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The history of computing is longer than the history of computing hardware and modern computing technology and includes the history of methods intended for pen and paper or for chalk and slate, with or without the aid of tables. The timeline of computing presents a summary list of major developments in computing by date.

Concrete devices

Computing is intimately tied to the representation of numbers. But long before abstractions like number arose, 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, which was eventually abstracted into number;
comparison to a standard, a method for as

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 Computing is intimately tied to the representation of ''numbers''. But long before abstractions like ''number'' arose, 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 [[counting|count]] ''how many'' items, say on a [[tally stick]], which was eventually abstracted into ''number'';
-*''comparison to a standard'', a method for assuming ''[[reproducibility]]'' in a [[measurement]], the number of [[coin]]s, for example;
+*''comparison to a standard'', a method for as
-*the ''3-4-5'' right triangle was a device for assuring a ''right angle'', using [[rope]]s with 12 evenly spaced [[knot]]s, for example.
-==Numbers==
-Eventually, the concept of numbers became concrete and familiar enough for [[counting]] to arise, at times with sing-song mnemonics to teach [[sequence]]s to others. All the known languages have words for at least [[numbers in various languages|"one" and "two"]], and even some animals like the [[blackbird]] can distinguish a surprising number of items.
-Advances in the [[numeral system]] and [[mathematical notation]] eventually led to the discovery of mathematical operations such as addition, subtraction, multiplication, division, squaring, square root, and so forth. Eventually the operations were formalized, and concepts about the operations became understood well enough to be [[theorem|stated formally]], and even [[mathematical proof|proven]]. See, for example [[Euclidean algorithm|Euclid's algorithm]] for finding the greatest common divisor of two numbers.
-By medieval times, the [[positional notation|positional]] [[Hindu-Arabic numeral system]] had reached [[Europe]], which allowed for systematic computation of numbers. During this period, the representation of a calculation on [[paper]] actually allowed calculation of [[mathematical expression]]s, and the tabulation of [[mathematical function]]s such as the [[square root]] and the [[common logarithm]] (for use in multiplication and division) and the [[trigonometric function]]s. 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 Fermi]] would cover random scraps of paper with calculation, to satisfy their innate curiosity about an equation. Even into 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.
-==Navigation and astronomy==
-Starting with known special cases, the calculation of logarithms and trigonometric functions can be performed by looking up numbers in a [[mathematical table]], and [[interpolation|interpolating]] between known cases.  For small enough differences, this linear operation was accurate enough for use in [[navigation]] and [[astronomy]] in the [[Age of Exploration]]. The uses of interpolation have thrived in the past 500 years: by the [[twentieth century]] [[Leslie Comrie]] and [[W.J. Eckert]] systematized the use of interpolation in tables of numbers for [[history of computing hardware|punch card calculation]].
-In our time, even a student can simulate the motion of the planets, an N-body differential equation, using the concepts of [[numerical methods|numerical approximation]],  a feat which even Isaac Newton could admire, given his struggles with the motion of the Moon.
-==Weather prediction==
-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. To this day, the most powerful computer systems of the Earth are used for [[weather forecast]]s.
-==Symbolic computations==
-By the late [[1960s]], computer systems could perform symbolic algebraic manipulations well enough to pass college-level [[calculus]] courses.  Using programs like ''[[Maple computer algebra system|Maple]]'', ''[[Macsyma]] (now [[Maxima]])'' and ''[[Mathematica]]'', including some open source programs like ''[[yacas]]'', it is now possible to visualize concepts such as [[modular form]]s which were only accessible to the [[mathematics|mathematical]] imagination before this.
-==Books for further reading==
-See [[List of books on the history of computing]].
-==Journals==
-*''IEEE Annals of the History of Computing''
-===Writing computer history===
-The professionalization of computer [[historiography]] is a fairly recent phenomenon. As [[Paul N. Edwards]], a [[history of technology|historian of technology]] wrote, "Until the 1990s, this literature consisted almost entirely of memoirs by computer professionals, often tightly focused on the invention and design of particular machines or on the business history of early computer companies. A few important scholarly books, such as Williams’ ''A History of Computing Technology'', attempted to cover the whole sweep of computer history. Even these, however, generally focused on the computer as a technological object, rather than on applications or (especially) on the evolving social role of computers and networks." <ref>Paul N. Edwards, "[http://www.si.umich.edu/%7epne/PDF/makinghistory.pdf Making History: New Directions in Computer Historiography]", ''IEEE Annals of the History of Computing'', January-March, 2001.</ref> Edwards urges his colleagues to think "outside the box" to understand the social dynamics of the development and use of computers.
-Recent studies have begun to tell the story of the role of computers in the history of administration, business, communication and warfare.
-==Notes==
-<references/>
-==See also==
-* [[History of computing hardware]], [[Timeline of quantum computing]]
-* [[History of computer science]]
-* [[Algorithm]]
-* [[List of mathematicians]]
-* [[:Category:Computing timelines|Computing timelines]] category
-* [[Virtual Museum of Computing]]
-* The [[IBM 1130/snoopy calendar|Snoopy Calendar]] program is the classic [[Fortran]] program referenced in many nostalgic items on computer history (eg. '[[Real Programmers Don't Use Pascal]]').
-==External links==
-*[http://www.computer.org/portal/site/annals IEEE Annals of the History of Computing]
-*[http://www.algana.co.uk/HistoryofComputingGroup/HistoryofComputingGroup.htm Richmond (UK) History of Computing Group]
-*[http://ei.cs.vt.edu/~history/ The History of Computing] by J.A.N. Lee
-*[http://www.thocp.net/ The History of Computing Project]
-*[http://shot.press.jhu.edu/sigs/computers.htm SIG on Computers, Information and Society of the Society for the History of Technology]
-*[http://www.maxmon.com/history.htm A History of Computers]
-*[http://www.pbs.org/nerds/ Cringely's "Triumph of the Nerds"]
-*[http://www.computerhistory.org/ Computer History Museum]
-*[http://plato.stanford.edu/entries/computing-history/ Stanford Encyclopedia of Philosophy entry]
-*[http://www.myoddpc.com/other/history_of_computer.php The history of computer]
-*[http://www.cbi.umn.edu/ Charles Babbage Institute: Center for the History of Information Technology]
-*[http://www.tomandmaria.com/Tom/Resources/ResourceFile.htm Key Resources in the History of Computing]
-*[http://computerhistory.nicepods.biz History of the Computer]
-*[http://www.davros.org/misc/chronology.html A Chronology of Digital Computing Machines (to 1952)] by Mark Brader
-* [http://www.bitsavers.org/ Bitsavers], an effort to capture, salvage, and archive historical computer software and manuals from minicomputers and mainframes of the 50s, 60s, 70s, and 80s
-*[http://www.rk86.com/frolov/ Soviet calculators and computers collection] by Sergei Frolov
-*[http://www.emula3.com emula3.com] Emulation plus historic documents and images (see Library and Gallery sections)
-[[Category:History of computing| ]]
-[[Category:History of technology|Computing]]
-[[de:Computergeschichte]]
-[[es:Historia de la Informática]]
-[[fr:Histoire de l'informatique]]
-[[nl:Geschiedenis van de computer]]
-[[oc:Istòric de l'informatica]]
-[[pl:Historia informatyki]]
-[[sl:Zgodovina računalništva]]
-[[sv:Datorhistoria]]