We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.
Carl Friedrich GaussRead
It is always noteworthy that all those who seriously study this science [the theory of numbers] conceive a sort of passion for it.
Interpretation
Studying the theory of numbers evokes a strong passion in those who delve into it.
Carl Friedrich Gauss emphasizes the deep connection and passion that individuals tend to develop for the study of numbers and mathematical theories. This suggests that engaging with complex scientific material can transform into a profound affection, illustrating the beauty and allure of mathematics.
In practice
This quote could be shared during a mathematics conference to inspire students.
We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.
I protest against the use of infinite magnitude ..., which is never permissible in mathematics.
Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.
To praise it would amount to praising myself. For the entire content of the work... coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years.
The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.
Life stands before me like an eternal spring with new and brilliant clothes.
Indeed, the whole human species is endangered, by nuclear weapons or by other means of wholesale destruction which further advances in science are likely to produce.
The process of discovery is very simple. An unwearied and systematic application of known laws to nature, causes the unknown to reveal themselves. Almost any mode of observation will be successful at last, for what is most wanted is method.
The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform... But it is likely to exert an indirect and reciprocal influence on science itself.
The upshot of all this is that we live in a universe whose age we can't quite compute, surrounded by stars whose distances we don't altogether know, filled with matter we can't identify, operating in conformance with physical laws whose properties we donβt truly understand.
I told him that for a modern scientist, practicing experimental research, the least that could be said, is that we do not know. But I felt that such a negative answer was only part of the truth. I told him that in this universe in which we live, unbounded in space, infinite in stored energy and, who knows, unlimited in time, the adequate and positive answer, according to my belief, is that this universe may, also, possess infinite potentialities.
Matter, though divisible in an extreme degree, is nevertheless not infinitely divisible. That is, there must be some point beyond which we cannot go in the division of matter. ... I have chosen the word βatomβ to signify these ultimate particles.
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