Discovery in mathematics

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This work explores the discovery of mathematics and its ties to notation, representation, and language. Drawing from modeling systems theory in semiotics and cognitive science's blending theory, it proposes that discovery is closely linked to representation, revealing deeper structures inherent in mathematical models. The focus is on how diagrammatic reasoning informs mathematicians' thought processes, serving as a catalyst for new ideas, conceptualizations, theories, and branches within the discipline. The book is structured into several sections: the first discusses the concepts of discovery, invention, and proof, along with mathematical hermeneutics. The second section delves into notation and compression, addressing symbology and the principle of least effort. The third section examines diagrams and modeling, including existential graphs and the rebus principle. The fourth section contrasts induction, deduction, and abduction, highlighting the tension between mythos and lógos. Finally, the work addresses the relationship between mathematics, science, and reality, culminating in concluding remarks. This interdisciplinary study, edited by Marcel Danesi, aims to deepen the understanding of mathematical discovery and its foundational elements.