The Difference Engine's name comes from what mathematical method?

The Difference Engine’s name comes from the mathematical method of finite differences.

Finite differences let a calculator generate successive values of a polynomial by repeatedly adding differences instead of performing multiplication from scratch. For a quadratic equation, the second differences remain constant; for a cubic, the third differences remain constant. By storing the appropriate values and adding them in sequence, a machine can produce numerical tables efficiently.

Charles Babbage designed his Difference Engine in the 1820s to automate the production of mathematical, astronomical, and navigational tables. Such tables were essential in engineering, surveying, and navigation, but human typesetters and calculators could introduce errors. Babbage’s machine was intended to calculate and print the results mechanically, reducing both labour and mistakes.

The method did not make the engine a general-purpose computer. The Difference Engine was specialised for tabulating polynomial functions, often used to approximate more complicated functions such as logarithms and trigonometric functions. Babbage later pursued the much more flexible Analytical Engine, which separated memory from calculation and could follow punched-card instructions.

Fourier analysis, Boolean algebra, and matrix inversion are important mathematical ideas, but none supplied the name of Babbage’s specialised calculating machine.