<human>: Augusta Ada King-Noel, Countess of Lovelace (nee Byron; 10 December 1815 - 27 November 1852) was an English mathematician and writer, chiefly known for her work on Charles Babbage's proposed mechanical general-purpose computer, the Analytical Engine. She was the first to recognise that the machine had applications beyond pure calculation, and published the first algorithm intended to be carried out by such a machine. As a result, she is sometimes regarded as the first to recognise the full potential of a "computing machine" and the first computer programmer. Ada Lovelace was the only legitimate child of the poet Lord Byron, and his wife Anne Isabella "Annabella" Milbanke, Lady Wentworth.

Throughout her illnesses, she continued her education. Her mother's obsession with rooting out any of the insanity of which she accused Byron was one of the reasons that Ada was taught mathematics from an early age. She was privately schooled in mathematics and science by William Frend, William King, and Mary Somerville, the noted researcher and scientific author of the 19th century. One of her later tutors was the mathematician and logician Augustus De Morgan. From 1832, when she was seventeen, her mathematical abilities began to emerge, and her interest in mathematics dominated the majority of her adult life. In a letter to Lady Byron, De Morgan suggested that her daughter's skill in mathematics could lead her to become "an original mathematical investigator, perhaps of first-rate eminence".  Lovelace often questioned basic assumptions by integrating poetry and science. While studying differential calculus, she wrote to De Morgan:  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  Lovelace believed that intuition and imagination were critical to effectively applying mathematical and scientific concepts. She valued metaphysics as much as mathematics, viewing both as tools for exploring "the unseen worlds around us". CANNOTANSWER

What age was she when she began to show her mathematical abilities?
<bot>: From 1832, when she was seventeen,