L. E. J. Brouwer



Luitzen Egbertus Jan Brouwer ForMemRS (27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, who worked in topology, set theory, measure theory and complex analysis.

Quotes

 * Life is a magic garden. With wondrous softly shining flowers, but between the flowers there are the little gnomes, they frighten me so much, they stand on their heads, and the worst is, they call out to me that I should also stand on my head, every once in a while I try, and I die of embarrassment; but sometimes the gnomes shout that I am doing very well, and that I’m indeed a real gnome myself after all. But on no account I will ever fall for that.
 * To C.S. Adama van Scheltema (1906); in Dirk van Dalen (ed.) The Selected Correspondence of L.E.J. Brouwer (2011), p. 23


 * The viewpoint of the formalist must lead to the conviction that if other symbolic formulas should be substituted for the ones that now represent the fundamental mathematical relations and the mathematical-logical laws, the absence of the sensation of delight, called "consciousness of legitimacy," which might be the result of such substitution would not in the least invalidate its mathematical exactness. To the philosopher or to the anthropologist, but not to the mathematician, belongs the task of investigating why certain systems of symbolic logic rather than others may be effectively projected upon nature. Not to the mathematician, but to the psychologist, belongs the task of explaining why we believe in certain systems of symbolic logic and not in others, in particular why we are averse to the so-called contradictory systems in which the negative as well as the positive of certain propositions are valid.
 * as translated by Arnold Dresden from: Brouwer, L. E. J. (1913). Intuitionism and formalism. Bulletin of the American Mathematical Society, 20(2), 81–96. (quote on p. 84)

Quotes about Brouwer

 * In 1908 Brouwer introduced for the first time "weak counterexamples", for the purpose of showing that certain classically acceptable statements are constructively unacceptable (Brouwer 1908). Too much emphasis on these examples has sometimes created the false impression that refuting claims of classical mathematics is the principle aim of intuitionism.
 * A. S. Troelstra and D. van Dalen in: Constructivism in Mathematics, Vol. 2, Elsevier (1988), pp. 8–9