Charles Babbage designed the first Turing-complete computing machine, called the Difference Engine, in 1849. A working model was not build until 2002. When the National Science Museum in London built on off of Babbage’s notes, it worked, and could run an algorithm for calculating Bernoulli numbers written by Babbage’s protege Ada Lovelace.
Basically, it works by the method of finite difference, which allows a polynomial to be solved using only simple addition. Once the first few values of the function are known, the programmer creates columns of the first and second difference by subtracting successive values from the previous column. The rest of the values can be calculated by reversing the process. The Difference engine has registers to hold one number from each column of the equation.
Short Version: Steampunk was real. There were actual Victorian hackers running around, presumably festooned with gears and reciting heroic couplets on all-night soldering runs. The Babbage engine is one of my favorite things ever, because it’s brilliant and anachronistic and proof that literally anything can be made Turing-complete with enough genius and steam power.