Mathematics is of two kinds, Rigorous and Physical. The former is Narrow: the latter Bold and Broad. To have to stop to formulate rigorous demonstrations would put a stop to most physico-mathematical inquiries. Am I to refuse to eat because I do not fully understand the mechanism of digestion?
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DA Edge (1983). "Oliver Heaviside (1850-1927) - Physical mathematician". Teaching mathematics and its applications 2: 55-61.Oliver Heaviside
» Oliver Heaviside - all quotes »
The Elements has been considered as offering models of scrupulously rigorous demonstrations. It is certainly true that in point of rigour it compares favourably with its modern rivals; but when examined in the light of strict mathematical logic, it has been pronounced by C.S. Peirce to be "riddled with fallacies." The results are correct only because the writer's experience keeps him on his guard.
Euclid
Stop the War and Stop the Genocide, read the banners being waved in the demonstrations in Rome and here in Bari. For Peace. Against War. Who is not? But how can you stop those bent on genocide without making war?
Susan Sontag
My son, my son. When I had my son I would explain all that to him when he was starry enough to like understand. But then I knew he would not understand or would not want to understand at all and would do all the veshches [things] I had done...and I would not be able to really stop him. And nor would he be able to stop his own son, brothers. And so it would itty on to like the end of the world.
Anthony Burgess
I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.
Bertrand Russell
Euclid … manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis does.
Lucio Russo
Heaviside, Oliver
Heazlewood, Justin
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