The Cambridge Mathematician Who Designed Two Computing Engines in the 1820s and 1830s and Built Neither of Them in His Lifetime

Charles Babbage (1791–1871) was a Cambridge-trained mathematician, Royal Society fellow, and minor English political-economic theorist. He held the Lucasian Chair of Mathematics at Cambridge from 1828 to 1839 (the post previously held by Isaac Newton and later by Stephen Hawking) without ever lecturing — the appointment was administratively held during his London-based engineering work.

In June 1822 he proposed to the Royal Astronomical Society the construction of an automatic mechanical calculator for producing astronomical, navigational, and actuarial tables. The proposal addressed a specific contemporary economic problem: the printed tables that the British navy and insurance industry used for navigation and risk calculation contained on the order of one error per page. Each error potentially translated into a shipwreck or a bankruptcy. The errors were unavoidable because they were generated by human “computers” — the labourers (mostly women) who did the long-hand arithmetic for the table publishers. A mechanical calculator that produced the tables directly would eliminate the human-error layer.

Babbage’s calculator, the Difference Engine, would mechanically compute the values of polynomial functions using the method of finite differences. The method had been classical for over a century; the engineering novelty was the brass machine that would implement it.

The £17,500

The Difference Engine project received its first £1,500 government grant in 1823, advanced through the Royal Society. By the time the grant tap was closed twenty years later in 1842, the British Treasury had committed approximately £17,500 to the project — at 1823–1842 prices, around £2 million in 2025 money. Babbage’s personal contribution was approximately another £6,000. A full-time precision engineering workshop had been built behind his Dorset Street house in London. The lead mechanic, the toolmaker Joseph Clement, was paid more per day than most contemporary cabinet ministers.

The machine was never finished. A partial demonstration assembly — comprising about one-seventh of the projected mechanism — was completed in 1832 and produced accurate calculations of small polynomial sequences. This partial assembly is now in the Science Museum London collection. The remaining six-sevenths were never built.

The reasons for non-completion are contested. Babbage’s own explanation was that the precision-engineering tolerances required for the brass gear trains were at or beyond the contemporary British metalworking industry’s capability — that he was building a 20th-century machine with early-19th-century technology. The Science Museum’s 1991 reconstruction tested this hypothesis (see below). Doron Swade’s archival research (1985-2002) emphasised a different factor: Babbage’s escalating personal conflict with Joseph Clement, his progressive design changes that obsoleted earlier components, and the project’s increasing distance from any plausible completion date. The Treasury’s decision to stop funding in 1842 — under the Astronomer Royal George Biddell Airy’s formal advice that the project would not produce a working machine — was administratively justified.

The Analytical Engine

While the Difference Engine was stalled, Babbage produced in 1837 the design for a substantially more ambitious machine: the Analytical Engine. Where the Difference Engine could compute only polynomial values, the Analytical Engine was a general-purpose programmable computer in the modern sense. It would have an arithmetic unit (“the mill”), separate working memory (“the store”), a program-input mechanism (punched cards adapted from the Jacquard loom industry), conditional branching, and looped repetition.

The Analytical Engine, had it been built, would have been a Turing-complete computer in mechanical brass. It would have predated ENIAC (1945) by 108 years.

Babbage circulated the Analytical Engine design through European mathematical correspondence between 1838 and 1842. The Italian mathematician Luigi Federico Menabrea wrote a 1842 description of the machine in French. The Countess of Lovelace — Ada Lovelace — translated Menabrea’s article into English and appended her own seven extensive translator’s notes. Note G included an algorithm for computing Bernoulli numbers — conventionally identified as the world’s first computer program.

The Analytical Engine never received government funding. Babbage spent the remainder of his life refining its design and lobbying for support. He died in October 1871, aged 79, with neither engine completed.

1991

The London Science Museum’s Director of Collections Doron Swade initiated in 1985 a project to build a complete working Difference Engine No. 2 — the simpler refined design Babbage had drawn up in 1849 — to verify whether the failure of the original project had been a Babbage-personal failure or a technological-tolerance failure.

The 1985–1991 reconstruction used exclusively materials and tolerances that had been available in the 1840s. The machine was built using contemporary precision-engineering techniques applied to the original Babbage drawings. The result — 8,000 individual parts, weighing 5 tons, standing 7 feet tall — was completed and demonstrated in 1991 for the bicentennial of Babbage’s birth.

The 1991 machine works. It computes 7th-order polynomials to 31 decimal places. The original 1840s tolerance specifications were achievable with 1840s metalworking technology.

The failure of the original Difference Engine had not been technological. The 1991 reconstruction demonstrated that Babbage and Clement, in 1830s London, had been physically capable of building the machine. They had not built it because of the combination of project-management failures, personal conflicts, and design changes that had absorbed the £17,500 of government funding without producing a working final assembly.

A second copy of the 1991 Difference Engine No. 2 was built for the private collector Nathan Myhrvold in 2008 and is on display at the Computer History Museum in Mountain View, California. The original Babbage parts of the unfinished 1830s machine remain at the Science Museum London.

The machine that should have been built in 1842 was finally built in 1991. The man who designed it had been dead for 120 years.