievements. Whatever the project was, it is unlikely that William was a junior partner. After Ada's death, the project disappeared. Then, two years later, Babbage, through one of his occasional outbursts of temper, demonstrated that he was able to decrypt one of the most powerful of secret codes, Vigenère's autokey cipher.  All contemporary diplomatic and military messages used a variant of this cipher. Babbage had made three important discoveries, namely, the mathematical law of this cipher, the principle of the key periodicity, and the technique of the symmetry of position. The technique is now known as the Kasiski examination, also called the Kasiski test, but Babbage got there first. At one time, he listed amongst his future projects, the writing of a book 'The Philosophy of Decyphering', but it never came to anything. This discovery was going to change the course of history, since it was used to decipher the Russians’ military dispatches in the Crimean war. Babbage himself played a role during the Crimean War as a cryptographical adviser to his friend, Rear-Admiral Sir Francis Beaufort of the Admiralty. This is as much as we can be certain about in trying to make sense of the bulk of the time that Charles Babbage and Ada Lovelace worked together. Nine years of intensive work, involving the 'Engine' and a great deal of mathematics and research seems to have been lost: or has it? I've argued in the past http://www.simple-talk.com/community/blogs/philfactor/archive/2008/06/13/59614.aspx that the cracking of the Vigenère autokey cipher, was a fundamental motive behind the British Government's support and funding of the 'Difference Engine'. The Duke of Wellington, whose understanding of the military significance of being able to read enemy dispatches, was the most steadfast advocate of the project. If the three friends were actually doing the work of cracking codes by mathematical techniques that used the techniques of key periodicity, and symmetry of position (the use of a book being passed quickly to and fro is very suggestive), intending to then use the 'Engine' to do the routine cracking of each dispatch, then this is a rather different story. The project was Ada and William's idea. (William had served in the diplomatic service and would be familiar with the use of codes). This makes Ada Lovelace the initiator of a project which, by giving both Britain, and probably the USA, a diplomatic and military advantage in the second part of the Nineteenth century, changed world history. Ada would never have wanted any credit for cracking the cipher, and developing the method that rendered all contemporary military and diplomatic ciphering techniques nugatory; quite the reverse. And it is clear from the gaps in the record of the letters between the collaborators that the evidence was destroyed, probably on her request by her irascible but intensely honorable executor, Charles Babbage. Charles Babbage toyed with the idea of going public, but the Crimean war put an end to that. The British Government had a valuable secret, and intended to keep it that way. Ada and Charles had quite often discussed possible moneymaking projects that would fund the development of the Analytic Engine, the first programmable computer, but their secret work was never in the running as a potential cash cow. I suspect that the British Government was, even then, working on the concealment of a discovery whose value to the nation depended on it remaining so. The success of code-breaking in the Crimean war, and the American Civil war, led to the British and Americans  subsequently giving much more weight and funding to the science of decryption. Paradoxically, this makes Ada's contribution even closer to the creation of Colossus, the first digital computer, at Bletchley Park, specifically to crack the Nazi’s secret codes.