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.
Sweetness is the opposite of machismo, which is everywhere-and I really don't get on with machismo. I'm interested in sensitivity, and weakness, and fear, and anxiety, because I think that, at the end of the day, behind our masks, that's what we are.
The suicide bomber's imagination leads him to believe in a brilliant act of heroism, when in fact he is simply blowing himself up pointlessly and taking other people's lives.
Routine is a declivity down which many governments slide, and routine says that freedom of the press is dangerous.
I'm an outlaw, not a philosopher, but I know this much: there's meaning in everything, all things are connected, and a good champagne is a drink.' Bernard began to sing again. Timidly, Leigh-Cheri joined in. Between verses, they opened another bottle. The popping of its cork echoed throughout the great stone chamber. Of the three billion people on earth, only Bernard and Leigh-Cheri heard the popping of the cork and its echoes. Only Bernard and Leigh-Cheri passed out under the tablecloth.
It is much more valuable to look for the strength in others. You can gain nothing by criticizing their imperfections.
Grace means undeserved kindness. It is the gift of God to man the moment he sees he is unworthy of God's favor.
Subscribe for the occasional hand-picked quote. No noise.