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To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.
--
As quoted in Fundamentals of Teaching Mathematics at University Level (2000) by Benjamin Baumslag, p. 214

 

Leonhard Euler

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Can we call something with which the concepts of position and motion cannot be associated in the usual way, a thing, or a particle? And if not, what is the reality which our theory has been invented to describe?
The answer to this is no longer physics, but philosophy. ... Here I will only say that I am emphatically in favour of the retention of the particle idea. Naturally, it is necessary to redefine what is meant. For this, well-developed concepts are available which appear in mathematics under the name of invariants in transformations. Every object that we perceive appears in innumerable aspects. The concept of the object is the invariant of all these aspects. From this point of view, the present universally used system of concepts in which particles and waves appear simultaneously, can be completely justified. The latest research on nuclei and elementary particles has led us, however, to limits beyond which this system of concepts itself does not appear to suffice. The lesson to be learned from what I have told of the origin of quantum mechanics is that probable refinements of mathematical methods will not suffice to produce a satisfactory theory, but that somewhere in our doctrine is hidden a concept, unjustified by experience, which we must eliminate to open up the road.

 

Max Born

 

I'm for mystery, not interpretive answers. ... The answer is never the answer. What's really interesting is the mystery. If you seek the mystery instead of the answer, you'll always be seeking. I've never seen anybody really find the answer, but they think they have. So they stop thinking. But the job is to seek mystery, evoke mystery, plant a garden in which strange plants grow and mysteries bloom. The need for mystery is greater than the need for an answer.

 

Ken Kesey

 

When you seek some unspecified and hidden property, you don't want extraneous complexity to interfere. In order to achieve homogeneity, I decided to make the motion end where it had started. The resulting motion biting its own tail created a distinctive new shape I call Brownian cluster. ... Today, after the fact, the boundary of Brownian motion might be billed as a "natural" concept. But yesterday this concept had not occurred to anyone. And even if it had been reached by pure thought, how could anyone have proceeded to the dimension 4/3? To bring this topic to life it was necessary for the Antaeus of Mathematics to be compelled to touch his Mother Earth, if only for one fleeting moment.

 

Benoit Mandelbrot

 

I know just enough about myself to know I cannot settle for one of those simplifications which indignant people seize upon to make understandable a world too complex for their comprehension. Astrology, health food, flag waving, bible thumping, Zen, nudism, nihilism -- all of these are grotesque simplifications which small dreary people adopt in the hope of thereby finding The Answer, because the very concept that maybe there is no answer, never has been, never will be, terrifies them.

 

John D. MacDonald

 

Here then is the pattern in my carpet, the sense of the eternal mysteries, the eternal beauty hidden beneath the crust of common and commonplace things; hidden and yet burning and glowing continually if you care to look with purged eyes.

 

Arthur Machen