The history of computation is longer than the history of computational hardware and includes the history of computing and methods of computing and computing . The timeline of computing presents a summary list of major developments in computing by date.
Digital computing is intimately linked to the representation of numbers .  But long before abstractions like the arose number , there were mathematical concepts to serve the purposes of civilization. These concepts are implicit in concrete practices such as:
- one-to-one correspondence , a rule to count how many items, say on a tally stick , eventually abstracted into numbers ;
- comparison to a standard , a method for assuming reproducibility in a measurement , for example, the number of corners
- the 3-4-5 right triangle was a device for assuring a right angle , using ropes with 12 evenly spaced knots , for example. 
Eventually, the concept of numbers est devenu concrete and familiar enough for counting to Arise, at times with sing-song mnemonics to teach sequences to others. All known languages have words for at least “one” and “two”(although this is disputed: see Piraha language ), and even some animals like the blackbird can distinguish a surprising number of items. 
Advances in the numerical system and mathematical notation eventually to the discovery of mathematical operations such as addition, subtraction, multiplication, division, squaring, square root, and so forth. Eventually the operations have been formalized, and the concepts of the operations have been stated formally , and even proven . See, for example, Euclid’s algorithm for finding the greatest common divisor of two numbers.
By the High Middle Ages, the positional Hindu-Arabic numeral system had reached Europe , which allowed for systematic computation of numbers. During this period, the representation of a calculation is paper Actually allowed calculation of mathematical expressions , and the tabulation of mathematical functions Such as the square root and the common logarithm (for use in multiplication and division) and the trigonometric functions . By the time of Isaac Newton’s research, paper or vellum was an important computing resource, and even in our present time, researchers like Enrico Fermiwould cover random scraps of paper with calculation, to satisfy their curiosity about an equation.  Even in the period of programmable calculators, Richard Feynman would unhesitatingly compute any steps which overflowed the memory of the calculators, by hand, just to learn the answer. [ quote needed ]
The earliest known tool for use in computation was the abacus , and it was thought to be invented in Babylon c. 2700-2300 BC. Its original style of use was made by pebbles. Abaci, of a more modern design, are still used as calculation tools today. Greek methods by 2.000 years old. [ quote needed ]
In c. 1050-771 BC, the south-pointing cart was invented in ancient China . It was the first Known geared mechanism to use a differential gear , qui Was later used in analog computers . The Chinese also invented a more sophisticated abacus from the 2nd century BC known as the Chinese abacus . [ quote needed ]
In the 5th century BC in ancient India , the grammarian Pāṇini formulated the grammar of Sanskrit in 3959 the rules known as Ashtadhyayi which was highly systematized and technical. Panini used metarules, transformations and recursions . 
In the 3rd century BC, Archimedes used the mechanical principle of balance (see Archimedes Palimpsest # Mathematical content ) to calculate mathematical problems, such as the number of grains of sand in the universe ( The sand reckoner ), which also requires a recursive notation for numbers (eg, the myriad myriad ).
The Antikythera mechanism is believed to be known mechanical analog computer.  It was designed to calculate astronomical positions. It was discovered in 1901 in the Antikythera wreck off the Greek island of Antikythera, between Kythera and Crete , and has been dated to circa 100 BC.
Mechanical analog computer devices Appeared again a thousand years later in the medieval Islamic world and Were developed by Muslim astronomers , Such As the mechanical geared astrolabe by Abu Rayhan al-Bīrūnī ,  and the torquetum by Jabir ibn Aflah .  According to Simon Singh , Muslim mathematicians also made important advances in cryptography , such as the development of cryptanalysis and frequency analysis by Alkindus .  Programmablemachines were also invented by Muslim engineers , such as the automatic flute player by the Banū Mūsā brothers,  and Al-Jazari ‘s humanoid robots [ citation needed ] and castle clock , which is considered to be the first programmable analog computer. 
During the Middle Ages, several European philosophers made attempts to produce analog computer devices. Influenced by the Arabs and Scholasticism , Majorcan philosopher Ramon Llull (1232-1315) Devoted a great life to share de son defining and designing Several logical machinery That, by single-combining and undeniable philosophical truths, Could Produce all knowledge as possible. These machines were never actually built, they were more of a thought experimentto produce new knowledge in systematic ways; they could make simple logical operations, they still needed a human being for the interpretation of results. Moreover, they lacked a versatile architecture, each machine serving only very concrete purposes. In spite of this, Llull’s work had a strong influence on Gottfried Leibniz (early 18th century), who developed his ideas further, and built several calculating tools using them.
Indeed, when John Napier discovered logarithms for computational purposes in the early 17th century, he followed a period of considerable progress by inventors and scientists in making calculating tools. The byproduct of this early stage of formal computing can be seen in the difference engine and its successor the analytical engine , both by Charles Babbage . The analytical engine combined concepts from that of a person who would have constructed a modern electronic computer. These properties include such features as an internal “scratch memory” equivalent to RAMA graphical plotter, and a programmable input-output “hard” memory of punch cards . The key advancement which has been developed in the past, and is one of the most important components of the machine. This was a fundamental shift in thought; previous computational devices served only a single purpose, but had to be at best disassembled and reconfigured to solve a new problem. Babbage’s devices could be reprogrammed to solve new problems, and act upon previous calculations within the same series of instructions. Ada Lovelacetook this concept one step further, by Creating a program for the analytical engine to calculate Bernoulli numbers , a complex calculation Requiring a recursive algorithm. This is considered to be the first example of a true computer program, a series of instructions which is not known in the program.
Several examples of analog computation survived into recent times. A planimeter is a device which is integrals, using distance as the analog quantity. Until the 1980s, HVAC systems used air Both have the analog quantity and the controlling element. Unlike modern digital computers, they are not very flexible, and need to be reconfigured (ie, reprogrammed) manually to switch them from one to another. Analog computers had an advantage over early digital computers in the United States.
Since computers Were uncommon in this era, the solutions Were Often hard-coded into paper forms Such As nomograms ,  qui Could Produce Then analog solutions to problems thesis, Such As the distribution of Pressures and temperatures in a heating system.
Digital electronic computers
The “brain” [computer] may one day come down to our level [of the common people] and help with our income tax and book-keeping calculations. But this is speculation and there is no sign of it so far.- British newspaper The Star in June 1949 news article about the EDSAC computer, long before the era of the personal computers. 
None of the early computational devices were really computers in the modern sense, and it had considerable advancement in mathematics and theory before the first modern computers could be designed.
The first recorded idea of using digital electronics for computing the 1931 paper “The Use of Thyratrons for High Speed Automatic Counting of Physical Phenomena” by CE Wynn-Williams . From 1934 to 1936, NEC engineer Akira Nakashima published a series of papers introducing switching circuit theory , using digital electronics for Boolean algebraic operations,   influencing Claude Shannon’s seminal 1938 paper ” A Symbolic Analysis of Relay and Switching Circuits “. 
The 1937 Atanasoff-Berry computer design was the first digital electronic computer (though not programmable), and the Z3 computer from 1941, by German inventor Konrad Zuse was the first working programmable, fully automatic computing machine.
Alan Turing modelling computation in terms of one-dimensional storage, leading to the idea of the Turing machine and Turing-complete programming systems.
The ENIAC (Electronic Numerical Integrator And Computer) was published in 1946. It was Turing-complete, [ citation needed ] digital, and capable of being reprogrammed to solve a full range of computing problems .
The Manchester Small-Scale Experimental Machine (SSEM), nicknamed Baby, was the first stored-program computer . It was built at the Victoria University of Manchester by Frederic C. Williams , Tom Kilburn and Geoff Tootill , and ran its first program on 21 June 1948.  The first stored-program transistor was the ETL Mark III, developed by Japan’s Electrotechnical Laboratory    from 1954  to 1956. 
The microprocessor was introduced with the Intel 4004 . It Began with the ” Busicom Project”  have Masatoshi Shima ‘s three-chip CPU design in 1968   before Sharp ‘s Tadashi Sasaki Conceived of a single-chip design CPU, qui he Discussed with Busicom and Intel in 1968.  The Intel 4004 was then developed as a single-chip microprocessor from 1969 to 1970, led by Intel’s Marcian Hoff and Federico Faggin and Busicom’s Masatoshi Shima. The microprocessor led to the development of microcomputers , and the microcomputer revolution .
The 1980s brought about significant advances with microprocessor that greatly impacted the fields of engineering and other sciences. The Motorola 68000 microprocessor had a processing speed that was far superior to the other microprocessors being used at the time. Because of this, having a newer, faster microprocessor allowed for the newer microcomputers that came into being more efficiently in the amount of computing they were able to do. This was evident in the 1983 release of the Apple computer Lisa. Lisa Was the first personal computer with graphical user interface (GUI) That Was Commercially sold, she ran on the Motorola 68000, dual floppy drives, 5 MB hard drive and HAD 1MB of RAM. After successful launching Lisa, a year later Apple released its first Macintosh computer still running on the Motorola 68000 microprocessor. Another advancement because of microprocessors came from Texas Instruments. Texas Instruments first introduced their TMS9900 processor in June 1976.  They then used their microprocessor in their TI 99/4 computer.
Late 1980s and the beginning of the early 1990s we have more news. [ clarification needed ] In 1990, Apple released the Portable Macintosh , it was heavy weighing 7.3 kg (16 lb) and extremely expensive. It was not up to two years later. That same year Intel introduced the Touchstone Delta supercomputer, which had 512 microprocessors. This advancement was very important as a model for some of the fastest multi-processors systems in the world. It was even used for a prototype for Caltech researchers who used the model for satellite images and simulating molecular models for various fields of research.
Navigation and astronomy
The calculation of logarithms and trigonometric functions in a mathematical table , and interpolating between known cases. For small enough differences, this linear operation was accurate enough for use in navigation and astronomyin the Age of Exploration . The uses of interpolation have been used in the past 500 years by the twentieth century Leslie Comrie and WJ Eckert systematized the use of interpolation in tables of numbers for punch card calculation.
The numerical solution of differential equations, notably the Navier-Stokes equations was an important stimulus to computing, with Lewis Fry Richardson’s numerical approach to solving differential equations. The first Computerized weather forecast Was Performed in 1950 by a team Composed of American meteorologists Jule Charney , Philip Thompson, Larry Gates, and Norwegian meteorologist Ragnar Fjørtoft , applied mathematician John von Neumann , and ENIAC program Klara Dan von Neumann .    To this day, some of the Most Powerful computer systems on Earth are used for weather forecasts. [ quote needed ]
By the late 1960s, computer systems could perform symbolic algebraic manipulations well enough to pass college-level calculus courses. [ quote needed ]
- Charles Babbage Institute – University of Minnesota
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