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
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.
In practice
In a lecture on the philosophy of mathematics, this quote can emphasize the importance of understanding the mental processes behind mathematical concepts.
The Navy is a master plan designed by geniuses for execution by idiots. If you are not an idiot, but find yourself in the Navy, you can only operate well by pretending to be one. All the shortcuts and economies and common-sense changes that your native intelligence suggests to you are mistakes. Learn to quash them. Constantly ask yourself, "How would I do this if I were a fool?" Throttle down your mind to a crawl. Then you will never go wrong.
The human qualities of the raw materials show through. Naivety, error, contradiction, even (as in the cursing Psalms) wickedness are not removed. The total result is not "the Word of God" in the sense that every passage in itself, gives impeccable science or history. It carries the Word of God.
The world that I should wish to see would be one freed from the virulence of group hostilities and capable of realizing that happiness for all is to be derived rather from co-operation than from strife. I should wish to see a world in which education aimed at mental freedom rather than imprisoning the minds of the young in rigid armor of dogma calculated to protect them through life against the shafts of impartial evidence.
As long as you are in that white privilege bubble, you don't need to see the world differently. You don't need to see the world through the eyes of minorities or women.
I think a person has to believe in something,_x000D_ or search out some kind of faith;_x000D_ otherwise life is empty, nothing._x000D_ How can you live not knowing why the cranes fly,_x000D_ why children are born, why there are stars in the sky..._x000D_ Either you know why you live,_x000D_ or it's all small, unnecessary bits.
If you don't visit the bad neighborhoods, the bad neighborhoods are going to visit you.
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