Middle Eastern mathematicians solved general linear and quadratic equations using variables.
He lived 770 to 840, used Hindu numbers and fractions, and studied algebra. Adelard of Bath and Gerard of Cremona [1100 to 1150] translated his works and so transferred Indian and Islamic philosophy to Europe.
He lived 953 to 1029 and invented completing the square.
He lived 1501 to 1576 and found general-cubic-equation and general-quartic-equation solutions. He studied negative-number square roots and essentially discovered complex numbers, finding complex-number roots of x + y = 10 and x*y = 40. Cubic equation can be x^3 = p*x + q, where p and q can be zero, positive, or negative. Cubic equation can have up to three roots, all real numbers. If there are three roots {casus irreducibilis}, intermediate steps to solution can require complex numbers. He also studied game probability and began probability theory.
Politics
Culture and politics relate, as actual states and history show.
He lived 1499 to 1557 and found general solution to cubic equation.
He lived 1522 to 1565 and found general solution to quartic equation [1542].
He lived 1560 to 1621, used modern algebra notation, and studied trajectories. He invented refraction law.
He lived 1704 to 1752 and invented Cramer's rule.
He lived 1735 to 1796 and invented determinant minor.
He lived 1791 to 1858 and studied algebra systems and permanence of form.
He lived 1806 to 1871 and studied divergent series. He invented De Morgan's laws [1849] of algebra of classes: commutation, association, inverse, identity, distribution, and null.
He lived 1871 to 1928 and studied algebraic field theory.
He lived 1887 to 1985 and studied problem solving and problem-solving heuristics and invented counting formula. Plausibility depends on authority or reliability of information source used to justify proposition, not on probabilities of alternatives. Reasoning-chain plausibility is least-plausible-proposition plausibility.
He lived 1928 to ? and studied hyperfunctions [1958].
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Date Modified: 2022.0225