Didier Roth (1800-1885) was born as son of Jewish parents in Cassovia in what was then Hungary and was named David. His father died when David was six years old and thenceforth his mother had to provide for the family. She worked in a kosher restaurant and later enabled her son to study medicine in Vienna. An outbreak of cholera in 1830 made Roth decide to leave Vienna. He settled in Paris where he practiced as a homeopath. One of his patients was the Austrian ambassador, Baron Rothschild. Roth, who was a cultured person with wide interests, in particular art, built up a noted collection of Dürer engravings, many of which are now in the National Library and the Louvre. But his most notable passion was inventing mechanical calculating machines. Apart from his extraordinarily cleverly conceived adding machines he also built the first automatic multiplying machine. The original machine as well as its prototype are today housed in the Musée des Arts et Métiers in Paris. An exact replica of the original machine was built for the Arithmeum in 2014. To this end the original was inspected and all the parts measured and documented in detail. Roth based his mechanism on pinwheels and could thus give his circular machine a decidedly flatter shape than Hahn’s machine. The setting mechanism is in the central portion and the entered numbers are transferred up to nine times into the result mechanism by means of the crank which is turned as far as the desired number and is then returned to its starting position by a ratchet. During this last step, the pinwheels transfer the number into the result mechanism the correct number of times. In order to prevent too high speeds in the mechanism, resulting in wheels turning too far, he provided a fly-brake. The tens-carry mechanism is rather elementary and works by means of a short toggle between the places of the result mechanism. Roth built no other circular machines. The replica is fully functional and clearly demonstrates Roth’s unique inventiveness.