Dust abacus is invented probably in Babylonia.

1800 B.C.

Babylonian mathematician develops algorithms to resolve numerical problems.

The quadrant, an astronomical calculation tool, becomes widely used in Europe.

It was around 1500 when Leonardo Da Vinci Invented a simple mechanical calculator, although it was not much of a use due to its lack of complexity.

Abacus instrument used in performing arithmetic calculations. A modern abacus consists of a wooden frame with beads on parallel wires, and a crossbar oriented perpendicular to the wires that divides the beads into two groups. Rounded piece of glass and wire originates in Egypt.  The abacus in the form we are most familiar with was first used in China in around 1300 A.D. The abacus is still used in China and Japan.

200 AD

Saun-pan computing tray is used in China, soroban computing tray used in Japan.

Gerbert of Aurillac or Pope Sylvester II devises a more efficient abacus

William Gilbert coins the term electricity from the Greek word elecktra.

Scotsman John Napier (1550-1617) published a paper outlining his discovery of the logarithm. Napier also invented an ingenious system of moveable rods (referred to as Napier's Rods or Napier's bones). These allowed the operator to multiply, divide and calculate square and calculate cube roots by moving the rods around and placing them in specially constructed boards.

Scottish inventor John Napier introduced a system called " Napier's Bones" uses bones to demonstrate division by subtraction and multiplication by addition. This device allowed the capability of multiplying by adding numbers and dividing by substracting.

English Inventor William Oughtred develops the slide rule in England.

The first known workable mechanical calculating machine is invented by Wilhelm Schickard (1592-1635), of Tuebingen, Wuerttemberg (now in Germany), This mechanical machine was capable of adding and subtracting up to 6 digit numbers, and warned of an overflow by ringing a bell. Operations were carried out by wheels, and a complete revolution of the units wheel incremented the tens wheel in much the same way counters on old cassette deck worked.

The machine and plans were lost and forgotten in the war that was going on, then rediscovered in 1935, only to be lost in war again, and then finally rediscovered in 1956 by the same man (Franz Hammer)! The machine was reconstructed in 1960, and found to be workable. Schickard was a friend of the astronomer Johannes Kepler since they met in the winter of 1617.

First four-function "Calculating Clock" at the university of Heidelberg builds by Wilhelm Schickard.

French philosopher, mathematician, and physicist Blaise Pascal invented a machine in 1642 (" Pascaline") that added and subtracted, automatically carrying and borrowing digits from column to column. Pascal built 50 copies of his machine, but most served as curiosities in parlors of the wealthy. Seventeenth-century German mathematician Gottfried Leibniz designed a special gearing system to enable multiplication on Pascal’s machine.

Sir Samuel Morland (1625-1695), of England, produces a non decimal adding machine, suitable for use with English money. Instead of a carry mechanism, it registers carries on auxiliary dials, from which the user must re-enter them as addends.

German mathematician, Gottfried von Leibniz designed a machine to carry out multiplication, the 'Stepped Reckoner'. It can multiple number of up to 5 and 12 digits to give a 16 digit operand. The machine was later lost in an attic until 1879. Leibniz was also the co-inventor of calculus.

German Mathematician Gottfried Von Leibniz presents a calculating machine. He present this machine to the Royal Society. It is the most advanced yet, capable of multiplication, division and extracting roots.

German mathematician Gottfried von Leibniz introduces binary arithmetic, in which only two symbols are used to represent all numbers. It will eventually pave the way for computers.

The first Telegraph is built

Charles, the third Earl Stanhope, of England, makes a successful multiplying calculator similar to Leibniz's.

Mathieus Hahn, somewhere in what will be Germany, also makes a successful multiplying calculator that he started in 1770.

American Benjamin Franklin discovers electricity

J. H. Mueller, of the Hessian army, conceives the idea of what came to be called a "difference engine". That's a special purpose calculator for tabulating values of a polynomial, given the differences between certain values so that the polynomial is uniquely specified; it's useful for any function that can be approximated by a polynomial over suitable intervals. Mueller's attempt to raise funds fails and the project is forgotten.

Dec 26, 1792: Charles Babbage, British inventor who designed the first digital computer, born in Teignmouth, Devon, England (1792–1871)

Joseph-Maire Jacuard developed an automatic loom controlled by punched cards.

November 2, 1815 : George Boole, English Mathematician who developed Boolean Algebra which is central to Computer Operations born in Lincoln, England

France’s Joseph-Marie Jacquard completes his fully automated loom that is programmed by punched cards.

Charles Xavier Thomas de Colmar (1785-1870), of France, makes his "Arithmometer", the first mass-produced calculator. It does multiplication using the same general approach as Leibniz's calculator; with assistance from the user it can also do division. It is also the most reliable calculator yet. Machines of this general design, large enough to occupy most of a desktop, continue to be sold for about 90 years.

In the 1820s Babbage began developing his Difference Engine, a mechanical device that can perform simple mathematical calculations. Babbage started to build his Difference Engine, but was unable to complete it because of a lack of funding. However, in 1991 British scientists, following Babbage's detailed drawings and specifications, constructed the Difference Engine. The machine works flawlessly, calculating up to a precision of 31 digits, proving that Babbage's design was sound. In the 1830s Babbage began developing his Analytical Engine, which was designed to carry out more complicated calculations, but this device was never built. Babbage's book Economy of Machines and Manufactures (1832) initiated the field of study known today as operational research.

Charles Babbage (1792-1871) designed his first mechanical computer, the first prototype for the difference engine. Babbage invented 2 machines the Analytical Engine (a general purpose mathematical device, see 1834) and the Difference Engine (a re-invention of Mueller's 1786 machine for solving polynomials), both machines were too complicated to be built (although attempt was made in 1832) - but the theories worked. The analytical engine (outlined in 1833) involved many processes similar to the early electronic computers - notably the use of punched cards for input.

1827

George Simon Ohm introduces Ohm's law in the book Die galvanische Kette, mathematisch bearbeitet

Joseph Henry of Princeton invents the first working telegraph.

Charles Babbage and Joseph Clement produce a prototype segment of his difference engine, which operates on 6-digit numbers and 2nd-order differences (i.e. can tabulate quadratic polynomials). The complete engine, which would be room-sized, is planned to be able to operate both on 6th-order differences with numbers of about 20 digits, and on 3rd-order differences with numbers of 30 digits. Each addition would be done in two phases, the second one taking care of any carries generated in the first. The output digits would be punched into a soft metal plate, from which a plate for a printing press could be made. But there are various difficulties, and no more than this prototype piece is ever assembled.

Charles Babbage designs the Analytical Machine that follows instructions from punched-cards. It is the first general purpose computer. it is a prototype of the modern computer, using levers, rods, and gears to perform calculations.