1. a) Mechanical calculators

The first known adding machine was made by Wilhelm Schickard. In 1623, Schickard, a polymath and then professor at the University of Tubingen in Wuerttemberg, now part of Germany, designed and constructed a mechanical device which he called the Calculating Clock. Blaise Pascal was only 18 years old when he conceived the Pascaline in 1642. A precocious French mathematician and philosopher, Pascal discovered at the age of 12 that the sum of the angles in a triangle is always 180 degrees. During a period of 30 years after Pascal's invention, several persons built calculating machines based on this design. It was 1672 when the famous German polymath, mathematician and philosopher, Gottfried Wilhelm Von Leibniz co-inventor of the differential calculus, decided to build a machine able to perform the four basic arithmetical operations. He was inspired by a steps-counting device he saw while on a diplomatic mission in Paris. Like Pascal, Leibniz was a child prodigy. He learned Latin by the age of 8 and got his second doctorate when he was 19. As soon as he knew about Pascal’s design, he absorbed all its details and improved the design so as to allow for multiplication and division. Charles Babbage, FRS was an English mathematician, philosopher, inventor and mechanical engineer who originated the concept of a programmable computer. Considered a "father of the computer” Babbage is credited with inventing the first mechanical computer that eventually led to more complex designs. Parts of his uncompleted mechanisms are on display in the London Science Museum. In 1991, a perfectly functioning difference engine was constructed from Babbage's original plans

b) Programming

Joseph Jacquard, the son of a silk weaver, was born in Lyon in 1752. He inherited his father's small weaving business but trade was bad and eventually went bankrupt. In 1790 he was given the task of restoring a loom made byJacques de Vaucasan. Although fifty years old, it was one of the earliest examples of an automatic loom. Working on this loom led to him developing a strong interest in the mechanization of silk manufacture. The French Revolution brought a temporary halt to Jacquard's experiments. Jacquard fought on the side of the Republicans but as soon as they achieved victory, he returned to work. In 1801 he constructed a loom that used a series of punched cards to control the pattern of longitudinal warp threads depressed before each sideways passage of the shuttle. Jacquard later developed a machine where the punched cards were joined to form an endless loop that represented the program for the repeating pattern used for cloth and carpet designs. Augusta Ada Byron, was an English writer chiefly known for her work on Charles Babbage's early mechanical general-purpose computer, the analytical engine. Her notes on the engine include what is recognised as the first algorithm intended to be processed by a machine; as such she is sometimes considered the "World's First Computer Programmer".

c) Computability

Goedel was born April 28, 1906, in Brno, Austria-Hungary into the ethnic German family of Rudolf Goedel, the manager of a textile factory, and Marianne Goedel. At the time of his birth the town had a slight German-speaking majority and this was the language of his parents. Goedel essentially constructed a formula that claims that it is unprovable in a given formal system. If it were provable, it would be false, which contradicts the idea that in a consistent system, provable statements are always true. Thus there will always be at least one true but unprovable statement. That is, for any computably enumerable set of axioms for arithmetic, there is a formula that obtains in arithmetic, but which is not provable in that system. To make this precise, however, Gödel needed to produce a method to encode statements, proofs, and the concept of provability as natural numbers. He did this using a process known as Goedel…