In a paper presented to the Royal Astronomical Society, English mathematician Charles Babbage proposed a difference engine (pictured), an automatic, mechanical calculator designed to tabulate polynomial functions.

The Royal Astronomical Society (RAS) is a learned society and charity that encourages and promotes the study of astronomy, solar-system science, geophysics and closely related branches of science. Its headquarters are in Burlington House, on Piccadilly in London. The society has over 4,000 members, known as fellows, most of whom are professional researchers or postgraduate students. Around a quarter of Fellows live outside the UK.

Charles Babbage was an English polymath. A mathematician, philosopher, inventor and mechanical engineer, Babbage originated the concept of a digital programmable computer.

A difference engine is an automatic mechanical calculator designed to tabulate polynomial functions. It was designed in the 1820s, and was created by Charles Babbage. The name difference engine is derived from the method of finite differences, a way to interpolate or tabulate functions by using a small set of polynomial co-efficients. Some of the most common mathematical functions used in engineering, science and navigation are built from logarithmic and trigonometric functions, which can be approximated by polynomials, so a difference engine can compute many useful tables.

In mathematics, a polynomial is a mathematical expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of a single indeterminate x is x² − 4x + 7. An example with three indeterminates is x³ + 2xyz² − yz + 1.