Instruct: Given a question, retrieve relevant passages that can help answer the question.
Query: What is the origin of the word "algorithm"?
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.
He developed, in the early 1960s, the first algorithm for discerning phylogenetic relationships among species based upon their respective character states observed over a set of characters. This work was honored by James Farris and Arnold Kluge in their later appellation of related algorithms as "Wagner parsimony."
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).
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.
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.
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.
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.
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).
In 1946, John Mauchly made the first mention of binary search as part of the Moore School Lectures, a seminal and foundational college course in computing. In 1957, William Wesley Peterson published the first method for interpolation search. Every published binary search algorithm worked only for arrays whose length is one less than a power of two until 1960, when Derrick Henry Lehmer published a binary search algorithm that worked on all arrays. In 1962, Hermann Bottenbruch presented an ALGOL 60 implementation of binary search that placed the comparison for equality at the end, increasing the average number of iterations by one, but reducing to one the number of comparisons per iteration. The uniform binary search was developed by A. K. Chandra of Stanford University in 1971. In 1986, Bernard Chazelle and Leonidas J. Guibas introduced fractional cascading as a method to solve numerous search problems in computational geometry.
The origins of the word "scarlet" have been debated quite extensively and are crucial to understanding what scarlet actually was in the Middle Ages. The word certainly came to English from Old French "escarlate", which is one of a wide range of similar words in the Romance languages such as Provençal "escarlat", Spanish and Portuguese "escarlate", Italian "scarlatto", and medieval Latin "scarlat(t)um". The origin of this romance word, however, has been more widely debated. For a long time the origin was thought to be a Persian word which takes forms like "saqalāt", "siqalāt", or "suqlāt". However, the romance word is now thought to come from Arabic "siklāt" (later "siklātūn"), denoting very expensive, luxury silks dyed scarlet-red using the exceptionally expensive dye kermes. Arabic "siklāt" is first attested around the ninth century, and now thought also to be the origin of the Persian word, which is first attested around the 1290s. The origin of the word "siklāt" is itself uncertain and may come from the Late Roman term "sigillatus" (Latin)/"σιγιλλατον" (Greek), denoting a kind of cloth decorated with seal-like patterns (from Latin "sigillum" 'seal'). The word then came to be used of woollen cloth dyed with the same dye. The most obvious route for the Arabic word "siklāt" to have entered the Romance languages would be via the Arabic-speaking Iberian region of Al-Andalus, particularly Almería, where kermes was produced extensively.
Al-Karkhi (953–1029), also known as Al-Karaji, was the successor of Abū al-Wafā' al-Būzjānī (940–998) and he discovered the first numerical solution to equations of the form ax + bx = c. Al-Karkhi only considered positive roots. Al-Karkhi is also regarded as the first person to free algebra from geometrical operations and replace them with the type of arithmetic operations which are at the core of algebra today. His work on algebra and polynomials, gave the rules for arithmetic operations to manipulate polynomials. The historian of mathematics F. Woepcke, in "Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi" (Paris, 1853), praised Al-Karaji for being "the first who introduced the theory of algebraic calculus". Stemming from this, Al-Karaji investigated binomial coefficients and Pascal's triangle.
In 1908, Wilsdorf registered the trademark "Rolex" and opened an office in La Chaux-de-Fonds, Switzerland. The book "The Best of Time: Rolex Wristwatches: An Unauthorized History" by Jeffrey P. Hess and James Dowling says that the name was just made up. One story, never confirmed by Wilsdorf, recounts that the name came from the French phrase "horlogerie exquise", meaning "exquisite clockwork" or as a contraction of "horological excellence". Wilsdorf was said to want his watch brand's name to be easily pronounceable in any language. He also thought that the name "Rolex" was onomatopoeic, sounding like a watch being wound. It is easily pronounceable in many languages and, as all its upper-case letters have the same size, can be written symmetrically. It was also short enough to fit on the face of a watch.
"Eureka" comes from the Ancient Greek word "heúrēka", meaning "I found (it)", which is the first person singular perfect indicative active of the verb "heuriskō" "I find". It is closely related to heuristic, which refers to experience-based techniques for problem solving, learning, and discovery.
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.
The most commonly used system of numerals is the Hindu–Arabic numeral system. Two Indian mathematicians are credited with developing it. Aryabhata of Kusumapura developed the place-value notation in the 5th century and a century later Brahmagupta introduced the symbol for zero. The numeral system and the zero concept, developed by the Hindus in India, slowly spread to other surrounding countries due to their commercial and military activities with India. The Arabs adopted and modified it. Even today, the Arabs call the numerals which they use "Rakam Al-Hind" or the Hindu numeral system. The Arabs translated Hindu texts on numerology and spread them to the western world due to their trade links with them. The Western world modified them and called them the Arabic numerals, as they learned them from the Arabs. Hence the current western numeral system is the modified version of the Hindu numeral system developed in India. It also exhibits a great similarity to the Sanskrit–Devanagari notation, which is still used in India and neighbouring Nepal.
The priority dispute had an effect of separating English-speaking mathematicians from those in the continental Europe for many years. Only in the 1820s, due to the efforts of the Analytical Society, did Leibnizian analytical calculus become accepted in England. Today, both Newton and Leibniz are given credit for independently developing the basics of calculus. It is Leibniz, however, who is credited with giving the new discipline the name it is known by today: "calculus". Newton's name for it was "the science of fluents and fluxions".
The origin of the word "sicaricon" (or "saqrīqūn") is now obscure. The word is believed by some to be a corruption of the Greek word χαισαρίχιον, or what is called in Latin "caesaricium". Others, namely, Heinrich Graetz and M.S. Zuckermandel, think the word to be derived from "Sicarii", a group associated with murders, brigandage and robbery during the Second Temple period. Largely mentioned in regard to assassinations, there is no historical evidence, however, to connect the "Sicarii" with the expropriation of land. The author of "Sefer Arukh" brings down a different interpretation, saying that the word is merely an acronym for: שא קרקעי והניחני (= "Take my land, but leave me alone"), a view supported by Talmudic exegetes, Rashi and Solomon Sirilio. In any case, the word unanimously refers to a Roman or foreign molester who expropriates land from its Jewish owner, usually by a decree made by a tyrant king (Caesar).
The first one-way encryptions were likely developed by James H. Ellis, Clifford Cocks, and Malcolm Williamson at the UK intelligence agency GCHQ during the 1960s and 1970s and were published independently by Diffie and Hellman in 1976 (History of cryptography). Common modern one-way encryption algorithms, including MD5 (message digest) and SHA-512 (secure hash algorithm) are similar to the first such algorithms in that they also contain no mechanism to disclose the original data. The output of these modern one-way encryptions offer high privacy but are not homomorphic, meaning that the results of the one-way encryptions do not allow high order math operations (such as match). For example, we cannot use two SHA-512 sums to compare the closeness of two encrypted documents. This limitation makes it impossible for these one-way encryptions to be used to support classifying models in machine learning—or nearly anything else.
The word "epistemology" is derived from the ancient Greek "epistēmē" meaning "knowledge" and the suffix "-logy", meaning "logical discourse" (derived from the Greek word "logos" meaning "discourse"). It is analogue to the German "Wissenschaftslehre" (literally, theory of science) which was introduced by philosophers Johann Fichte and Bernard Bolzano in the late 18th century. The word first appeared in English in 1847 as a translation of the German in New York's "Eclectic Magazine" review of a philosophical novel by German author Jean Paul:
Writing was introduced by the Greeks and from there also brought to the Romans (6th century BC). There are five alphabets in regular use in the areas generally considered Europe. The Latin alphabet was developed into several scripts. In the early years of Europe, the Carolingian minuscules were the most important variety of the Latin script. From this two branches developed, the Gothic/Fracture/German tradition, which Germans used well into the 20th century, and the Italian/Italic/Antiqua/Latin tradition, still used. For some nations the integration into Europe meant giving up older scripts, e.g. the Germanic gave up the runes (Futhark) (3rd to 17th centuries), the Irish the Ogham script (4th to 7th centuries). The Cyrillic script is the second most widespread alphabet in Europe, and was developed in the 9th century under the influence of the Greek, Latin and Glagolitic alphabets. Both the Latin and Cyrillic alphabets are used for multiple languages in multiple states, both inside and outside Europe. As well as these two, there are three alphabets used primarily for a single language, although they are occasionally applied to minority languages in the states from which they originate. The oldest of these alphabets is the Greek alphabet, which could be considered the progenitor of all the surviving alphabets of Europe, with the earliest recorded inscriptions appearing in the 9th century BC. The other two are both found in the Caucasus, both originating in the 5th century. The Georgian alphabet is used primarily to write Georgian, though it is also used to write the other Kartvelian languages, Svan, Mingrelian and Laz, all of which are found largely within the borders of Georgia. The Armenian alphabet is used to write the Armenian language, which has two dialects, and has been used to write Turkish in the past.
The common terms used in the theory are chiefly due to the founders. Argand called formula_140 the "direction factor", and formula_141 the "modulus"; Cauchy (1828) called formula_140 the "reduced form" (l'expression réduite) and apparently introduced the term "argument"; Gauss used for formula_143, introduced the term "complex number" for , and called the "norm". The expression "direction coefficient", often used for formula_140, is due to Hankel (1867), and "absolute value," for "modulus," is due to Weierstrass.
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.
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):
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.
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.