A good teacher is a master of simplification and an enemy of simplism.

A teacher effects eternity; [s]he can never tell where [her] his influence stops.

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.

Each generation has its few great mathematicians, and mathematics would not even notice the absence of the others. They are useful as teachers, and their research harms no one, but it is of no importance at all. A mathematician is great or he is nothing.

Early in my school career, I turned out to be an incorrigible disciplinary problem. I could understand what the teacher was saying as fast as she could say it, I found time hanging heavy, so I would occasionally talk to my neighbor. That was my great crime, I talked in school.

Every fool believes what his teachers tell him, and calls his credulity science or morality as confidently as his father called it divine revelation.

Good teachers deserve apples; great teachers deserve chocolate.
A favorite quotation, written in calligraphy on his office door.

He who can, does. He who cannot, teaches.

I can but think that the world would be better and brighter if our teachers would dwell on the duty of happiness as well as the happiness of duty; for we ought to be as bright and genial as we can, if only because to be cheerful ourselves is a most effectual contribution to the happiness of others.

I once knew an otherwise excellent teacher who compelled his students to perform all their demonstrations with incorrect figures, on the theory that it was the logical connection of the concepts, not the figure, that was essential.

I really see no harm which can come of giving our children a little knowledge of physiology. ... The instruction must be real, based upon observation, eked out by good explanatory diagrams and models, and conveyed by a teacher whose own knowledge has been acquired by a study of the facts; and not the mere catechismal parrot-work which too often usurps the place of elementary teaching.

If I were summing up the qualities of a good teacher of medicine, I would enumerate human sympathy, moral and intellectual integrity, enthusiasm, and ability to talk, in addition, of course, to knowledge of his subject.

If I would be a young man again and had to decide how to make my living, I would not try to become a scientist or scholar or teacher. I would rather choose to be a plumber or a peddler in the hope to find that modest degree of independence still available under present circumstances.

It may sound like a lot of work to keep up with organic chemistry, and it is; however, those who haven't the time to do it become subject to decay in the ability to teach and to contribute to the Science—a sort of first-order process the half-life of which can't be much more than a year or two.

Liebig was not a teacher in the ordinary sense of the word. Scientifically productive himself in an unusual degree, and rich in chemical ideas, he imparted the latter to his advanced pupils, to be put by them to experimental proof; he thus brought his pupils gradually to think for themselves, besides showing and explaining to them the methods by which chemical problems might be solved experimentally.

Poor is the pupil who does not surpass his master.

Scientific observation has established that education is not what the teacher gives; education is a natural process spontaneously carried out by the human individual, and is acquired not by listening to words but by experiences upon the environment. The task of the teacher becomes that of preparing a series of motives of cultural activity, spread over a specially prepared environment, and then refraining from obtrusive interference. Human teachers can only help the great work that is being done, as servants help the master. Doing so, they will be witnesses to the unfolding of the human soul and to the rising of a New Man who will not be a victim of events, but will have the clarity of vision to direct and shape the future of human society.