Meaning: Max Bill, a renowned architect, artist, and designer, highlights the relationship between clarity of thought and the mathematical way of thinking in the provided quote. In this quote, Bill suggests that a clear and concise expression of a concept, along with a comprehensive unity of its fundamental idea, brings it closer to the principles of mathematical thinking. This notion sheds light on the intersection of mathematics, logic, and conceptual understanding in various fields, including architecture, design, and art.

The idea expressed by Max Bill underscores the importance of precision and coherence in conveying a train of thought. By emphasizing the significance of succinctness and comprehensive unity, Bill implies that a well-structured and logically presented idea mirrors the characteristics of mathematical reasoning. In mathematics, concepts are often expressed with conciseness and clarity, and the unity of fundamental principles forms the basis for logical deductions and problem-solving. Similarly, in various disciplines, including architecture, the ability to articulate a clear and unified concept is essential for effective communication and meaningful design.

The relationship between the expounded train of thought and the mathematical way of thinking suggests a parallel between the principles of logic and the structured nature of mathematical reasoning. Just as mathematical concepts are built upon interconnected and coherent principles, the expounded train of thought benefits from a unified and comprehensive foundation. This connection implies that the principles of mathematical thinking can serve as a guide for organizing and expressing ideas in a clear and logical manner.

Moreover, the quote by Max Bill alludes to the idea that the mathematical way of thinking transcends the boundaries of pure mathematics and extends into various domains of human cognition and expression. The emphasis on succinctness and comprehensive unity as prerequisites for the mathematical way of thinking implies that these characteristics are valued not only in mathematical discourse but also in intellectual endeavors across disciplines. Whether in architecture, design, art, or other fields, the ability to convey a coherent and logically structured train of thought aligns with the principles of mathematical reasoning.

From an architectural perspective, the quote by Max Bill underscores the importance of clarity and coherence in the conceptualization and communication of design ideas. Architects often rely on precise and unified concepts to convey their vision effectively. Just as mathematical proofs and theorems require a logical progression and interconnectedness of ideas, architectural designs benefit from a clear and comprehensive unity of fundamental principles. The parallel drawn by Bill between the expounded train of thought and the mathematical way of thinking serves as a reminder of the importance of logical reasoning and conceptual cohesion in architectural practice.

In summary, Max Bill's quote encapsulates the idea that a clear and concise expression of a train of thought, coupled with a comprehensive unity of its fundamental idea, brings it closer to the principles of mathematical thinking. This notion resonates across various disciplines, highlighting the universal value of logical reasoning and coherent expression. Whether in mathematics, architecture, design, or other fields, the principles of mathematical thinking provide a framework for organizing and articulating ideas in a manner that reflects clarity, precision, and logical coherence.