Instruct: Given a question, retrieve relevant documents that can help answer the question.
Query: Who developed the first algorithms?
Since the 18th century, women have developed scientific computations, including Nicole-Reine Lepaute's prediction of Halley's Comet, and Maria Mitchell's computation of the motion of Venus. The first algorithm intended to be executed by a computer was designed by Ada Lovelace who was a pioneer in the field. Grace Hopper was the first person to design a compiler for a programming language. Throughout the 19th and early-20th century, and up to World War II, programming was predominantly done by women; significant examples include the Harvard Computers, codebreaking at Bletchley Park and engineering at NASA.
Abstract algebra was developed in the 19th century, deriving from the interest in solving equations, initially focusing on what is now called Galois theory, and on constructibility issues. George Peacock was the founder of axiomatic thinking in arithmetic and algebra. Augustus De Morgan discovered relation algebra in his "Syllabus of a Proposed System of Logic". Josiah Willard Gibbs developed an algebra of vectors in three-dimensional space, and Arthur Cayley developed an algebra of matrices (this is a noncommutative algebra).
The Xerox Alto, developed at Xerox PARC in 1973, was the first computer to use a mouse, the desktop metaphor, and a graphical user interface (GUI), concepts first introduced by Douglas Engelbart while at International. It was the first example of what would today be recognized as a complete personal computer. The first machines were introduced on 1 March 1973,
The Needleman–Wunsch algorithm is an algorithm used in bioinformatics to align protein or nucleotide sequences. It was one of the first applications of dynamic programming to compare biological sequences. The algorithm was developed by Saul B. Needleman and Christian D. Wunsch and published in 1970. The algorithm essentially divides a large problem (e.g. the full sequence) into a series of smaller problems and uses the solutions to the smaller problems to reconstruct a solution to the larger problem. It is also sometimes referred to as the optimal matching algorithm and the global alignment technique. The Needleman–Wunsch algorithm is still widely used for optimal global alignment, particularly when the quality of the global alignment is of the utmost importance.
The history of game making begins with the development of the first video games, although which video game is the first depends on the definition of "video game". The first games created had little entertainment value, and their development focus was separate from user experience—in fact, these games required mainframe computers to play them. "OXO", written by Alexander S. Douglas in 1952, was the first computer game to use a digital display. In 1958, a game called "Tennis for Two", which displayed its output on an oscilloscope, was made by Willy Higinbotham, a physicist working at the Brookhaven National Laboratory. In 1961, a mainframe computer game called "Spacewar!" was developed by a group of Massachusetts Institute of Technology students led by Steve Russell.
In Rubik's cubers' parlance, a memorised sequence of moves that has a desired effect on the cube is called an algorithm. This terminology is derived from the mathematical use of "algorithm", meaning a list of well-defined instructions for performing a task from a given initial state, through well-defined successive states, to a desired end-state. Each method of solving the Rubik's Cube employs its own set of algorithms, together with descriptions of what effect the algorithm has, and when it can be used to bring the cube closer to being solved.
Stefan of Pise translated into Latin around 1127 an Arab manual of medical theory. The method of algorism for performing arithmetic with Indian-Arabic numerals was developed by the Persian al-Khwarizmi in the 9th century, and introduced in Europe by Leonardo Fibonacci (1170–1250). A translation by Robert of Chester of the "Algebra" by al-Kharizmi is known as early as 1145. Ibn al-Haytham (Alhazen, 980–1037) compiled treatises on optical sciences, which were used as references by Newton and Descartes. Medical sciences were also highly developed in Islam as testified by the Crusaders, who relied on Arab doctors on numerous occasions. Joinville reports he was saved in 1250 by a “Saracen” doctor.
The numeral system employed, known as algorism, is positional decimal notation. Various symbol sets are used to represent numbers in the Hindu–Arabic numeral system, potentially including both symbols that evolved from the Brahmi numerals, and symbols that developed independently. The symbols used to represent the system have split into various typographical variants since the Middle Ages:The evolution of the numerals in early Europe is shown here in a table created by the French scholar Jean-Étienne Montucla in his "Histoire de la Mathematique", which was published in 1757:
It was invented between the 1st and 4th centuries by Indian mathematicians. The system was adopted in Arabic mathematics by the 9th century. Influential were the books of Muḥammad ibn Mūsā al-Khwārizmī ("On the Calculation with Hindu Numerals", ) and Al-Kindi ("On the Use of the Hindu Numerals", ). The system later spread to medieval Europe by the High Middle Ages.
Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. As a result, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. Pythagoras established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The Pythagoreans are credited with the first proof of the Pythagorean theorem, though the statement of the theorem has a long history, and with the proof of the existence of irrational numbers. Although he was preceded by the Babylonians and the Chinese, the Neopythagorean mathematician Nicomachus (60–120 AD) provided one of the earliest Greco-Roman multiplication tables, whereas the oldest extant Greek multiplication table is found on a wax tablet dated to the 1st century AD (now found in the British Museum). The association of the Neopythagoreans with the Western invention of the multiplication table is evident in its later Medieval name: the "mensa Pythagorica".
Pickover states, “The Latin translation [of Al-Khuwarizmi's Algebra] introduced the decimal positional number system to Europe” (84). Later, Pickover writes that Fibonacci's Liber Abaci "introduced the Hindu-Arabic numerals and decimal system to Western Europe" (100).
Gottfried Leibniz, in memoranda not published before the late 19th and early 20th centuries, invented Boolean logic. His notation was isomorphic to that of "LoF": concatenation read as conjunction, and "non-("X")" read as the complement of "X". Leibniz's pioneering role in algebraic logic was foreshadowed by Lewis (1918) and Rescher (1954). But a full appreciation of Leibniz's accomplishments had to await the work of Wolfgang Lenzen, published in the 1980s and reviewed in Lenzen (2004).
The World Wide Web Worm (WWWW) was one of the earliest search engines for the World Wide Web (WWW). It is claimed by some to be the first search engine, though it was not released until March 1994, by which time a number of other search engines had been made publicly available. It was developed in September 1993 by Oliver McBryan at the University of Colorado as a research project.
Historically, there was much debate over whether it was Newton or Leibniz who first "invented" calculus. This argument, the Leibniz and Newton calculus controversy, involving Leibniz, who was German, and the Englishman Newton, led to a rift in the European mathematical community lasting over a century. Leibniz was the first to publish his investigations; however, it is well established that Newton had started his work several years prior to Leibniz and had already developed a theory of tangents by the time Leibniz became interested in the question.
It is not known how much this may have influenced Leibniz. The initial accusations were made by students and supporters of the two great scientists at the turn of the century, but after 1711 both of them became personally involved, accusing each other of plagiarism.
Also in 1973 Hewlett Packard introduced fully BASIC programmable microcomputers that fit entirely on top of a desk, including a keyboard, a small one-line display, and printer. The Wang 2200 microcomputer of 1973 had a full-size cathode ray tube (CRT) and cassette tape storage. These were generally expensive specialized computers sold for business or scientific uses. The introduction of the microprocessor, a single chip with all the circuitry that formerly occupied large cabinets, led to the proliferation of personal computers after 1975.
1974 saw the introduction of what is considered by many to be the first true "personal computer", the Altair 8800 created by Micro Instrumentation and Telemetry Systems (MITS). Based on the 8-bit Intel 8080 Microprocessor, the Altair is widely recognized as the spark that ignited the microcomputer revolution as the first commercially successful personal computer. The computer bus designed for the Altair was to become a "de facto" standard in the form of the S-100 bus, and the first programming language for the machine was Microsoft's founding product, Altair BASIC.
Academics working at the university include Sir Tim Berners-Lee, inventor of the World Wide Web, Wendy Hall, inventor of Microcosm (hypermedia system) a predecessor of the World Wide Web, founding director of the Web Science Trust between the University of Southampton and MIT, José Antonio Bowen, President of Goucher College and a Fellow of the Royal Society of Arts, Erich Zepler, who made leading contributions to radio receiver development, David Payne, who invented EDFA for use in fibre optics cables, Sir Barry Cunliffe, a pioneer of modern British archaeology, Ray Monk, the biographer of Ludwig Wittgenstein, Albie Sachs, former Judge of the Constitutional Court of South Africa, and Tim Holt, former President of the Royal Statistical Society and Office for National Statistics.
The Morse code was developed so that operators could translate the indentations marked on the paper tape into text messages. In his earliest code, Morse had planned to transmit only numerals, and to use a codebook to look up each word according to the number which had been sent. However, the code was soon expanded by Alfred Vail in 1840 to include letters and special characters, so it could be used more generally. Vail estimated the frequency of use of letters in the English language by counting the movable type he found in the type-cases of a local newspaper in Morristown. The shorter marks were called "dots", and the longer ones "dashes", and the letters most commonly used were assigned the shorter sequences of dots and dashes. This code was used since 1844 and became known as "Morse landline code" or "American Morse code".
From India, the thriving trade between Islamic sultans and Africa carried the concept to Cairo. Arabic mathematicians extended the system to include decimal fractions, and Muḥammad ibn Mūsā al-Ḵwārizmī wrote an important work about it in the 9th  century. The modern Arabic numerals were introduced to Europe with the translation of this work in the 12th century in Spain and Leonardo of Pisa's "Liber Abaci" of 1201. In Europe, the complete Indian system with the zero was derived from the Arabs in the 12th century.
The work was translated into Arabic around 820 by Al-Khwarizmi, whose "On the Calculation with Hindu Numerals" was in turn influential in the adoption of the Hindu-Arabic numerals in Europe from the 12th century.
Mathematical topics typically emerge and evolve through interactions among many researchers. Set theory, however, was founded by a single paper in 1874 by Georg Cantor: "On a Property of the Collection of All Real Algebraic Numbers".
Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy. The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. It is in Babylonian mathematics that elementary arithmetic (addition, subtraction, multiplication and division) first appear in the archaeological record. The Babylonians also possessed a place-value system, and used a sexagesimal numeral system, still in use today for measuring angles and time.
Historically, the first randomized algorithm was a method developed by Michael O. Rabin for the closest pair problem in computational geometry.
The study of randomized algorithms was spurred by the 1977 discovery of a randomized primality test (i.e., determining the primality of a number) by Robert M. Solovay and Volker Strassen. Soon afterwards Michael O. Rabin demonstrated that the 1976 Miller's primality test can be turned into a randomized algorithm. At that time, no practical deterministic algorithm for primality was known.
The LR algorithm was developed in the early 1950s by Heinz Rutishauser, who worked at that time as a research assistant of Eduard Stiefel at ETH Zurich. Stiefel suggested that Rutishauer use the sequence of moments "y" "A" "x", "k" = 0, 1, … (where "x" and "y" are arbitrary vectors) to find the eigenvalues of "A". Rutishauer took an algorithm of Alexander Aitken for this task and developed it into the "quotient–difference algorithm" or "qd algorithm". After arranging the computation in a suitable shape, he discovered that the qd algorithm is in fact the iteration "A" = "L""U" (LU decomposition), "A" = "U""L", applied on a tridiagonal matrix, from which the LR algorithm follows.
As the first published stemming algorithm, Lovins' work set a precedent and influenced future work in stemming algorithms, such as the Porter Stemmer published by Martin Porter in 1980 which has been recognized widely as the most common stemming algorithm for stemming English. Additionally, the Dawson Stemmer developed by John Dawson is an extension of the Lovins stemmer.
From the beginning of computing, the sorting problem has attracted a great deal of research, perhaps due to the complexity of solving it efficiently despite its simple, familiar statement. Among the authors of early sorting algorithms around 1951 was Betty Holberton (née Snyder), who worked on ENIAC and UNIVAC. Bubble sort was analyzed as early as 1956. Comparison sorting algorithms have a fundamental requirement of Ω("n" log "n") comparisons (some input sequences will require a multiple of "n" log "n" comparisons); algorithms not based on comparisons, such as counting sort, can have better performance. Although many consider sorting a solved problem—asymptotically optimal algorithms have been known since the mid-20th century—useful new algorithms are still being invented, with the now widely used Timsort dating to 2002, and the library sort being first published in 2006.