On Numbers: On Prime Numbers (1970-1989)

"But the laws of addition and multiplication (the associative laws, for example) are not a human invention. They are unintended consequences of human invention, and they were discovered. And the existence of prime numbers - indivisible numbers that are the product only of themselves and unity - is also a discovery, no doubt quite a late one. The prime numbers were discovered in the series of natural numbers, not by everyone but by people who studied these numbers and their special peculiarities - by real mathematicians." (Karl R Popper, "Notes of a Realist on the Body-Mind Problem", [in "All Life is Problem Solving", 1999] 1972)

"The communication of modern science to the ordinary citizen, necessary, important, desirable as it is, cannot be considered an easy task. The prime obstacle is lack of education. [...] There is also the difficulty of making scientific discoveries interesting and exciting without completely degrading them intellectually. [...] It is a weakness of modern science that the scientist shrinks from this sort of publicity, and thus gives an impression of arrogant mystagoguery." (John M Ziman,"The Force of Knowledge: The Scientific Dimension of Society", 1976)

"I hope that ... I have communicated a certain impression of the im- mense beauty of the prime numbers and the endless surprises which they have in store for us." (Don Zagier, 1977) 

"There are two facts about the distribution of prime numbers of which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts. The first is that, despite their simple definition and role as the building blocks of the natural numbers, the prime numbers belong to the most arbitrary and ornery objects studied by mathematicians: they grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout. The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behaviour, and that they obey these laws with almost military precision.” (Don Zagier, “The First 50 Million Prime Numbers”, The Mathematical Intelligencer Vol. 0, 1977)

“[…] there is no apparent reason why one number is prime and another not. To the contrary, upon looking at these numbers one has the feeling of being in the presence of one of the inexplicable secrets of creation.” (Don Zagier, “The First 50 Million Prime Numbers”, The Mathematical Intelligencer, Volume 0, 1977)

"Prime numbers have always fascinated mathematicians, professional and amateur alike. They appear among the integers, seemingly at random, and yet not quite: there seems to be some order or pattern, just a little below the surface, just a little out of reach." (Underwood Dudley, “Elementary Number Theory”, 1978)

"Some order begins to emerge from this chaos when the primes are considered not in their individuality but in the aggregate; one considers the social statistics of the primes and not the eccentricities of the individuals." (Philip J Davis & Reuben Hersh, “The Mathematical Experience”, 1981)

"Meaning does not reside in the mathematical symbols. It resides in the cloud of thought enveloping these symbols. It is conveyed in words; these assign meaning to the symbols." (Marvin Chester, "Primer of Quantum Mechanics", 1987)

"A tendency to drastically underestimate the frequency of coincidences is a prime characteristic of innumerates, who generally accord great significance to correspondences of all sorts while attributing too little significance to quite conclusive but less flashy statistical evidence." (John A Paulos, "Innumeracy: Mathematical Illiteracy and its Consequences", 1988)