"An experiment is a question which man asks of nature; one result of the observation is an answer which nature yields to man." (Ferdinand Gonseth, "The Primeval Atom", 1950)
"No one will get very far or become a real mathematician without certain indispensable qualities; he must have hope, faith, and curiosity, and prime necessity is curiosity.(Louis J Mordell, "Reflections of a Mathematician", 1959)
"The prime numbers are useful in analyzing problems concerning divisibility, and also are interesting in themselves because of some of the special properties which they possess as a class. These properties have fascinated mathematicians and others since ancient times, and the richness and beauty of the results of research in this field have been astonishing." (Carl H Denbow & Victor Goedicke, “Foundations of Mathematics”, 1959)
"It seems to me that a worthwhile distinction can be drawn between two types of pure mathematics. The first - which unfortunately is somewhat out of style at present - centers attention on particular functions and theorems which are rich in meaning and history, like the gamma function and the prime number theorem, or on juicy individual facts […] The second is concerned primarily with form and structure."
“No branch of number theory is more saturated with mystery than the study of prime numbers: those exasperating, unruly integerst hat refuse to be divided evenly by any integers except themselves and 1. Some problems concerning primes are so simple that a child can understand them and yet so deep and far from solved that many mathematicians now suspect they have no solution. Perhaps they are ‘undecidable’. Perhaps number theory, like quantum mechanics, has its own uncertainty principle that makes it necessary, in certain areas, to abandon exactness for probabilistic formulations." (Martin Gardner, "The remarkable lore of the prime numbers", Scientific American, 1964)
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