Herbert S. Gaskill Quotes

“It is an unfortunate fact that proofs can be very misleading. Proofs exist to establish once and for all, according to very high standards, that certain mathematical statements are irrefutable facts. What is unfortunate about this is that a proof, in spite of the fact that it is perfectly correct, does not in any way have to be enlightening. Thus, mathematicians, and mathematics students, are faced with two problems: the generation of proofs, and the generation of internal enlightenment. To understand a theorem requires enlightenment. If one has enlightenment, one knows in one's soul why a particular theorem must be true.”

“It is an unfortunate fact that proofs can be very misleading. Proofs exist to establish once and for all, according to very high standards, that certain mathematical statements are irrefutable facts. What is unfortunate about this is that a proof, in spite of the fact that it is perfectly correct, does not in any way have to be enlightening. Thus, mathematicians, and mathematics students, are faced with two problems: the generation of proofs, and the generation of internal enlightenment. To understand a theorem requires enlightenment. If one has enlightenment, one knows in one's soul why a particular theorem must be true.”

“One can be enlightened about proofs as well as theorems. Without enlightenment, one is merely reduced to memorizing proofs. With enlightenment about a proof, its flow becomes clear and it can become an item of astonishing beauty. In addition, the need to memorize disappears because the proof has become part of your soul.”

“The expression often used by Mr. Herbert Spencer of the Survival of the Fittest is more accurate, and is sometimes equally convenient.”

“Allan praised Herbert for a job well done and for acting the part well. Herbert blushed, while dismissing the praise, saying it wasn't hard to play stupid when you are stupid. Allan said that he didn't know how hard it was, because the idiots Allan had met so far in his life had all tried to do the opposite.”

“In the future I see open fields for more important researches. Psychology will be securely based on the foundation already laid by Mr. Herbert Spencer, that of the necessary acquirement of each mental power and capacity by graduation.”

“Be calm in arguing: for fierceness makes Error a fault, and truth discourtesy.”

“I will complain, yet praise;I will bewail, approve:And all my sowre-sweet dayesI will lament, and love.”

“Man is no star, but a quick coalOf mortal fire:Who blows it not, nor doth controlA faint desire,”

“Sweet day, so cool, so calm, so bright,The bridal of the earth and sky;The dew shall weep thy fall tonight,For thou must die.”

“Who says that fictions only and false hairBecome a verse? Is there in truth no beauty?Is all good structure in a winding stair?”