•Babbage (first half of XIXth century) spent a personal fortune attempting to build up an analytical engine...
From Babbage's notebook, July 1836:
“This day I had for the first time a general but very indistinct conception of the possibility of making an engine work out algebraic developments --I mean, without any reference to the value of letters. My notion is that as the cards (Ja[c]quards) of the calc. engine direct a series of operations and then recommence with the first, so it might perhaps be possible to cause the same cards to punch other equivalent to any given number of repetitions. But these holes might perhaps be small pieces of formulae previously made by the first cards...”
Conference at Torino (1840) ---->
Luigi Menabrea, french paper at the Bibliotheque Universelle de Geneve (1842) “Notions sur la machine analytique de M. C. Babbage” ---->
Translated with notes (triple the size of the orginal paper) in Taylor's Scientific Memoirs, 1843, byAda Agusta, countess of Lovelace, Lord Byron's daugther ---->
Lord Bowden (1953), second printing in “Faster than Thought: A Symposium on Digital Computing Machines”, Pitman, Londres.
“...the analytical engine weaves algebraic patterns just as the Jacquard loom weaves flowers and leaves...”
“...in enabling mechanism to combine together general symbols in successions of unlimited variety and extent, a uniting link is established between the operations of matter and the abstract mental process of the most abstract branch of mathematical science...”
“There are many ways in which it may be desired in special cases to distribute and keep separate the numerical values of different parts of an algebraic formula; and the power of effecting such distributions to any extent is essential to the algebraical character of the Analytical Engine”
“The engine can arrange and combine its numerical quantities exactly as if they were letters or any other general symbols; and in fact it might bring out its results in algebraical notation, were provisions made accordingly. It might develop three sets of results simultaneously, viz. symbolic results...numerical results (its chief and primary object) and algebraical results in literal notation”
(Ada Lovelace, 1843)
See also, J. P. Bowen: A brief history of algebra and computing: an ecclectic oxonian view. Bull. of the Institute of Mathematics and its Applications. 31. 6-9.
...but its true goal was to develop a symbolic language to describe mechanisms,
“I look upon it as one of the most important additions I have made to human knowledge. It has placed the construction of machinery in the rank of a demonstrative science. The day will arrive when no school of mechanical drawing will be thought complete without teaching it.” (Babbage, Passages from the life of a philosopher, 1869).