"Thus, they are free to replace some objects by others so long as the relations remain unchanged"

This quote by Henri Poincare is describing the concept of invariance, which is the concept that certain homes of a system stay the same even when the items within the system are altered. Simply put, the quote is recommending that it is possible to replace particular things within a system without changing the general structure of the system. This principle is very important in mathematics, physics, and other scientific fields, as it permits the study of systems without needing to consider the specific objects within them. For instance, in physics, the laws of motion stay the same no matter the mass of the things included. This quote by Poincare is emphasizing the significance of invariance in understanding the behavior of systems.