Number theory
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.
Algorithms-Aided Design (AAD)
Algorithms-Aided Design (AAD) is the use of specific algorithms-editors to assist in the creation, modification, analysis, or optimization of a design. The algorithms-editors are usually integrated with 3D modeling packages and read several programming languages, both scripted or visual (RhinoScript®, Grasshopper®, MEL®, C#, Python®). The Algorithms-Aided Design allows designers to overcome the limitations of traditional CAD software and 3D computer graphics software, reaching a level of complexity which is beyond the human possibility to interact with digital objects. The acronym appears for the first time in the book AAD Algorithms-Aided Design, Parametric Strategies using Grasshopper, published by Arturo Tedeschi in 2014.