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.
The Press, Watson, is a most valuable institution, if you only know how to use it.
Throughout history, people have studied pure science from a desire to understand the universe rather than practical applications for commercial gain. But their discoveries later turned out to have great practical benefits.
Nobody ever told us all matter radiated. We just assumed it did.
If there is no solace in the fruits of our research, there is at least some consolation in the research itself. Men and women are not content to comfort themselves with tales of gods and giants, or to confine their thoughts to the daily affairs of life; they also build telescopes and satellites and accelerators and sit at their desks for endless hours working out the meaning of the data they gather.
Forging differs from hoaxing, inasmuch as in the later the deceit is intended to last for a time, and then be discovered, to the ridicule of those who have credited it; whereas the forger is one who, wishing to acquire a reputation for science, records observations which he has never made.
I think the rise of quantitative econometrics and a highly mathematical approach to risk management was the obverse of a decline in interest in financial history.
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