Nothing in the affairs of men is worthy of great anxiety.
PlatoRead
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.
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