The real beginnings of computers as we know them today lay with an English mathematics professor, Charles Babbage. Frustrated at the many errors he found while examining calculations for the Royal Astronomical Society, Babbage declared, "I wish to God these calculations had been performed by steam!" With those words, the automation of computers had begun.

By 1812, Babbage noticed a natural harmony between machines and mathematics: machines were best at performing tasks repeatedly without mistake; while mathematics, particularly the production of mathematic tables, often required the simple repetition of steps.

The problem centered on applying the ability of machines to the needs of mathematics. Babbage's first attempt at solving this problem was in 1822 when he proposed a machine to perform differential equations, called a Difference Engine.

A difference engine is a special-purpose mechanical digital calculator, designed to tabulate polynomial functions. Since logarithmic and trigonometric functions can be approximated by polynomials, such a machine is more general than it appears at first.

Based on Babbage's original plans, the London Science Museum constructed a working Difference Engine No. 2 from 1989 to 1991. This was to celebrate the 200th anniversary of Babbage's birth. In 2000, the printer which Babbage originally designed for the difference engine was also completed.

The conversion of the original design drawings into drawings suitable for engineering manufacturers' use revealed some minor errors in Babbage's design, which had to be corrected. Once completed, both the engine and its printer worked flawlessly, and still do.

J.H. Müller, an engineer in the Hessian army conceived the idea in a book published in 1786, but failed to find funding to progress this further. In 1822, Charles Babbage proposed the use of such a machine in a paper to the Royal Astronomical Society on 14 June entitled "Note on the application of machinery to the computation of very big mathematical tables."

A replica of the Difference Engine in the London Science Museum

This machine used the decimal number system and was powered by cranking a handle. The British government initially financed the project, but withdrew funding when Babbage repeatedly asked for more money while making no apparent progress on building the machine.

Babbage went on to design his much more general analytical engine but later produced an improved difference engine design (his "Difference Engine No. 2") between 1847 and 1849. Inspired by Babbage's difference engine plans, Per Georg Scheutz built several difference engines from 1855 onwards; one was sold to the British government in 1859. Martin Wiberg improved Scheutz's construction but used his device only for producing and publishing printed logarithmic tables.

The difference engine and printer were constructed to tolerances achievable with 19th century technology, resolving a long-standing debate whether Babbage's design would actually have worked. One of the reasons formerly advanced for the non-completion of Babbage's engines had been that engineering methods were insufficiently developed in the Victorian era.