spoke Al-Khwarizmi"), where "Algorizmi" was the translator's Latinization of Al-Khwarizmi's name. Al-Khwarizmi was the most widely read mathematician in Europe in the late Middle Ages, primarily through another of his books, the Algebra. In late medieval Latin, algorismus, English "algorism", the corruption of his name, meant the "decimal number system". In the 15th century, under the influence of the Greek word ἀριθμός (arithmos), "number" (cf. "arithmetic"), the Latin word was altered to algorithmus, and the corresponding English term "algorithm" is first attested in the 17th century; the modern sense was introduced in the 19th century. Indian mathematics was predominantly algorithmic. Algorithms that are representative of the Indian mathematical tradition range from the ancient Śulbasūtrās to the medieval texts of the Kerala School.Brahmagupta devoted several chapters of Brāhmasphuṭasiddhānta to mathematics. In chapters 12 and 18 in particular, he laid the foundations of the two major fields of Indian mathematics, pati-ganita (“mathematics of procedures,” or algorithms) and bija-ganita (“mathematics of seeds,” or equations), which roughly correspond to arithmetic (including mensuration) and algebra, respectively. In English, the word algorithm was first used in about 1230 and then by Chaucer in 1391. English adopted the French term, but it was not until the late 19th century that "algorithm" took on the meaning that it has in modern English. Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu. It begins with: which translates to: The poem is a few hundred lines long and summarizes the art of calculating with the new styled Indian dice (Tali Indorum), or Hindu numerals. A partial formalization of 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. Informal definition An informal definition could be "a set of rules that precisely defines a sequence of operations", which would include all computer programs (including programs that do not perform numeric calculations), and (for example) any prescribed bureaucratic procedure or cook-book recipe. In general, a program is only an algorithm if it stops eventually—even though infinite loops may sometimes prove desirable. A prototypical example