What is the origin of the word "algorithm"?
21527#64
While the word "algorithm" goes back only to certain readers of al-Khwārizmī, careful descriptions of methods of solution are older than proofs: such methods (that is, algorithms) are as old as any recognisable mathematics—ancient Egyptian, Babylonian, Vedic, Chinese—whereas proofs appeared only with the Greeks of the classical period.
An interesting early case is that of what we now call the Euclidean algorithm. In its basic form (namely, as an algorithm for computing the greatest common divisor) it appears as Proposition 2 of Book VII in "Elements", together with a proof of correctness. However, in the form that is often used in number theory (namely, as an algorithm for finding integer solutions to an equation formula_78,
or, what is the same, for finding the quantities whose existence is assured by the Chinese remainder theorem) it first appears in the works of Āryabhaṭa (5th–6th century CE) as an algorithm called
"kuṭṭaka" ("pulveriser"), without a proof of correctness.
Number theory
775#3
The word "algorithm" itself derives from the 9th century mathematician Muḥammad ibn Mūsā al-Khwārizmī, Latinized "Algoritmi". A partial formalization of what would become the modern concept of algorithm began with attempts to solve the Entscheidungsproblem (decision problem) posed by David Hilbert in 1928. Later formalizations were framed as attempts to define "effective calculability" or "effective method". Those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, and Alan Turing's Turing machines of 1936–37 and 1939.
Algorithm
775#4
The word 'algorithm' has its roots in Latinizing the name of Muhammad ibn Musa al-Khwarizmi in a first step to "algorismus". Al-Khwārizmī (, , c. 780–850) was a Persian mathematician, astronomer, geographer, and scholar in the House of Wisdom in Baghdad, whose name means 'the native of Khwarezm', a region that was part of Greater Iran and is now in Uzbekistan.
Algorithm
103533#2
With respect to the terms "source" and "target" there are two distinct traditions of usage:In ancient Greek the word "αναλογια" ("analogia") originally meant proportionality, in the mathematical sense, and it was indeed sometimes translated to Latin as "proportio". From there analogy was understood as identity of relation between any two ordered pairs, whether of mathematical nature or not. Kant's "Critique of Judgment" held to this notion. Kant argued that there can be exactly the same relation between two completely different objects. The same notion of analogy was used in the US-based SAT tests, that included "analogy questions" in the form "A is to B as C is to "what"?" For example, "Hand is to palm as foot is to ____?" These questions were usually given in the Aristotelian format: HAND : PALM : : FOOT : ____ While most competent English speakers will immediately give the right answer to the analogy question ("sole"), it is more difficult to identify and describe the exact relation that holds both between pairs such as "hand" and "palm", and between "foot" and "sole". This relation is not apparent in some lexical definitions of "palm" and "sole", where the former is defined as "the inner surface of the hand", and the latter as "the underside of the foot". Analogy and abstraction are different cognitive processes, and analogy is often an easier one. This analogy is not comparing "all" the properties between a hand and a foot, but rather comparing the "relationship" between a hand and its palm to a foot and its sole. While a hand and a foot have many dissimilarities, the analogy focuses on their similarity in having an inner surface. A computer algorithm has achieved human-level performance on multiple-choice analogy questions from the SAT test. The algorithm measures the similarity of relations between pairs of words (e.g., the similarity between the pairs HAND:PALM and FOOT:SOLE) by statistical analysis of a large collection of text. It answers SAT questions by selecting the choice with the highest relational similarity.
Analogy
14400#42
In mathematics, the mathematician Muhammad ibn Musa al-Khwarizmi (c. 780–850) gave his name to the concept of the algorithm, while the term algebra is derived from "al-jabr", the beginning of the title of one of his publications. What is now known as Arabic numerals originally came from India, but Muslim mathematicians made several key refinements to the number system, such as the introduction of decimal point notation.
History of science
25971#30
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.
Rubik's Cube
775#11
An "enumerably infinite set" is one whose elements can be put into one-to-one correspondence with the integers. Thus, Boolos and Jeffrey are saying that an algorithm implies instructions for a process that "creates" output integers from an "arbitrary" "input" integer or integers that, in theory, can be arbitrarily large. Thus an algorithm can be an algebraic equation such as "y = m + n" – two arbitrary "input variables" "m" and "n" that produce an output "y". But various authors' attempts to define the notion indicate that the word implies much more than this, something on the order of (for the addition example):
Algorithm
13477275#6
Simplified LESK Algorithm with smart default word sense (Vasilescu et al., 2004) 
The COMPUTEOVERLAP function returns the number of words in common between two sets, ignoring function words or other words on a stop list. The original Lesk algorithm defines the context in a more complex way.
Lesk algorithm
14046416#2
This enzyme belongs to the family of oxidoreductases, specifically those acting on paired donors, with O2 as oxidant and incorporation or reduction of oxygen. The oxygen incorporated need not be derived from O2 with 2-oxoglutarate as one donor, and incorporation of one atom o oxygen into each donor. The systematic name of this enzyme class is N6,N6,N6-trimethyl-L-lysine,2-oxoglutarate:oxygen oxidoreductase (3-hydroxylating). Other names in common use include trimethyllysine alpha-ketoglutarate dioxygenase, TML-alpha-ketoglutarate dioxygenase, TML hydroxylase, 6-N,6-N,6-N-trimethyl-L-lysine,2-oxoglutarate:oxygen oxidoreductase, and (3-hydroxylating). This enzyme participates in lysine degradation and L-carnitine biosynthesis and requires the presence of iron and ascorbate.
Trimethyllysine dioxygenase
5255884#1
Ƨ was used in the Zhuang alphabet from 1957 to 1986 to indicate the second, or falling, tone (), due to its resemblance to the numeral 2, along with four other letters resembling numbers. (See table). In 1986, Ƨ was replaced by the similarly shaped, but fully Latin, Z, when the alphabet was simplified for use in computers.
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