Alas, the spheres of truth are less transparent than those of illusion.

- L. E. J. Brouwer

Oil is seldom found where it is most needed, and seldom most needed where it is found.

- L. E. J. Brouwer

One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activ…

- L. E. J. Brouwer

Mathematics is nothing more, nothing less, than the exact part of our thinking.

- L. E. J. Brouwer

...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 poli…

- L. E. J. Brouwer

The construction itself is an art, its application to the world an evil parasite.

- L. E. J. Brouwer

The subject for which I am asking your attention deals with the foundations of mathematics. To understand the development of the opposing theories ex…

- L. E. J. Brouwer

Beyond the natural numbers, addition, multiplication, and mathematical induction are intuitively clear.

- L. E. J. Brouwer