The construction of modern computers, logically similar to Charles Babbage's design, have changed the whole of mathematics and it is even not an exaggeration to say that they have changed the whole world.
Born: 26 Dec 1791 in London, England Died: 18 Oct 1871 in London, England 
Both the date and place of Charles Babbage‘s birth were uncertain but have now been firmly established. For example, his date of birth is given as 26 December 1792 and both give the place of his birth as near Teignmouth. Also it is stated:
Little is known of Mr Babbage’s parentage and early youth except that he was born on 26 December 1792. 
However, a nephew wrote to The Times a week after the obituary appeared, saying that Babbage was born on 26 December 1791. There was little evidence to prove which was right until Hyman ( in 1975 found that Babbage’s birth had been registered in St Mary’s Newington, London on 6 January 1792. Babbage’s father was Benjamin Babbage, a banker, and his mother was Betsy Plumleigh Babbage. Given the place that his birth was registered Hyman says that it is almost certain that Babbage was born in the family home of 44 Crosby Row, Walworth Road, London. 
Babbage suffered ill health as a child, as he relates: Having suffered in health at the age of five years, and again at that of ten by violent fevers, from which I was with difficulty saved, I was sent into Devonshire and placed under the care of a clergyman (who kept a school at Alphington, near Exeter), with instructions to attend to my health; but, not to press too much knowledge upon me: a mission which he faithfully accomplished. 
Since his father was fairly wealthy, he could afford to have Babbage educated at private schools. After the school at Alphington he was sent to an academy at Forty Hill, Enfield, Middlesex where his education properly began. He began to show a passion for mathematics but a dislike for the classics. On leaving the academy, he continued to study at home, having an Oxford tutor to bring him up to university level. Babbage lists the mathematics books he studied in this period with the tutor:
Amongst these were Humphry Ditton’s ‘Fluxions’, of which I could make nothing; Madame Agnesi‘s ‘Analytical Instructions’ from which I acquired some knowledge; Woodhouse‘s ‘Principles of Analytic Calculation’, from which I learned the notation of Leibniz; and Lagrange‘s ‘Theorie des Fonctions’. I possessed also the Fluxions of Maclaurin and of Simson. 
Babbage enter Trinity College, Cambridge in October 1810. However the grounding he had acquired from the books he had studied made him dissatisfied with the teaching at Cambridge. He wrote: Thus it happened that when I went to Cambridge I could work out such questions as the very moderate amount of mathematics which I then possessed admitted, with equal facility, in the dots of Newton, the d’s of Leibniz, or the dashes of Lagrange. I thus acquired a distaste for the routine of the studies of the place, and devoured the papers of Euler and other mathematicians scattered through innumerable volumes of the academies of St Petersburg, Berlin, and Paris, which the libraries I had recourse to contained. Under these circumstances it was not surprising that I should perceive and be penetrated with the superior power of the notation of Leibniz. 
It is a little difficult to understand how Woodhouse’s Principles of Analytic Calculation was such an excellent book from which to learn the methods of Leibniz, yet Woodhouse was teaching Newton’s calculus at Cambridge without any reference to Leibniz’s methods. Woodhouse was one of Babbage’s teachers at Cambridge yet he seems to have taken no part in the Society that Babbage was to set up to try to bring the modern continental mathematics to Cambridge. 
Babbage tried to buy Lacroix’s book on the differential and integral calculus but this did not prove easy in this period of war with Napoleon. When he did find a copy of the work he had to pay seven guineas for it – an incredible amount of money in those days. Babbage then thought of setting up a Society to translate the work: I then drew up the sketch of a society to be instituted for translating the small work of Lacroix on the Differential and Integral Calculus. It proposed that we should have periodical meetings for the propagation of d’s; and consigned to perdition all who supported the heresy of dots. it maintained that the work of Lacroix was so perfect that any comment was unnecessary.

Babbage talked with his friend Edward Bromhead (who would become George Green’s friend some years later see the article on Green) who encouraged him to set up his Society. The Analytical Society was set up in 1812 and its members were all Cambridge undergraduates. Nine mathematicians attended the first meeting but the two most prominent members, in addition to Babbage, were John Herschel and George Peacock. 
Babbage and Herschel produced the first of the publications of the Analytical Society when they published Memoirs of the Analytical Society in 1813. This is a remarkably deep work when one realises that it was written by two undergraduates. They gave a history of the calculus, and of the Newton, Leibniz controversy they wrote: It is a lamentable consideration, that that discovery which has most of any done honour to the genius of man, should nevertheless bring with it a train of reflections so little to the credit of his heart. 
Two further publications of the Analytical Society were the joint work of Babbage, Herschel and Peacock. These are the English translation of Lacroix’s Sur le calcul différentiel et intégral published in 1816 and a book of examples on the calculus which they published in 1820. 
Babbage had moved from Trinity College to Peterhouse and it was from that College that he graduated with a B.A. in 1814. However, Babbage realised that Herschel was a much more powerful mathematician than he was so: He did not compete for honours, believing Herschel sure of first place and not caring to come out second. 
Indeed Herschel was first Wrangler, Peacock coming second. Babbage married in 1814, then left Cambridge in 1815 to live in London. He wrote two major papers on functional equations in 1815 and 1816. Also in 1816, at the early age of 24, he was elected a fellow of the Royal Society of London. He wrote papers on several different mathematical topics over the next few years but none are particularly important and some, such as his work on infinite series, are clearly incorrect. 
Babbage was unhappy with the way that the learned societies of that time were run. Although elected to the Royal Society of London, he was unhappy with it. He was to write of his feelings on how the Royal Society was run: The Council of the Royal Society is a collection of men who elect each other to office and then dine together at the expense of this society to praise each other over wine and give each other medals. 
However in 1820 he was elected a fellow of the Royal Society of Edinburgh, and in the same year he was a major influence in founding the Royal Astronomical Society. He served as secretary to the Royal Astronomical Society for the first four years of its existence and later he served as vicepresident of the Society. 
Babbage, together with Herschel, conducted some experiments on magnetism in 1825, developing methods introduced by Arago. In 1827 Babbage became Lucasian Professor of Mathematics at Cambridge, a position he held for 12 years although he never taught. The reason why he held this prestigious post yet failed to carry out the duties one would have expected of the holder, was that by this time he had become engrossed in what was to became the main passion of his life, namely the development of mechanical computers. 
Babbage is without doubt the originator of the concepts behind the present day computer. The computation of logarithms had made him aware of the inaccuracy of human calculation around 1812. He wrote in: … I was sitting in the rooms of the Analytical Society, at Cambridge, my head leaning forward on the table in a kind of dreamy mood, with a table of logarithms lying open before me. Another member, coming into the room, and seeing me half asleep, called out, Well, Babbage, what are you dreaming about?” to which I replied “I am thinking that all these tables (pointing to the logarithms) might be calculated by machinery. 
Certainly Babbage did not follow up this idea at that time but in 1819, when his interests were turning towards astronomical instruments, his ideas became more precise and he formulated a plan to construct tables using the method of differences by mechanical means. Such a machine would be able to carry out complex operations using only the mechanism for addition. Babbage began to construct a small difference engine in 1819 and had completed it by 1822. He announced his invention in a paper Note on the application of machinery to the computation of astronomical and mathematical tables read to the Royal Astronomical Society on 14 June 1822. 
Although Babbage envisaged a machine capable of printing out the results it obtained, this was not done by the time the paper was written. An assistant had to write down the results obtained. Babbage illustrated what his small engine was capable of doing by calculating successive terms of the sequence n^{2} + n + 41. 
The terms of this sequence are 41, 43, 47, 53, 61, … while the differences of the terms are 2, 4, 6, 8, .. and the second differences are 2, 2, 2, ….. The difference engine is given the initial data 2, 0, 41; it constructs the next row 2, (0+2), (41+(0+2)), that is 2, 2, 43; then the row 2, (2+2), (43+(2+2)), that is 2, 4, 47; then 2, 6, 53; then 2, 8, 61; … Babbage reports that his small difference engine was capable of producing the members of the sequence n^{2} + n + 41 at the rate of about 60 every 5 minutes. 
Babbage was clearly strongly influenced by de Prony’s major undertaking for the French Government of producing logarithmic and trigonometric tables with teams of people to carry out the calculations. He argued that a large difference engine could do the work undertaken by teams of people saving cost and being totally accurate. 
On 13 July 1823 Babbage received a gold medal from the Astronomical Society for his development of the difference engine. He then met the Chancellor of the Exchequer to seek public funds for the construction of a large difference engine. The Royal Society had already given positive advice to the government: Mr Babbage has displayed great talent and ingenuity in the construction of his machine for computation, which the committee thanks fully adequate to the attainment of the objects proposed by the inventory; and they consider Mr Babbage as highly deserving of public encouragement, in the prosecution of his arduous undertaking. 
His initial grant was for 1500 and he began work on a large difference engine which he believed he could complete in three years. He set out to produce an engine with:
… six orders of differences, each of twenty places of figures, whilst the first three columns would each have had half a dozen additional figures. 
Such an engine would easily have been able to compute all the tables that de Prony had been calculating, and it was intended to have a printer to print out the results automatically. However the construction proceeded slower than had been expected. By 1827 the expenses were getting out of hand. 
The year 1827 was a year of tragedy for Babbage; his father, his wife and two of his children all died that year. He own health gave way and he was advised to travel on the Continent. After his travels he returned near the end of 1828. Further attempts to obtain government support eventually resulted in the Duke of Wellington, the Chancellor of the Exchequer and other members of the government visiting Babbage and inspecting the work for themselves. By February 1830 the government had paid, or promised to pay, 9000 towards the project. 
In 1830 Babbage published Reflections on the Decline of Science in England, a controversial work that resulted in the formation, one year later, of the British Association for the Advancement of Science. In 1834 Babbage published his most influential work On the Economy of Machinery and Manufactures, in which he proposed an early form of what today we call operational research. 
The year 1834 was the one in which work stopped on the difference engine. By that time the government had put 17000 into the project and Babbage had put 6000 of his own money. For eight years from 1834 to 1842 the government would make no decision as to whether to continue support. In 1842 the decision not to proceed was taken by Robert Peel’s government. Dubbey writes: Babbage had every reason to feel aggrieved about his treatment by successive governments. They had failed to understand the immense possibilities of his work, ignored the advice of the most reputable scientists and engineers, procrastinated for eight years before reaching a decision about the difference engine, misunderstood his motives and the sacrifices he had made, and … failed to protect him from public slander and ridicule. 
By 1834 Babbage had completed the first drawings of the analytical engine, the forerunner of the modern electronic computer. His work on the difference engine had led him to a much more sophisticated idea. Although the analytic engine never progressed beyond detailed drawings, it is remarkably similar in logical components to a present day computer. Babbage describes five logical components, the store, the mill, the control, the input and the output. The store contains:
… all the variables to be operated upon, as well as all those quantities which had arisen from the results of other operations. 
The mill is the analogue of the cpu in a modern computer and it is the place:
… into which the quantities about to be operated upon are always bought. 
The control on the sequence of operations to be carried out was by a Jacquard loom type device. It was operated by punched cards and the punched cards contained the program for the particular task:
Every set of cards made for any formula will at any future time recalculate the formula with whatever constants may be required. Thus the Analytical Engine will possess a library of its own. Every set of cards once made will at any time reproduce the calculations for which it was first arranged. 
The store was to hold 1000 numbers each of 50 digits, but Babbage designed the analytic engine to effectively have infinite storage. This was done by outputting data to punched cards which could be read in again at a later stage when needed. Babbage decided, however, not to seek government support after his experiences with the difference engine. 
Babbage visited Turin in 1840 and discussed his ideas with mathematicians there including Menabrea. During Babbage’s visit, Menabrea collected all the material needed to describe the analytical engine and he published this in October 1842. Lady Ada Lovelace translated Menabrea’s article into English and added notes considerably more extensive than the original memoir. This was published in 1843 and included: … elaborations on the points made by Menabrea, together with some complicated programs of her own, the most complex of these being one to calculate the sequence of Bernoulli numbers. 
Although Babbage never built an operational, mechanical computer, his design concepts have been proved correct and recently such a computer has been built following Babbage’s own design criteria. He wrote in 1851:
The drawings of the Analytical Engine have been made entirely at my own cost: I instituted a long series of experiments for the purpose of reducing the expense of its construction to limits which might be within the means I could myself afford to supply. I am now resigned to the necessity of abstaining from its construction… 
Despite this last statement, Babbage never did quite give up hope that the analytical engine would be built writing in 1864 in:
… if I survive some few years longer, the Analytical Engine will exist… 
After Babbage’s death a committee,whose members included Cayley and Clifford, was appointed by the British Association:
… to report upon the feasibility of the design, recorded their opinion that its successful realisation might mark an epoch in the history of computation equally memorable with that of the introduction of logarithms… 
This was an underestimate. The construction of modern computers, logically similar to Babbage’s design, have changed the whole of mathematics and it is even not an exaggeration to say that they have changed the whole world. 
Article by: J J O’Connor and E F Robertson