No system of regulation can safely be substituted for the operation of individual liberty as expressed in competition.
Louis D. BrandeisRead
One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics.
Interpretation
What this quote means
The essence of mathematics goes beyond its language and requires an understanding of the mental processes involved in mathematical thinking.
Brouwer emphasizes that to truly understand mathematics, one must look beyond the symbols and language used to express it. This involves examining the cognitive processes that underlie mathematical thought, suggesting that without this deeper inquiry, one merely engages with mathematics superficially, missing its fundamental essence and operations.
Themes
MathematicsUnderstandingCognitionPhilosophyEssence
In practice
Example use cases
In a lecture on the philosophy of mathematics, this quote can emphasize the importance of understanding the mental processes behind mathematical concepts.
Similar quotes
Here's the reality. The image of a white Jesus has been used to justify enslavement, conquest, colonialism, the genocide of indigenous peoples. There are literally millions of human beings whose lives have been snuffed out by people who conquered under the banner of a white god.
Tim WiseRead
I would say that the thrust of my life has been initially about getting free, and then realizing that my freedom is not independent of everybody else. Then I am arriving at that circle where one works on oneself as a gift to other people so that one doesn't create more suffering. I help people as a work on myself and I work on myself to help people.
Ram DassRead
I never have felt that people should feel that they are better than others, simply because they just happen to possess a larger share of material items and monetary wealth than others less fortunate. I believe in sharing, assisting, and just lending a helping hand to people.
Michael JacksonRead
In order to deal with reality successfully - to pursue and achieve the values which his life requires - man needs self-esteem; he needs to be confident of his efficacy and worth.
Ayn RandRead
The 2003 invasion of Iraq by U.S. and coalition partners stands as one of the greatest blunders in American history. The Islamic State, also known as ISIL or ISIS, rose out of the the chaos, throwing the region into turmoil that hasn't been equaled since the fall of the Ottoman Empire.
Lawrence WrightRead