A Quote by Raymond Louis Wilder
There is nothing mysterious, as some have tried to maintain, about the applicability of mathematics. What we get by abstraction from something can be returned.
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To criticize mathematics for its abstraction is to miss the point entirely. Abstraction is what makes mathematics work. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools: analogy, generality, and simplicity. Mathematics is the ultimate in technology transfer.
I have tried, with little success, to get some of my friends to understand my amazement that the abstraction of integers for counting is both possible and useful. Is it not remarkable that 6 sheep plus 7 sheep makes 13 sheep; that 6 stones plus 7 stones make 13 stones? Is it not a miracle that the universe is so constructed that such a simple abstraction as a number is possible? To me this is one of the strongest examples of the unreasonable effectiveness of mathematics. Indeed, I find it both strange and unexplainable.
The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. . . . Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.
Abstraction returned as soon as artists tried to come to closer grips with reality than naturalistic representation permitted.
I don't want to convince you that mathematics is useful. It is, but utility is not the only criterion for value to humanity. Above all, I want to convince you that mathematics is beautiful, surprising, enjoyable, and interesting. In fact, mathematics is the closest that we humans get to true magic. How else to describe the patterns in our heads that - by some mysterious agency - capture patterns of the universe around us? Mathematics connects ideas that otherwise seem totally unrelated, revealing deep similarities that subsequently show up in nature.
I consider my work non-objective and I think abstract is an abstraction of something, like a landscape. Abstraction means something is abstracted. It relates to something. Non-objective relates to nothing. It has no object.
What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else.
Only since the turn of the century has abstraction again become recognized as an artistic means of representation. It was then that one returned to the recognition of the immense role abstraction plays in the human mind by its power of concentration upon absolute essentials.
I tried to fit it in with some previous broad conceptual understanding of some part of mathematics that would clarify the particular problem I was thinking about.
I have always tried to maintain a sense of humanity in my work, to create something that will take on its own personality but also reflect something about our world.
The increased abstraction in mathematics that took place during the early part of this century was paralleled by a similar trend in the arts. In both cases, the increased level of abstraction demands greater effort on the part of anyone who wants to understand the work.
The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation of it.
I was brought up on rock-'n'-roll. It was sort of funny because I couldn't get interested in anything else - I tried and tried but I couldn't get into science...or mathematics, I just cut myself off from anything else there was to get interested in.
The red carpet is kind of a surreal experience. There's nothing normal about it, so for me the most important thing is to maintain some normality right until the point you get out of the car.
You can keep counting forever. The answer is infinity. But, quite frankly, I don't think I ever liked it. I always found something repulsive about it. I prefer finite mathematics much more than infinite mathematics. I think that it is much more natural, much more appealing and the theory is much more beautiful. It is very concrete. It is something that you can touch and something you can feel and something to relate to. Infinity mathematics, to me, is something that is meaningless, because it is abstract nonsense.
What is mathematics? Ask this question of person chosen at random, and you are likely to receive the answer "Mathematics is the study of number." With a bit of prodding as to what kind of study they mean, you may be able to induce them to come up with the description "the science of numbers." But that is about as far as you will get. And with that you will have obtained a description of mathematics that ceased to be accurate some two and a half thousand years ago!
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