L. E. J. Brouwer famous quotes

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.
-- L. E. J. Brouwer

#Essence #Mind #Foundation

Alas, the spheres of truth are less transparent than those of illusion.
-- L. E. J. Brouwer

#Spheres #Illusion

Oil is seldom found where it is most needed, and seldom most needed where it is found.
-- L. E. J. Brouwer

#Oil #Found #Needed

Mathematics is nothing more, nothing less, than the exact part of our thinking.
-- L. E. J. Brouwer

#Thinking #Mathematics

The construction itself is an art, its application to the world an evil parasite.
-- L. E. J. Brouwer

#Art #Evil #World

Beyond the natural numbers, addition, multiplication, and mathematical induction are intuitively clear.
-- L. E. J. Brouwer

#Numbers #Mathematics #Natural

The subject for which I am asking your attention deals with the foundations of mathematics. To understand the development of the opposing theories existing in this field one must first gain a clear understnding of the concept "science"; for it is as a part of science that mathematics originally took its place in human thought.
-- L. E. J. Brouwer

#Foundation #Attention #Asking

...an incorrect theory, even if it cannot be inhibited by any contradiction that would refute it, is none the less incorrect, just as a criminal policy is none the less criminal even if it cannot be inhibited by any court that would curb it.
-- L. E. J. Brouwer

#Criminals #Contradiction #Court

At its core, meditation is about touching the spiritual essence that exists within us all. Our spiritual essence is not something that we create through meditation it's already there, deep within, behind all the barriers, patiently waiting for us to recognize it.

Patience is the essence of clicking great Photographs!!

No state, upon its own mere motion, can lawfully get out of the Union. Plainly, the central idea of secession, is the essence of anarchy.

You cannot have a good character today and at the same time have a small mind and a little heart. You cannot have a good character today and be merely a petty reformer.

The minds of stone lovers had colonised stones as lichens clung to them with golden or grey-green florid stains. The human world of stones is caught in organic metaphors like flies in amber. Words came from flesh and hair and plants. Reniform, mammilated, botryoidal, dendrite, haematite. Carnelian is from carnal, from flesh. Serpentine and lizardite are stone reptiles ; phyllite is leafy-green.

Middle age has been defined as what happens when a person's broad mind and narrow waist change places.

And unlike the rest of you, he hasn’t yet time to ruin his career or his mind." "Then he won’t do. Send him home. Get us another lunatic." "Excuse me!" [hopping up to stand in his seat] "Elassar Targon, master of the universe, reporting for duty!" "I withdraw my objection.

The national government...will maintain and defend the foundations on which the power of our nation rests. It will offer strong protection to Christianity as the very basis of our collective morality.

Your inner strength is your outer foundation

The foundation stones of a great building are destined to groan and be pressed upon; it is not for them to crown the edifice.