Applied research methodology in the exact sciences is essential for translating theoretical knowledge into practical solutions. These methods enable researchers to establish patterns, test hypotheses, and make predictions based on empirical evidence. Statistical analysis is a cornerstone of quantitative research, allowing scientists to interpret numerical data through various methods. Researchers employ descriptive statistics to summarize and describe the characteristics of a dataset, providing insights into measures such as mean, median, mode, variance, and standard deviation. This scientific research background led to the construction of this text based on the hypothetical deductive method. The Hypothetical Deductive Method is a structured approach to experimentation and theory testing that involves the formulation of hypotheses and the deduction of observable implications from these hypotheses. According to Popper, scientific theories cannot be proven definitively; instead, they can only be tentatively corroborated through rigorous testing. In addition, an approach between mathematics and philosophy is explored from Kurt Gödel's point of view and incompleteness theorems transformed the landscape of mathematics and logic and opened new avenues of inquiry across multiple disciplines. They serve as a reminder of the complexities and limitations inherent in the pursuit of knowledge, urging scholars to embrace the nuances and uncertainties that define human viewpoint of truth and proof. Therefore, the objective of the research is to analyze the methodology of applied scientific research in the exact sciences, from the Bunge vision to Hooke, without leaving aside Comte, Hegel and Feuerbach. The scientific method stands as a cornerstone of inquiry in the exact sciences, providing a systematic framework for investigating natural phenomena; is a structured approach that enables scientists to formulate hypotheses, conduct experiments, and analyze results to draw about the world around us. Its importance cannot be overstated; it promotes a disciplined approach to research and fosters an environment of skepticism and verification, which are integral for knowledge advancement.
The authors explore through four chapters that mathematics, often regarded as the language of the universe, serves as a foundational pillar across various fields, ranging from natural to social sciences. At the heart of mathematical advancement lies a robust research methodology that guides scholars in their quest for knowledge and prognosis. Mathematical research encompasses the systematic investigation of mathematical concepts, theories, and problems. It involves the formulation of hypotheses, the development of models, and the exploration of new ideas through rigorous reasoning and logical deduction.
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