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.
...as our friend Zach has often noted, in our days those who do the best for astronomy are not the salaried university professors, but so-called dillettanti, physicians, jurists, and so forth.Lamenting the fragmentary time left to a professor has remaining after fulfilling his teaching duties.
Interpretation
What this quote means
The quote highlights that passionate amateurs often contribute more to astronomy than those in academia who are constrained by their responsibilities.
In this quote, Carl Friedrich Gauss expresses a sentiment that the most significant contributions to astronomy come from dedicated amateurs, or 'dilettanti', rather than from university professors who are often bogged down by administrative and teaching duties. Gauss laments how these obligations fragment the time available for professors to pursue their passion for research, leading to a situation where those outside traditional educational institutions, such as physicians and lawyers, may have the freedom to delve deeper into astronomical studies and make notable advancements.
Themes
In practice
Example use cases
In a speech about promoting interest in science, a speaker could use this quote to encourage involvement from non-professionals.
More from Carl Friedrich Gauss
All quotes →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.
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The central difficulty lies in the fact that all of the sciences have made such great progress during the last century that they have got quite beyond the reach of man
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You make observations, write theories to fit them, try experiments to disprove the theories and, if you can't, you've got something.