The text’s main idea reveals that the development of a formalized mathematical language was crucial to the advancement of contemporary mathematical physics. The purpose of symbolism and the unique approaches of the physical fields of study will be misunderstood if the mathematical demonstration is seen as merely a tool. A tool favored solely because the perspectives of natural scientific knowledge can be expressed by “symbols” in the primary and most precise manner possible (Klein, 1992). It has ultimately become impossible to distinguish between the form and substance of mathematical physics following three centuries of vigorous development. It is impossible, and always has been, to understand what we now refer to as physics separately from its mathematical form, even though fundamental explanations of complex science are nevertheless popular. The close relationship between the formal mathematical jargon and the subject matter of mathematical physics results from a unique type of conceptualization that is a by-product of modern science.
Therefore, there arises the task of looking into the history and conceptual framework of this precise manner before discussing the issues that mathematical physics is currently facing. Hence, the fundamental question regarding the inner relationships between physics and mathematics of “theory” and “experiment,” of “systematic” and “empirical” processes within applied mathematics, will be entirely bypassed in this study (Klein, 1992). Instead, it will focus on the specific task of partially recovering the sources of modern symbolic mathematics, which are currently almost entirely hidden from view. However, because the underlying subject is so closely tied to the conceptual issues currently emerging in mathematical physics, the investigation would never lose sight of it. Modern algebra was founded on the same principles used to create the technical language of mathematics. From the thirteenth through the middle of the 16th century, the West adopted the Arabic theory of equations known as “algebra,” which was likely borrowed from both Indian and Greek origins (Klein, 1992).
Regarding the Greek sources, it is clear that the Mathematics of Diophantus had a specific influence on the contents, and far more notably on the style, of this Arabic science, at least from the 10th century on. Diophantus’s manuscript started gaining popularity and influence in the fifteenth century (Klein, 1992). At the same time, the concept of equations that the Arabs had introduced to the West was being developed, particularly in Italy. However, Vieta did not begin to expand and alter Diophantus’ method in a genuinely significant way till the last quarter of the 1600s. Thus, he established himself as the birth father of modern mathematics (Klein, 1992).
The importance of the resurgence and incorporation of Greek arithmetic in the 16th century is not missed in the traditional explanations of the chronology of this development. The nature of the conceptual transition that took place during this absorption is not usually understood, and that is a necessary prerequisite for contemporary mathematical symbolism. Additionally, most conventional histories try to understand Greek mathematics on their own using contemporary symbolism, as if this latter concept were a completely external “form” that could be adapted to any desired “content” (Klein, 1992). It seems to be common to find that research aimed at gaining an accurate knowledge of Greek science begins from a theoretical level, concerning the ideas governed by contemporary ways of thought. Thus, the main goal must be to distance ourselves as much as possible from these patterns.
Reference
Jacob Klein: Greek Mathematical Thought and the Origin of Algebra, Dover Books on Mathematics, 1992, pp. 3-5.