The most natural way for mathematical theories to progress is by generalising existing concepts and structures. It is akin to searching for other planets in our solar system after realising we live on one. Though the planets are vastly different (for instance, only one currently sustains life), they all share certain intrinsic properties, such as their shape or the nature of their orbits around the Sun. It is through the discovery of these common features that we gain insight into the entire solar system. This process of broadening our perspective—from our own planet to the solar system and beyond to the galaxy—illustrates how science, along with our understanding of nature, expands.

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Basic Notions

  • Subhajit Paul

摘要

The most natural way for mathematical theories to progress is by generalising existing concepts and structures. It is akin to searching for other planets in our solar system after realising we live on one. Though the planets are vastly different (for instance, only one currently sustains life), they all share certain intrinsic properties, such as their shape or the nature of their orbits around the Sun. It is through the discovery of these common features that we gain insight into the entire solar system. This process of broadening our perspective—from our own planet to the solar system and beyond to the galaxy—illustrates how science, along with our understanding of nature, expands.