the following timeline outlines the development of algorithms (mainly "mathematical recipes") since their inception. ==before modern era== * before - writing about "recipes" (on cooking, rituals, agriculture and other themes) * c. 1600 bc - babylonians develop earliest known algorithms for factorization and finding square roots * c. 300 bc - euclid's algorithm * c. 200 bc - the sieve of eratosthenes * 263 ad - gaussian elimination described by liu hui * 628 - chakravala method described by brahmagupta * c. 820 - al-khawarizmi described algorithms for solving linear equations and quadratic equations in his algebra; the word algorithm comes from his name * 825 - al-khawarizmi described the algorism, algorithms for using the hindu-arabic numerals, in his treatise on the calculation with hindu numerals, which was translated into latin as algoritmi de numero indorum, where "algoritmi", the translator's rendition of the author's name gave rise to the word algorithm (latin algorithmus) with a meaning "calculation method" * c. 850 - cryptanalysis and frequency analysis algorithms developed by al-kindi (alkindus) in a manuscript on deciphering cryptographic messages, which contains algorithms on breaking encryptions and ciphers.simon singh, the code book, pp. 14-20 * c. 1025 - ibn al-haytham (alhazen), was the first mathematician to derive the formula for the sum of the fourth powers, and in turn, he develops an algorithm for determining the general formula for the sum of any integral powers, which was fundamental to the development of integral calculusvictor j. katz (1995). "ideas of calculus in islam and india", mathematics magazine 68 (3), p. 163-174. * c. 1400 - ahmad al-qalqashandi gives a list of ciphers in his subh al-a'sha which include both substitution and transposition, and for the first time, a cipher with multiple substitutions for each plaintext letter; he also gives an exposition on and worked example of cryptanalysis, including the use of tables of letter frequencies and sets of letters which can not occur together in one word ==before 1940== * 1614 - john napier develops method for performing calculations using logarithms * 1671 - newtonâraphson method developed by isaac newton * 1690 - newtonâraphson method independently developed by joseph raphson * 1706 - john machin develops a quickly converging inverse-tangent series for Ï and computes Ï to 100 decimal places, * 1789 - jurij vega improves machin's formula a
Algorithms Computing_timelines Mathematics_timelines