The Study of the Genesis of Novel Mathematical and Mechanical Theories Provides an Inspiration for Future Original Research

Abstract

In this introductory chapter we present the motivations that prompted the authors and editors to work on this volume. The fil rouge followed in the discussion presented below is based on the following consideration: the study of the genesis of mathematical and mechanical theories does not have a merely philological purpose, but can influence and even inspire the development of new original ideas. We present some examples that clarify our thesis: the development of the model of planetary motion and a historical-critical study of the development of Continuum Mechanics. Clearly understanding the main errors and misunderstandings that other than pure research logics have introduced in the scientific discussion is the only way to learn a serious and rigorous approach to Science. An idea that has guided us in the development of this chapter is that fragmentation of culture brings to inability to deal with complexity. The only way to study and, above all, understand the complexity of our world is through a unified vision of knowledge.

Maestro and his pupils: History of a scientific production

“…Piezoelectric materials (a revival of) [191]; 8. History of Science investigations (a revival of) [192][193][194] Funding The author(s) received no financial support for the research, authorship, and/or publication of this article.…”

The «materialization» of forces: Why confounding mathematical concept and physical entity makes the design of metamaterials arduous

“…That the multidisciplinarity approach is the most effective one is proven by many historical examples: Among the most prominent and most ancient one, we can cite that of Archimedes of Syracuse. We refer to Spagnuolo et al [80] for a discussion about the long and tormented process of transmission of the fundamental works by Archimedes to our modern science from Hellenistic one. Here we simply recall that, obviously, when a change of the used language in science occurs very often a large part of the knowledge stored in the books written in the old language is misunderstood and sometimes forgotten and therefore apparently lost.…”

“…In history of science, it can be observed rather frequently the occurrence of the confusion between mathematical objects and mathematical models with the physical objects and physical phenomena. The list of these occurrences could be very long and we limit ourselves (for more details see, e.g., Spagnuolo et al [80]) to cite here two among the most paradigmatic ones: (i) when confusing the concept of rational number (a mathematical entity from modeling quantities) with the length of a segment, some Pythagoreans are said to have believed that reality is paradoxical, as the hypotenuse of an isosceles rectangular triangle, with catheti whose length is 1, does not exist, as its length would be √ 2, which is not rational; (ii) when misunderstanding the nature of mathematical model of the "moving spheres" of the planets, many scholars materialized them arriving to believe that planets were physically connected to gigantic metallic "armillary" spheres in the sky.…”

Deformation-induced coupling of the generalized external actions in third-gradient materials

“…Notwithstanding this, a debate characterized the modern (re-)discovery of higher-order gradient models involving Mindlin, Sedov, Toupin and Germain among the others on the one side, and Truesdell and his followers on the other, concerning the nature of such "exotic" β-forces and their role in mathematical physics, see e.g. [53][54][55]. It is true that with extreme difficulty the generalized loading can enter the postulation of mechanics based on the balance of forces and of moments of forces: Some attempts have been made, leading to an extension named "quasi-balanced power" [56].…”