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 have had my results for a long time: but I do not yet know how I am to arrive at them.
Interpretation
What this quote means
The quote reflects the struggle of understanding and navigating the process of achieving one's goals, despite having the outcomes in mind.
In this quote, Carl Friedrich Gauss expresses the dilemma of being aware of the results he aims to achieve, yet being uncertain about the path needed to reach those results. It captures the essence of planning, the importance of the journey, and the challenges inherent in the pursuit of knowledge and success. Even great thinkers can find themselves at a crossroads between their ambitions and the methods required to turn those ambitions into reality.
Themes
In practice
Example use cases
This quote can be shared during a motivational speech to emphasize perseverance in reaching goals.
More from Carl Friedrich Gauss
All quotes βI 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.
Similar quotes
Just as Mars - a desert planet - gives us insights into global climate change on Earth, the promise awaits for bringing back to life portions of the Red Planet through the application of Earth Science to its similar chemistry, possibly reawakening its life-bearing potential.
I conclude that, while it is true that science cannot decide questions of value, that is because they cannot be intellectually decided at all, and lie outside the realm of truth and falsehood. Whatever knowledge is attainable, must be attained by scientific methods; and what science cannot discover, mankind cannot know.
Without deductive logic science would be entirely useless. It is merely a barren game to ascend from the particular to the general, unless afterwards we can reverse the process and descend from the general to the particular, ascending and descending like angels on Jacob's ladder.
When I had satisfied myself that no star of that kind had ever shone before, I was led into such perplexity by the unbelievability of the thing that I began to doubt the faith of my own eyes.
Politicians, real-estate agents, used-car salesmen, and advertising copy-writers are expected to stretch facts in self-serving directions, but scientists who falsify their results are regarded by their peers as committing an inexcusable crime. Yet the sad fact is that the history of science swarms with cases of outright fakery and instances of scientists who unconsciously distorted their work by seeing it through lenses of passionately held beliefs.
Normal television limits what you can do. With science fiction, you can exercise your imagination more. I fell in love with it.