Meaning: The quote "Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts" is attributed to David Hilbert, a renowned mathematician. This quote encapsulates Hilbert's perspective on the interconnectedness and unity of mathematical science. In this statement, Hilbert emphasizes the holistic nature of mathematics, highlighting the interdependence of its various branches and concepts.

Hilbert's assertion that mathematical science is an "indivisible whole" underscores the idea that mathematics is a unified and integrated discipline. Rather than being a collection of disparate topics, Hilbert suggests that mathematics forms a cohesive and interconnected system. This perspective aligns with the foundational principles of mathematics, where different areas such as algebra, geometry, calculus, and number theory are interconnected and build upon each other. By viewing mathematics as an "indivisible whole," Hilbert emphasizes the importance of recognizing the interconnected nature of mathematical concepts and theories.

Moreover, Hilbert's analogy of mathematical science as an "organism" conveys the idea that mathematics exhibits a sense of vitality and dynamism. By likening it to an organism, he implies that mathematics possesses a living and evolving quality. This characterization underscores the notion that mathematics is not static but rather constantly evolving and adapting, much like a living organism. This analogy also suggests that the various components of mathematics are interconnected and reliant on each other for the discipline's vitality and growth.

Furthermore, Hilbert's assertion that the vitality of mathematical science is "conditioned upon the connection of its parts" emphasizes the significance of the relationships and connections within mathematics. According to Hilbert, the strength and vitality of mathematics are contingent upon the interplay and connections between its various components. This perspective underscores the importance of understanding the interconnectedness of different mathematical concepts and the ways in which they inform and support each other. It also highlights the idea that advancements in one area of mathematics can have implications and applications in other areas, emphasizing the interdependence of mathematical knowledge.

In essence, Hilbert's quote reflects his deep appreciation for the unity and interconnectedness of mathematical science. By characterizing mathematics as an "indivisible whole" and an "organism," he emphasizes the holistic nature of the discipline and its dynamic, interconnected components. This perspective aligns with the fundamental principles of mathematics, which emphasize the interdependence of different areas and the ways in which they collectively contribute to the discipline's advancement.

In summary, David Hilbert's quote encapsulates his perspective on the unified and interconnected nature of mathematical science. By emphasizing the indivisible whole and organismic vitality of mathematics, Hilbert underscores the importance of recognizing the interconnectedness and interdependence of its various components. This quote serves as a reminder of the holistic and dynamic nature of mathematics, highlighting the significance of understanding its interconnected parts and their contributions to the discipline as a whole.