Mathematicians do not study objects, but the relations between objects…

Henri Poincare
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Mathematicians do not study objects, but the relations between objects. ✨ The Value of Science: Essential Writings of Henri Poincare.
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Mathematical discoveries, small or great are never born of spontaneous generation.
Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the logic piano imagined by Stanley Jevons; or … ▶
Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.
If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of the same universe at a succeeding moment.
Hypotheses are what we lack the least. ✨ Henri Poincare (2012). The Value of Science: Essential Writings of Henri Poincare, p.225, Modern Library

Mathematicians do not study objects, but the relations between objects. ✨ The Value of Science: Essential Writings of Henri Poincare.

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