What mathematical concept did Ada Lovelace explain in her notes on the Analytical Engine?

Ada Lovelace explained how the Analytical Engine could calculate Bernoulli numbers. Her method appeared in Note G, the final and most famous section of her 1843 notes on Charles Babbage’s proposed mechanical computer.

Bernoulli numbers are a sequence of rational numbers that arise in number theory and in formulas for sums of powers, such as the sum of squares or cubes. Lovelace’s description showed how the Engine could follow a structured sequence of operations using punched cards and stored intermediate results.

The Analytical Engine was never completed, so Lovelace’s algorithm was not run on the actual machine. Even so, Note G is often called the first published computer program. Babbage had written earlier unpublished programs for the Engine, which is why historians sometimes qualify the claim by calling Lovelace’s work the first published algorithm intended for a general-purpose computer. Her notes also argued that such machines might someday manipulate symbols, music, or other kinds of information—not just numbers.