TL;DR
This paper explores the foundational basis of modern mathematics, linking it to sensory knowledge of the physical world and detailing how formal systems encapsulate deep realities about mathematical concepts.
Contribution
It provides a detailed analysis of how modern mathematical formalism originates from sensory experience and systematically develops through number systems to complex numbers.
Findings
Mathematical formalism encodes deep realities about the physical world.
The development from senses to natural, rational, and real numbers is systematically explained.
Complex numbers formalism is derived from foundational principles.
Abstract
Modern mathematics is known for its rigorous proofs and tight analysis. Math is the paradigm of objectivity for most. We identify the source of that objectivity as our knowledge of the physical world given through our senses. We show in detail, for the core of modern mathematics, how modern mathematical formalism encapsulates deep realities about extension into a system of symbols and axiomatic rules. In particular, we proceed from the foundations in our senses to the natural numbers through integers, rational numbers, and real numbers, including introducing the concept of a field. An appendix shows how the formalism of complex numbers arises.
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Taxonomy
TopicsHistory and Theory of Mathematics · Mathematical and Theoretical Analysis