The differential was first invented in China, in the third century, A.D.

(87BC) Differential assembly in the Antikythera
Mechanism.

(1810) Differential gear invented by German Rudolph Ackermann revolutionizes carriage steering.

1827 - modern automotive differential patented by French watchmaker Onésiphore Pecqueur (1792-1852) His differential gearing was conceived for a steam-powered machine.

1832 - Richard Roberts of England patents 'gear of compensation', a differential for road locomotives.

.. in the late1800's. A compulsive tinkerer, Mr. Worksman invented a differential gear for an early three-wheeled Harley-Davidson
motorcycle

James Starley (1830-1881), perfected the basic mechanism of the sewing machine (1850+), designed the traditional spoked bicycle wheel with solid rubber tyres (1870+), and invented a chain-drive differential gear in 1877.

1897 - first use of differential on an Australian steam car by David Shearer.

1913 - Packard introduces the spiral-gear differerential, which cuts gear noise.

1926 - Packard introduces the hypoid differerential, which enables the propeller shaft and its hump in the interior of the car to be lowered.

Most of all branches of engineering owe something to clock making; for example, the thermostat in a oven, the chain
drive of a dredger, and the differential gear in the back axle of a car. They were all fist invented for clockwork.

Best description so far on how a differential works can be found on Wikipedia