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
The struggle against poverty in the world and the challenge of cutting wealthy country emissions all has a single, very simple solution... Here it is: Put a price on carbon.
The increase of disorder or entropy with time is one example of what is called an arrow of time, something that distinguishes the past from the future, giving a direction to time.
Let both sides seek to invoke the wonders of science instead of its terrors. Together let us explore the stars, conquer the deserts, eradicate disease, tap the ocean depths, and encourage the arts and commerce.
Some experts say we are moving back to the pre-antibiotic era. No. This will be a post-antibiotic era. In terms of new replacement antibiotics, the pipeline is virtually dry. A post-antibiotic era means, in effect, an end to modern medicine as we know it. Things as common as strep throat or a child's scratched knee could once again kill.
As a scientist, I want to go to Mars and back to asteroids and the Moon because I'm a scientist. But I can tell you, I'm not so naive a scientist to think that the nation might not have geopolitical reasons for going into space.
A mind is accustomed to mathematical deduction, when confronted with the faulty foundations of astrology, resists a long, long time, like an obstinate mule, until compelled by beating and curses to put its foot into that dirty puddle.