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The Babylonians solved cubic equations with the help of tables (Allen, n.d).
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In the book Shushu Jiuzhang, perhaps the most brilliant Chinese mathematician of this time was Qin Jiushao, a rather violent and corrupt imperial administrator and warrior, who explored solutions to quadratic and even cubic equations using a method of repeated approximations (The Story of Mathematics, n.d.).
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Sharaf al-Dīn al-Ṭūsī in his book Al-muʿādalāt included a work devoted to the solution of cubic equations (Berggren & Sharaf Al-Dīn, 1990). (Image from Qatar Digital Library. (2015, May 22). al-Muʿādalāt المعادلات [66v] (63/290). Retrieved June 6, 2020, from https://www.qdl.qa/en/archive/81055/vdc_100044790015.0x00008e).
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Some of Bhaskara's contributions to mathematics include in Lilavati, solutions of quadratic, cubic and quartic indeterminate equations (New World Encyclopedia, n.d.).
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Omar Khayyám, made significant progress in developing the theory of cubic equations and published his findings in Treatise on Demonstration of Problems of Algebra (McKay, n.d.).
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Wang Xiaotong, established and solved 25 cubic equations (McKay, n.d).
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Archimedes, in his monumental work The Sphere and Cylinder,
considers the problem of cutting a sphere by a plane so that the
two segments shall have a given ratio; this leads to a cubic
equation solution(The University of Colorado Denver, n.d.). -
Hippocrates of Chios reduced
duplicating the cube to a problem in mean proportionals (Brown University, 2018). -
Menaechmus’ work in conic; where the greeks were aware of methods to solve certain cubic equations using
intersecting conics, but did not consider general cubic equations because their framework was too influenced by geometry (Brown University, 2018). -
The main topics of Jaina mathematics in around 150 BC were: the theory of numbers, arithmetical operations, geometry, operations with fractions, simple equations, cubic equations, quartic equations, and permutations and combinations (MacTutor, n.d.).
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Fibonacci computed the positive solution to x^3 + 2 x^2 + 10x = 20 to 8 decimal places (although he gives his solution in sexagesimal) (Brown, 2018).
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Scipione del Ferro (1465-1526), who solved the depressed cubic equation (Brown, 2018).
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In 1530, another Italian named Tartaglia claimed a solution to two cubics presented by Zuanne da Coi (Brown, 2018).
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Cardano learned that Tartaglia’s work was known to del Ferro, he
broke the agreement and published Ars Magna in 1545 (Brown, 2018). He proposed a method for solving cubic equations, which is now known today as Cardano’s method (McKay, n.d.). -
Tartaglia then challenged Cardano, who declined and the challenge eventually passed to Ferrari. Ferrari understood cubics better and bested Tartaglia at his own game (Brown, 2018).
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François Viète, known as the father of modern algebraic notation, derived the trigonometric solution for the cubic equation with three real roots (McKay, n.d.).
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René Descartes, a French philosopher, mathematician, and scientist and dubbed the father of modern Western philosophy, summarized and extended Viète’s study (McKay, n.d.).
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The cubic equation is utilized for volume, measurements, and other applications. Some other applications of cubic functions or equations are found in the fields of physics, chemistry, economics, or additional areas of mathematics (McKay, n.d.).
