History of the Mathematics. The history background of the renaissance of mathematics

History of Mathematics
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History of Mathematics
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1 The history background of the renaissance of mathematics
The term renaissance refers to the tremendous revival of arts and literature, including mathematics. It also refers to a period of transition characterized by a great change from an ecclesiastical and feudal culture to a national, urban, lay and secular culture. After the invention of printing and paper as a writing material, a number of books were printed of which few were focused on mathematics. Many of the mathematical works that were authored in the mid-1400s appeared in print much later (Burton, 2011). However, some mathematical works were unoriginal and below the standards of the mathematicians of the 13-14 centuries and thus were not published. In 1478, the first mathematical work, referred to as Treviso Arithmetic, was published (Burton, 2011). This publication served as a milestone for later works. In Italy alone, more than 200 textbooks of mathematics had been published prior to the end of the 15th century (Burton, 2011).
2 The liberation of algebra
One of the most popular algebra textbooks, The Whetstone of Witte, was published in 1557 (Burton, 2011). Robert Recorder authored such book as well as popularized books written in English language. The textbooks on algebra were dominant in Germany. To simplify the complexity associated with algebra, some algebraists introduced the concept of symbolism, which enhanced the compactness and efficiency of algebraic writing. However, the improvements on algebraic writings lacked uniformity in symbols. Additionally, algebraic expressions only dealt with concrete examples. Francois Vi`eta (1540–1603) was a French mathematician who introduced the concept of using vowels and consonants to denote the unknown and known variables in algebra, respectively (Burton, 2011). As such, he liberalized algebra from only having to deal with concrete examples.
3 The contributions of Cardan, Tartaglia, Ferrari, Bombelli, Abel and Galois
Nicolo Tartaglia was among the greatest contributors of the 1500s Italian mathematics. Burton (2011) acknowledges Tartaglia for being among the most critical “restorers of the algebraic tradition” (p. 317). Raised by a widowed mother in desperately poor family, Tartaglia could not afford to pay for his formal education but taught himself on how to write and read using a book he stole from his tutor. Having acquired mathematical proficiency, he started teaching mathematical in both Venice and Veronica. Tartaglia’s pioneering book was referred to as Scientia and was published in 1937 (Burton, 2011). It focused on the application of mathematical concepts to artillery. He also contributed to the mathematics of falling bodies. Overall, Tartaglia is prominent for finding solutions to the equations of the form x3 + px2 = q.
On the other hand, Girolamo Cardano, also called Cardan, a mathematician, prolific writer, philosopher and physician. Specifically, he taught mathematics at various universities in Bologna, Pavia and Milan. In 1545, he published his mathematical work, Ars Magna, which included the solution to the cubic problem: x3 + px2 = q (Burton, 2011). The book introduced the concepts of complex numbers and solutions of cubic equations. His work also contributed to the probability theory.
Ludovico Ferrari contributed to solving a quartic equation, also called the fourth-degree equation: x4 + ax3 + bx2 + cx + d = 0. He used the rules for solving third-degree (cubic) equations to solve quartic equations and his contributions were incorporated in Cardan’s book, Ars Magna. He also played a key role in determining the outcome of the mathematical dissipates between Cardan and Tartaglia regarding to solution to the cubic equation.
Rafael Bombelli was a great Bolognese mathematician of the 16th century. Particularly, he is acknowledged for being the first mathematician to embrace the use of imaginary numbers, and hence solving the impasse relating to the so-called irreducible cubic equations. His work, Algebra, not only extended the algebraic works of his predecessors but also completed the movement on algebra.
The Norwegian mathematician, Niels Henrik Abel, made great contributions in underscoring the insolvability of fifth-degree (quintic) and higher degree equations using the methods that had been proposed by his predecessors. He contributed 22 published papers in the Crelle’s Journal, which was published in 1826 (Burton, 2011). Notably, he introduced the so-called Abel-Ruffini theorem, which acted as a precursor to latter works by other algebraists.
It is noteworthy that Abel-Ruffini theorem applicable only to general equations. In light of this, Evariste...