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* In applied mathematics, Jacobi develops [[Jacobi method|technique for solving numerical equations]].<ref>[http://canum2006.univ-rennes1.fr/exposes_et_posters/vandervorst.pdf Jacobi's Ideas on Eigenvalue Computation in a modern context], Henk van der Vorst.</ref><ref>[http://www.encyclopediaofmath.org/index.php/Jacobi_method Jacobi method], [[Encyclopedia of Mathematics]].</ref><ref>[http://www.siam.org/meetings/la09/talks/benzi.pdf The Early History of Matrix Iterations: With a Focus on the Italian Contribution], Michele Benzi, 26 October 2009. SIAM Conference on Applied Linear Algebra, Monterey Bay – Seaside, California.</ref>
* Gauss Seidel first published.
* To help with computing tides, [[Harmonic Analyser]] is built in 1886.
* 850 CE: Al-Kindi's frequency analysis – First systematic cryptanalysis technique for breaking substitution ciphers.<ref>{{Cite web |title=History of Algorithms |url=https://www.enjoyalgorithms.com/blog/history-of-algorithms/ |access-date=2025-07-12 |website=www.enjoyalgorithms.com}}</ref>
* 1206: Al-Jazari's programmable orchestra – Mechanical automata using pegged cylinders for sequence control (early program storage).<ref name=":1">{{Citation |title=Timeline of artificial intelligence |date=2025-07-12 |work=Wikipedia |url=https://en.wikipedia.org/w/index.php?title=Timeline_of_artificial_intelligence&oldid=1300048042 |access-date=2025-07-12 |language=en}}</ref>
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