825 –Al-Khawarizmi described thealgorism, algorithms for using theHindu–Arabic numeral system, in his treatiseOn the Calculation with Hindu Numerals, which wastranslated into Latin asAlgoritmi de numero Indorum, where "Algoritmi", the translator's rendition of the author's name gave rise to the wordalgorithm (Latinalgorithmus) with a meaning "calculation method"
c. 1025 –Ibn al-Haytham (Alhazen), was the first mathematician to derive the formula for the sum of the fourthpowers, and in turn, he develops an algorithm for determining the general formula for the sum of anyintegral powers[2]
c. 1400 –Ahmad al-Qalqashandi gives a list ofciphers in hisSubh al-a'sha which include bothsubstitution andtransposition, and for the first time, a cipher with multiple substitutions for eachplaintext letter; he also gives an exposition on and worked example ofcryptanalysis, including the use of tables ofletter frequencies and sets of letters which can not occur together in one word
1706 –John Machin develops a quickly converging inverse-tangent series for π and computes π to 100 decimal places
1768 –Leonhard Euler publishes his method for numerical integration of ordinary differential equations in problem 85 of Institutiones calculi integralis[3]
1789 –Jurij Vega improves Machin's formula and computes π to 140 decimal places,
1995 – soft-marginsupport vector machine algorithm was published byVladimir Vapnik andCorinna Cortes. It adds a soft-margin idea to the 1992 algorithm by Boser, Nguyon, Vapnik, and is the algorithm that people usually refer to when saying SVM
^Kublanovskaya, Vera N. (1961). "On some algorithms for the solution of the complete eigenvalue problem".USSR Computational Mathematics and Mathematical Physics.1 (3):637–657.doi:10.1016/0041-5553(63)90168-X. Also published in: Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki [Journal of Computational Mathematics and Mathematical Physics], 1(4), pages 555–570 (1961).
