"I may remark that the curious transformations many formulae can undergo, the unsuspected and to a beginner apparently impossible identity of forms exceedingly dissimilar at first sight, is I think one of the chief difficulties in the early part of mathematical studies. I am often reminded of certain sprites and fairies one reads of, who are at one's elbows in one shape now, and the next minute in a form most dissimilar."

“A large, coarse-skinned young woman but with something of my friend's features, particularly the mouth.”

“Perhaps you have felt already, from the tone of my letter, that I am more than ever now the bride of science. Religion to me is science, and science is religion. In that deeply-felt truth lies the secret of my intense devotion to the reading of God's natural works. It is reading Him. His will — His intelligence; and this again is learning to obey and to follow that will! For he who reads, who interprets the Divinity with a true and simple heart, then obeys and submits in acts and feelings as by an impupulse and instinct. He can't help doing so. At least, it appears so to me.”

“When I behold the scientific and so-called philosophers full of selfish feelings, and of a tenency to war against circumstances and Providence, I say to myself: They are not true priests, they are but half prophets — if not absolutely false ones. They have read the great page simply with the physical eye, and with none of the spirit within. The intellectual, the moral, the religious seem to me all naturally bound up and interlinked together in one great and harmonious whole... That God is one, and that all the works and the feelings He has called into existence are ONE; this is a truth not in my opinion developed to the apprehension of most people in its really deep and unfanthomable meaning. There is too much tendency to making separate and independent bundles of both the physical and the moral facts of the universe. Whereas, all and everything is naturally related and interconnected. A volume could I write you on this subject.”

“Circumstances have been such, that I have lived almost entirely secluded for some time. Those who are much in earnest and with single minds devoted to any great object in life, must find this occasionally inevitable.... You will wonder at having heard nothing from me; but you have experience and candour enough to perceive and know that God has not given to us more than very limited powers of expression of one's ideas and feelings... I shall be very desirous of again seeing you. You know what that means from me, and that it is no form, but the simple expression and result of the respect and attraction I feel for a mind that ventures to read direct in God's own book, and not merely thro' man's translation of that same vast and mighty work.”

“All but one of the programs cited in her notes had been prepared by Babbage from three to seven years earlier. The exception was prepared by Babbage for her, although she did detect a 'bug' in it. Not only is there no evidence that Ada ever prepared a program for the Analytical Engine, but her correspondence with Babbage shows that she did not have the knowledge to do so.”

“might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine...Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.”