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
Theory attracts practice as the magnet attracts iron.
Interpretation
Theoretical knowledge draws practical application, similar to how a magnet draws metal.
In this quote, Gauss expresses the idea that theoretical concepts have a compelling power to inspire and guide practical actions, just as a magnet naturally attracts iron. It highlights the intrinsic relationship between theory and practice, suggesting that well-founded theories can lead to tangible results and advancements in various fields, particularly in science and mathematics.
In practice
A professor might use this quote to emphasize the importance of applying theoretical knowledge in research.
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.
It is generally believed that our science is empirical and that we draw our concepts and our mathematical constructs from the empirical data. If this were the whole truth, we should, when entering into a new field, introduce only such quantities as can directly be observed, and formulate natural laws only by means of these quantities.
Our great struggle in medicine these days is not just with ignorance and uncertainty. It's also with complexity: how much you have to make sure you have in your head and think about. There are a thousand ways things can go wrong.
The prediction of nuclear winter is drawn not, of course, from any direct experience with the consequences of global nuclear war, but rather from an investigation of the governing physics.
Without any doubt, the regularity which astronomy shows us in the movements of the comets takes place in all phenomena. The trajectory of a simple molecule of air or vapour is regulated in a manner as certain as that of the planetary orbits; the only difference between them is that which is contributed by our ignorance. Probability is relative in part to this ignorance, and in part to our knowledge.
If global warming is not contained, the West will face a choice of a refugee crisis of unimaginable proportions, or direct complicity in crimes against humanity.
As a child, I wanted to know how things worked and to control them. With a friend, I built a number of complicated models that I could control.
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