All the modern higher mathematics is based on a calculus of operations, on laws of thought. All mathematics, from the first, was so in reality; but the evolvers of the modern higher calculus have known that it is so. Therefore elementary teachers who, at the present day, persist in thinking about algebra and arithmetic as dealing with laws of number, and about geometry as dealing with laws of surface and solid content, are doing the best that in them lies to put their pupils on the wrong track for reaching in the future any true understanding of the higher algebras. Algebras deal not with laws of number, but with such laws of the human thinking machinery as have been discovered in the course of investigations on numbers. Plane geometry deals with such laws of thought as were discovered by men intent on finding out how to measure surface; and solid geometry with such additional laws of thought as were discovered when men began to extend geometry into three dimensions.

An educated person is one who has learned that information almost always turns out to be at best incomplete and very often false, misleading, fictitious, mendacious—just dead wrong.

I have no patience with attempts to identify science with measurement, which is but one of its tools, or with any definition of the scientist which would exclude a Darwin, a Pasteur or a Kekulé. The scientist is a practical man and his are practical aims. He does not seek the ultimate but the proximate. He does not speak of the last analysis but rather of the next approximation. His are not those beautiful structures so delicately designed that a single flaw may cause the collapse of the whole. The scientist builds slowly and with a gross but solid kind of masonry. If dissatisfied with any of his work, even if it be near the very foundations, he can replace that part without damage to the remainder. On the whole, he is satisfied with his work, for while science may never be wholly right it certainly is never wholly wrong; and it seems to be improving from decade to decade.

It is better to go near the truth and be imprisoned than to stay with the wrong and roam about freely, master Galilei. In fact, getting attached to falsity is terrible slavery, and real freedom is only next to the right.

The fact that man knows right from wrong proves his intellectual superiority to other creatures; but the fact that he can do wrong proves his moral inferiority to any creature that cannot.

The major religions on the Earth contradict each other left and right. You can't all be correct. And what if all of you are wrong? It's a possibility, you know. You must care about the truth, right? Well, the way to winnow through all the differing contentions is to be skeptical. I'm not any more skeptical about your religious beliefs than I am about every new scientific idea I hear about. But in my line of work, they're called hypotheses, not inspiration and not revelation.

There are many hypotheses in science which are wrong. That's perfectly all right; they're the aperture to finding out what's right. Science is a self-correcting process. To be accepted, new ideas must survive the most rigorous standards of evidence and scrutiny.

There must be a marsh in the brains of these men or there would not be so many frogs of wrong ideas gathered in their heads.

When I entered the field of space physics in 1956, I recall that I fell in with the crowd believing, for example, that electric fields could not exist in the highly conducting plasma of space. It was three years later that I was shamed by S. Chandrasekhar into investigating Alfvén's work objectively. My degree of shock and surprise in finding Alfvén right and his critics wrong can hardly be described. I learned that a cosmic ray acceleration mechanism basically identical to the famous mechanism suggested by Fermi in 1949 had [previously] been put forth by Alfvén.