Charles Babbage (1791–1871) was an avid mathematician with very wide interests. He is well-known for envisioning the idea of computers and single-handedly developed what he called a Difference Engine to make serial calculations. It was a mechanical machine with a series of axles and gears to make calculations, with the output being a printed table. I recently began reading his 1864 book, Passages from the Life of a Philosopher, where he explains how the Difference Engines came to be.

One of the problems his Engine was designed to solve relates to the idea of children playing with marbles and arranging them in a progressive pyramidal shape, with one marble in the top row, two in the second, three in the third, and so on. For small pyramids, you can simply count the marbles to find how many there are. But Babbage wanted to create an automatic list or table with one column showing the number of rows and another column showing the total number of marbles.

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