Charles Babbage was a prolific inventor, a mathematician, scientist, political economist and critic of the scientific establishment. His controversial book Reflections on the Decline of Science in England, published in 1830, was so influential that only a year later the British Association for the Advancement of Science was formed. He published six full-length works and nearly ninety papers between 1813 and 1868, including 1834’s Economy of Machinery and Manufacturers, an influential work that proposed an early form of operational research. He is best known today for creating his Difference Engine and for conceiving of the Analytic Engine.
Included in his writing and research were suggestions that are still being discussed today. He was a pioneer of lighthouse signaling, proposed ‘black box’ recorders to monitoring conditions preceding railway catastrophes, favored introducing decimal currency and advocated the development of tidal power to be used once coal reserves were exhausted. He campaigned for the introduction of Continental theories into British mathematics education, and wrote about the neglect of science and the status of scientists. 
However, it is for his pioneering work in computation that his reputation has endured. His aim in manufacturing machines that calculated and printed without any human intervention was to eliminate errors in astronomical and mathematical tables, and his reputation in computer history rests on this work. For this purpose he invented two kinds of engines - Difference Engines and Analytical Engines – that were much larger and more sophisticated than earlier attempts.
There are different accounts of Babbage’s birth dates. His original obituary in The Times gave his date and place of birth as 26th December 1792, Teignmouth, Devon. However, his nephew wrote to The Times a week after the obituary appeared, saying that he was born on 26th December 1791. There was little evidence to prove which of these two versions was right until 1975, when a researcher named Hyman found that Babbage’s birth had been registered in St Mary’s Newington, London, on January 6th 1792. Given this place of registration, Hyman says that it is almost certain that Babbage was born in the family home, 44 Crosby Row, Walworth Road, London.
His father, Benjamin Babbage, was a partner in the banking firm of Praed, Mackworth and Babbage and his mother’s name was Elizabeth, although she was known in the family as Betsy.
Because he suffered from ill health as a child, Babbage was privately educated, first in Devon at Alphington, near Exeter, and then at Forty Hill in Enfield, Middlesex. He was passionate about mathematics, and after he left school continued to study at home with a tutor before he went to Cambridge, first to Trinity College and then to Peterhouse, where he graduated in 1814 and received his master’s degree in 1817.
During his studies before going up to Cambridge, Babbage had encountered the work of European mathematicians such as Leibniz, Euler and Lacroix, and found himself unsatisfied with the standard of teaching at Cambridge. He tried to buy Lacroix’s book on differential and integral calculus, but the Napoleonic Wars made it difficult to purchase anything from Europe, and he eventually had to pay seven guineas for it, which was a very large sum of money in those days.
Together with his friends and fellow-students John Herschel and George Peacock, he founded the Analytical Society of Cambridge in 1812, with the purpose of translating Lacroix’s work and bringing his methods into the mathematics curriculum. Their Memoirs of the Analytical Society was published in 1813, giving a history of the calculus and the Newton-Leibniz controversy. They later published in 1816 an English translation of Lacroix’s Sur le calcul différentiel et integral and in 1820 a book of examples on the calculus.
After leaving Cambridge, Babbage lived in Devonshire Street, London, until 1828 and then in 1 Dorset Street, Manchester Square, London, until his death on 18th October 1871, aged 78. He was buried at Kensal Green Cemetery in London. 
Babbage was elected a fellow of the Royal Society in 1816, although he did not prize this honor highly, writing of it:
- 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, despite this cynicism, in 1820 he was elected a fellow of the Royal Society of Edinburgh, and in that year was also a major influence in the foundation of the Royal Astronomical Society. He was the secretary to the Royal Astronomical Society until 1824, and later its vice-president. He also occupied the Lucasian chair of mathematics at Cambridge University from 1828 to 1839, although he never actually taught there, as by that time he had devoted all his attention to his computational machines.
In 1819, Babbage began to design his first Difference Engine, so-called because it was based on the mathematical method of finite differences. It was completed by 1822 and announced in a paper, Note on the application of machinery to the computation of astronomical and mathematical tables, read to the Royal Astronomical Society in June of that year. According to the website Engineering.com:
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 n2 + 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 n2 + n + 41 at the rate of about 60 every 5 minutes.
The Astronomical Society awarded him a gold medal for this work, and the government gave him public money to construct a larger difference engine, which would not only calculate but print out the results, preventing inevitable errors caused by manual transcription. He expected this to take three years, but work proceeded very slowly and was interrupted by the terrible year for Babbage of 1827, in which his father, his wife, and two of his children died, and his health gave way. By 1834, work had stopped on the Difference Engine, after the government had put £17,000 into it, and Babbage had invested £6000 of his own money. For the next eight years the government refused to make a decision about further funding, and in 1842 decided not to continue with it. 
However, in 1834, even though he had not completed his first Difference Engine, Babbage conceived the Analytical Engine, This engine - far more ambitious and technically demanding than his earlier Difference Engine – was the revolutionary machine that established his reputation as a computer pioneer.
The similarities between the logical components of the Analytical Engine and those in a modern computer are obvious. Babbage described its logical components: the store, the mill, the control, the input and the output.
- The store, he wrote, 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 analog of the cpu in a modern computer and it is the place:... into which the quantities about to be operated upon are always brought.
- The control on the sequence of operations to be carried out was by a device like a Jacquard loom, operated by punched cards that 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 designed to hold 1000 numbers, which each had 50 digits, but Babbage designed the analytic engine to effectively have infinite storage. This was done by outputting data to punched cards that could be read in again at a later stage when needed.
When he visited Turin in 1840, Babbage discussed his ideas with mathematicians there, including Menabrea. During that visit, Menabrea collected the material he needed to describe the analytical engine and published it as an article in October 1842. Lady Ada Lovelace, sister of the poet George Gordon, Lord Byron, translated Menabrea's article into English and added notes of her own that were far 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.
Babbage never recovered from his disastrous experience with government funding, so he resigned himself to his Analytical Engine never being constructed. However, in 1847 he started to use the techniques he had developed on the Analytical Engine in the design of his second Difference Engine.
The main reason why Babbage did not complete the construction of any of his engines, was the weaknesses in accuracy of the technology of his day. However, his work inspired those who followed him. The construction of modern computers that are logically similar to Babbage's design, have changed both mathematics and the world.