Arithmetic (~20,000 BC) - Counting abstract objects
The invention of arithmetic provided a way to compute abstractly about numbers of objects.

Written language (~4000 BC) - A systematic way to record knowledge
A central event in the emergence of civilization, written language provided a systematic way to record and transmit  knowledge.

Babylonian astronomy (~500 BC) - Using arithmetic to predict the heavens
The Babylonians introduced mathematical calculation as a way to find the behavior of planets and a few other systems in nature.

Pythagoras (~500 BC) - Numbers are the key to nature
The Pythagoreans promoted the idea that numbers could be used to systematically understand and compute aspects of nature, music, and the world.

Panini (~400 BC) - Finding the rules of human language
Panini created a grammar for Sanskrit, forming the basis for systematic linguistics.

Aristotle (~350 BC) - Classifying the world, and introducing logic
Aristotle tried to systematize knowledge, first by classifying objects in the world, and second by inventing the idea of logic  as a way to formalize human reasoning.

Library of Alexandria (~300 BC) - Collecting the world’s knowledge
The Library of Alexandria collected perhaps half a million scrolls, with works covering all areas of knowledge.

Archimedes (~250 BC) - Computing as a basis for technology
Archimedes used mathematics to create and understand technological devices, and may have built gear-based, mechanical astronomical calculators.

Ramon Llull (1300) - Creating knowledge by combinations
Ramon Llull promoted a scheme for systematically creating knowledge from formal combinations of ideas.

John Graunt (1662) - Inventing the idea of statistics
Graunt and others started to systematically summarize demographic and economic data using statistical ideas based on mathematics.

Gottfried Leibniz (1684) - Answering questions using computation
Leibniz promoted the idea of answering all human questions by converting them to a universal symbolic language, then  applying logic using a machine. He also tried to organize the systematic collection of knowledge to use in such a system.

Isaac Newton (1687) - Mathematics as a basis for natural science
Newton introduced the idea that mathematical rules could be used to systematically compute the behavior of systems in nature.

Carl Linnaeus (1750) - Creating a taxonomy for life
Linnaeus systematized the classification of living organisms, introducing ideas like binomial naming.

Encyclopædia Britannica etc. (1768) - Printing collected knowledge
The Encyclopædia Britannica—and the Encyclopédie of Diderot and d’Alembert—attempted to summarize all current knowledge in book form.

Charles Babbage (1830) - Printing mathematical tables by machine
Babbage constructed a mechanical computer to automate the creation of mathematical knowledge.

Melvil Dewey (1876) - Classifying the world’s knowledge
Dewey invented the Dewey Decimal System for classifying the world’s knowledge and specifying how to organize books in libraries.

Gottlob Frege (1879) - Axiomatizing knowledge through logic
Frege created a formal system and language in which mathematical and other knowledge could be represented in terms of an extended form of logic.

Oxford English Dictionary (1880s) - Collecting every word in English
With extensive information supplied by a network of volunteers, theOED was a systematic project to get complete knowledge of all the words in the English language.

Alan Turing (1936) - The concept of universal computation
Turing showed that any reasonable computation could be done by programming a fixed universal machine—and then  speculated that such a machine could emulate the brain.

Digital computers (1940s) - Automating the process of computation
The arrival of digital electronic computers provided the mechanism by which computations of all kinds could be automated with increasing efficiency.

Computational linguistics (1950s) - Algorithms for human language
Computational linguistics put the concepts of grammar into an algorithmic form that promised to automate processes of language understanding.

Computer languages (1957) - Languages for programming tasks
Fortran, COBOL, and other early computer languages defined the concept of a precise formal representation for tasks to be performed by computers.

Pop-culture computers (1950s-1960s) - Imagining intelligent machines
From the Tracy and Hepburn movie Desk Set to TV’s Batman and Star Trek to HAL in 2001: A Space Odyssey and the  robots of Isaac Asimov, the public became used to the idea that computers would eventually have human-like knowledge  and reasoning.

Artificial Intelligence (1950s-1960s) - Making computers intelligent
Artificial Intelligence defined a research program for developing computers that show general intelligence–and led to many spinoffs important for specific purposes.

Interactive computing (1970s-1980s) - Getting immediate results from computers
With the emergence of progressively cheaper computers, it became possible to do computations immediately, integrating  them as part of the everyday process of working with knowledge.

Neural networks (1980s) - Handling knowledge by emulating the brain
With precursors in the 1940s, neural networks emerged in the 1980s as a concept for storing and manipulating various types of knowledge using connections reminiscent of nerve cells.

Cyc (1984) - Creating a computable database of common sense
Cyc has been a long-running project to encode common sense facts in a computable form.

The Web (1989) - Collecting the world’s information
The web has grown to provide billions of pages of freely available information from all corners of civilization.

Google (1997) - An engine to search the web
Google and other search engines provided highly efficient capabilities to do textual searches across the whole content of the web.

Wikipedia (2001) - Self-organized encyclopedia
Volunteer contributors have assembled millions of pages of encyclopedia material, providing textual descriptions of practically all areas of human knowledge.

Web 2.0 (early 2000s) - Societally organized information
Social networking and other collective websites defined a mechanism for collectively assembling information by and about people.

A New Kind of Science (2002) - Exploring the computational universe
Stephen Wolfram explored the universe of possible simple programs, and showed that knowledge about many natural and artificial processes could be represented in terms of surprisingly simple programs.