query: Who is considered the founder of algebra?
passage: Algebra
In the context where algebra is identified with the theory of equations, the Greek mathematician Diophantus has traditionally been known as the "father of algebra" and in context where it is identified with rules for manipulating and solving equations, Persian mathematician al-Khwarizmi is regarded as "the father of algebra".[14][15][16][17] A debate now exists whether who (in general sense) is more entitled to be known as "the father of algebra". Those who support Diophantus point to the fact that the algebra found in Al-Jabr is slightly more elementary than the algebra found in Arithmetica and that Arithmetica is syncopated while Al-Jabr is fully rhetorical.[18] Those who support Al-Khwarizmi point to the fact that he introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation) which the term al-jabr originally referred to,[19] and that he gave an exhaustive explanation of solving quadratic equations,[20] supported by geometric proofs, while treating algebra as an independent discipline in its own right.[21] His algebra was also no longer concerned "with a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study". He also studied an equation for its own sake and "in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems".[22]
passage: Hodge algebra
In mathematics, a Hodge algebra or algebra with straightening law is a commutative algebra that is a free module over some ring "R", together with a given basis similar to the basis of standard monomials of the coordinate ring of a Grassmannian. Hodge algebras were introduced by , who named them after W. V. D. Hodge.