"[...] gradually and unwittingly mathematicians began to introduce concepts that had little or no direct physical meaning. Of these, negative and complex numbers were most troublesome. It was because these two types of numbers had no 'reality' in nature that they were still suspect at the beginning of the nineteenth century, even though freely utilized by then. The geometrical representation of negative numbers as points or vectors in the complex plane, which, as Gauss remarked of the latter, gave them intuitive meaning and so made them admissible, may have delayed the realization that mathematics deals with man-made concepts. But then the introduction of quaternions, non-Euclidean geometry, complex elements in geometry, n-dimensional geometry, bizarre functions, and transfinite numbers forced the recognition of the artificiality of mathematics." (Morris Kline, "Mathematical Thought from Ancient to Modern Times", 1972)
"Statistics is ’hocuspocus’ with numbers." (Audrey Haber & Richard P Runion,"General Statistics", 1973)
"We know the laws of trial and error, of large numbers and probabilities. We know that these laws are part of the mathematical and mechanical fabric of the universe, and that they are also at play in biological processes. But, in the name of the experimental method and out of our poor knowledge, are we really entitled to claim that everything happens by chance, to the exclusion of all other possibilities?" (Albert Claude, "The Coming Age of the Cell", Nobel Prize Lecture] 1974)
"Numbers are not just counters; they are elements in a system." (Scott Buchanan,"Poetry and Mathematics", 1975)
"The physicist who states a law of nature with the aid of a mathematical formula is abstracting a real feature of a real material world, even if he has to speak of numbers, vectors, tensors, state-functions, or whatever to make the abstraction." (Hilary Putnam, "Mathematics, matter, and method", 1975)
"The theory of number is the epipoem of mathematics." (Scott Buchanan, "Poetry and Mathematics", 1975)
"Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world." (Steven Weinberg, "The First Three Minutes", 1977)
"Surreal numbers are an astonishing feat of legerdemain. An empty hat rests on a table made of a few axioms of standard set theory. Conway waves two simple rules in the air, then reaches into almost nothing and pulls out an infinitely rich tapestry of numbers that form a real and closed field. Every real number is surrounded by a host of new numbers that lie closer to it than any other 'real' value does. The system is truly 'surreal.'" (Martin Gardner, "Mathematical Magic Show", 1977
"There is no more reason to expect one graph to ‘tell all’ than to expect one number to do the same." (John W Tukey, "Exploratory Data Analysis", 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)
"Numbers are the product of counting. Quantities are the product of measurement. This means that numbers can conceivably be accurate because there is a discontinuity between each integer and the next. Between two and three there is a jump. In the case of quantity there is no such jump, and because jump is missing in the world of quantity it is impossible for any quantity to be exact. You can have exactly three tomatoes. You can never have exactly three gallons of water. Always quantity is approximate." (Gregory Bateson, "Number is Different from Quantity", CoEvolution Quarterly, 1978)
"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)
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