A Quote by Oliver Heaviside
Mathematics is an experimental science, and definitions do not come first, but later on.
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Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.
Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.
Mathematics is often defined as the science of space and number . . . it was not until the recent resonance of computers and mathematics that a more apt definition became fully evident: mathematics is the science of patterns.
The subject for which I am asking your attention deals with the foundations of mathematics. To understand the development of the opposing theories existing in this field one must first gain a clear understnding of the concept "science"; for it is as a part of science that mathematics originally took its place in human thought.
If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.
Science, incidentally, not only ignores the question of indwelling 'essences' by looking instead at measurable relationships, but science also does not agree that knowledge is obtained through Rothbard's Medieval 'investigation by a reason,' i.e., by inventing definitions and then deducing what your definitions implicitly assumed.
I love to read and teach experimental fiction but yes, neither this work nor my first novel is really that experimental. It uses some experimental techniques but in the end, I would not say that it is experimental. I'm not sure why. I do a lot of writing on my own, and I have always just written this way.
I like science and mathematics. When I say mathematics, I don't mean algebra or math in that sense, but the mathematics of things.
We had principles in mathematics that were granted to be absolute in mathematics for over 800 years, but new science has gotten rid of those absolutism, gotten forward other different logics of looking at mathematics, and sort of turned the way we look at it as a science altogether after 800 years.
In fact, the answer to the question "What is mathematics?" has changed several times during the course of history... It was only in the last twenty years or so that a definition of mathematics emerged on which most mathematicians agree: mathematics is the science of patterns.
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!
Eve and the apple was the first great step in experimental science.
There was, I think, a feeling that the best science was that done in the simplest way. In experimental work, as in mathematics, there was "style" and a result obtained with simple equipment was more elegant than one obtained with complicated apparatus, just as a mathematical proof derived neatly was better than one involving laborious calculations. Rutherford's first disintegration experiment, and Chadwick's discovery of the neutron had a "style" that is different from that of experiments made with giant accelerators.
So in the end it wasn't Gödel, it wasn't Turing, and it wasn't my results that are making mathematics go into an experimental mathematics direction, in a quasi-empirical direction. The reason why mathematicians are changing their working habits is the computer. I think that this is an excellent joke!
Mathematics as we know it and as it has come to shape modern science could never have come into being without some disregard for the dangers of the infinite.
Even when I was studying mathematics, physics, and computer science, it always seemed that the problem of consciousness was about the most interesting problem out there for science to come to grips with.
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