Twentieth Century: 1975 - 2000
Computers and Mathematics
The availability of computers led to the solution of a long standing mathematical problem, the Four Colour Conjecture, in 1976. This was established by Kenneth Appel and Wolfgang Haken, whose proof made unprecedented use of large scale computers. The first attempt to prove this conjecture, which states that every map on the plane or the surface of a sphere can be coloured with only four colours so that no two adjacent countries have the same colour, was made by Kempe in 1879, but there was an error in his proof. The error was found by Heawood in 1890. Heawood showed however, that the conjecture becomes true when "four is replaced by "five." The results of both Heawood and Appel and Haken make use of many of Kempe's original ideas.
Appel and Haken completed their proof in June 1976 after using 1200 hours of computer time on three computers. Although the proof has now been simplified, it still requires a computer even to check it!
In 1978, Rivest, Shamir and Alderman published a paper on ciphers, which makes use of elementary number theory. In their cryptosystem, we begin by selecting two large primes p and q. Let n = pq and φ(n) = (p - 1)(q - 1). Encrytion and decryption keys c and d are selected so that
| C <- Me mod n (RSA encryption) |
The decryption of the ciphertext C is also performed with an exponentiation, using now the decryption key d as the exponent
| M <- Cd mod n (RSA decryption) |
The effectiveness of this system is tied to the difficulty of factorising large numbers.
Related to factorising is the problem of primality testing, that is, determining whether or not a number is prime. Such testing is known to take a rather long time even by computer, but the question is how long?
In 1971 S. A. Cook proved his famous theorem that the problem of deciding whether a given boolean expression is satisfiable, that is, has the value true for some assignment of boolean values to its variables, takes time bounded by a polynomial expression in the number of its variables on a nondeterministic computer. A nondeterministic automaton is one which can make an arbitrary choice between several alternative steps of computation; computers in common use are deterministic. Cook further showed that every problem which can be solved in nondeterministic polynomial time can be reduced to the problem of satisfiability; that is satisfiability is NP-complete. A list of other NP-complete problems -- problems with the property that every problem taking nondeterministic polynomial time can be reduced to them -- was soon compiled. A book on the subject was published in 1979 by Garey and Johnson.
Until 2002 when Manindra Agrawal and his coworkers established that primality testing could be carried out in deterministic polynomial time, it was unclear what the actual time complexity of primality was. However, Soloway and Strassen in 1977 published an algorithm which, given a confidence parameter k > 0, determines whether n is a prime with error probability 2-k by performing O(k log n) arithmetic operations.
Until 1981, when the IBM PC was intorduced, most computers were bulky and expensive. More material about the PC explosion can be found at http://www.eingang.org.Lecture/pcexp.html.
The next development was the creation of the World Wide Web, the website pbs.org gives the date as 1989, but we have to go into its history in more detail. In the United States the Department of Defense's Advenced Research Project Agency (ARPA) decided to connect some large computers so that they could share information and resources across whole states. Thus a system called ARPAnet was established in 1970.
In 1985 the National Science Foundation improved the system when it funded the NSFNET. This had a backbone of five supercomputer centres -- Princeton University, the University of Pittsburgh, the University of California in San Diego, the University of Illinois at Urbana-Champaign, and Cornell University to serve as highways for all state traffic.
NSF first allowed commercial use of the Internet in 1991 and in 1995 removed its funding completely.
The development of the Internet was largely a matter of creating software. Graphical User Interfaces had to be developed. Microsoft brought out Windows in 1985, which made use of the mouse, invented by Douglas Englebart in 1968. The other building blocks were the concept of the Uniform Resource Locator (URL) and Hypertext Markup Language (HTML). Tim Berners-Lee brought all this together and the first trials of the World Wide Web (WWW) were carried out at CERN Laboratories in December 1990.
On 30 April 1993, CERN's directors declared that WWW technology would be made freely usable by the public. Further information may be found at http://www.nethistory.info. Netscape was founded in 1994 and brought out JavaScript in 1995. This meant that programming could now be done with only the browser and an elementary text processor.
The first large commercial website was Amazon, which was developed in 1994. Search engines began to appear in the mid 1990s.
Space
The most significant discovery of the second half of the century made by a ground-based astronomer was the discovery on 22 Jun 1978 by James Christy of Pluto's major satellite Charon when he was examining highly magnified images of Pluto on photographic plates taken two months earlier. Pluto itself was discovered in 1931 by Clyde W. Tombaugh at Lowell Observatory, Arizona.
Space missions in the last quarter of the twentieth century added greatly to our knowledge of the solar system. In 1976 the two Viking landers reached Mars and, after a gap of twenty years, Mars Pathfinder lander landed successfully on Mars on 4 Jul 1997. The first spacecraft to land on Mars was the Mars 2, launched by the USSR in 1971.
In 1975 the European Space Agency began to work together with NASA on a plan that finally became the Hubble Space Telescope. This was finally launched into orbit aboard the Space Shuttle Discovery on 24 Apr 1990. it is still in operation, but in the years after the 2008 servicing mission, Hubble's components will slowly degrade to the point at which the telescope stops working. A photograph of Pluto and its moon Charon taken by Hubble is shown below.
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Photograph of Pluto and Charon taken by Hubble Space Telescope on 16 May 1994. An interesting video on Pluto is found at boogerflickr's flickr page |
Also of interest is the Mir Space Station. Its core module was launched on 20 Feb 1986 by the Proton booster. The Specktr module was originally designed for military purposes by the Soviet Union but was finally reassigned to Mir in May 1995 with the cooperation of NASA. The last module, Priroda, was finally docked to Mir on 26 Apr 1996. The mission was finally completed on 29 Mar 2001, when the Mir Space Station reentered the Earth's atmosphere and the debris splashed down into the Pacific Ocean.
Further information can be found at the links in the page on Space Science in the Yahoo Directory.
Cloning
The report of the cloning of a sheep by Ian Wilmut at the Roslin Institute, Scotland in 1996 created quite a sensation. An online report is found in Scientific American, Mar 1997.
The cloning of animals in fact goes back much earlier than this.
A detailed history is found at www.skewsme.com/cloning.html.
The Yahoo Directory lists 21 sites. More information can be found by direct search.
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