This quote suggests that mathematical reasoning is not just about precision and accuracy, but it also has its own unique standards for what is considered real or true. In other words, in mathematics, reality is not determined by our physical senses or subjective experiences, but by logical consistency and empirical evidence.

Mathematical reasoning is exact in the sense that it follows strict rules and principles. A mathematical statement is either true or false, there’s no in-between. This exactness allows for clarity, precision, and the ability to build complex ideas from simple ones.

The “criteria of reality” in mathematics refers to the standards or principles used to determine the validity of mathematical statements or concepts. For instance, a mathematical concept or theory is considered real or valid if it is logically consistent and if it can be derived or proven from accepted mathematical axioms or principles.

Applying this idea to today’s world, we can say that in any field or endeavor, whether it’s science, business, politics or personal development, we need to have a clear and exact understanding of the concepts and principles involved, and we need to have our own criteria of reality, our own standards for determining what is true or valid.

In personal development, for instance, we need to have a clear understanding of our goals, values, and principles, and we need to have our own criteria for success. We can’t just rely on other people’s definitions or standards of success. We need to define our own success based on our own values and principles, and we need to measure our progress based on these personal criteria. In this way, we can be sure that we are moving in the right direction and that we are making real progress towards our personal goals.

In conclusion, this quote is a reminder of the importance of clarity, precision, and personal standards in our thinking and in our pursuit of knowledge and personal growth.