Once you can reproduce a phenomenon, you are well on the way to understanding it.
That's one of those meaningless and unanswerable questions the mind keeps returning to endlessly, like the tongue exploring a broken tooth.
Training was one thing, reality another.
Men, I still think, ought to be weighed not counted.
Theories are just fantasies. And they change.
In my experience most mathematicians are intellectually lazy and especially dislike reading experimental papers. He seemed to have very strong biological intuitions but unfortunately of negative sign.
To say a thing is natural is to condone it, never to praise it.
All ignorance toboggans into know and trudges up to ignorance again.
Most writers on the subject seem to agree that the typical working mathematician is a Platonist on weekdays and a formalist on Sundays.
In the realm of ideas, of mental objects, those ideas whose properties are reproducible are called mathematical objects, and the study of mental objects with reproducible properties is called mathematics.
Language is not only the vehicle of thought, it is a great and efficient instrument in thinking.
A problem of statistical inference or, more simply, a statistics problem is a problem in which data that have been generated in accordance with some unknown probability distribution must be analyzed and some type of inference about the unknown distribution must be made.
Misinterpretation is the most deadly of human sins.
The obvious mathematical breakthrough would be development of an easy way to factor large prime numbers.
We have already noticed the difference in the attitude of a spectator and of an agent or participant. The former is indifferent to what is going on; one result is just as good as another, since each is just something to look at. The latter is bound up with what is going on; its outcome makes a difference to him.
It science involves an intelligent and persistent endeavor to revise current beliefs so as to weed out what is erroneous, to add to their accuracy, and, above all, to give them such shape that the dependencies of the various facts upon one another may be as obvious as possible.
The empiric easily degenerates into the quack. He does not know where his knowledge begins or leaves off, and so when he gets beyond routine conditions he begins to pretend-to make claims for which there is no justification, and to trust to luck and to ability to impose upon others-to "bluff."
Those who refused to respond to the new stimulus would perish. Adapt or perish.
Sometimes one must try anything, it is no disgrace. On the contrary, it is a sign of wisdom.
I never liked the idea of doing what a machine says. I hate having to salute something built in a factory.
It's not what happened but how it is told.
Either I've invented a whole new logic or, ahem, I'm not playing with a full deck.
Can we consider the universe real, and if so, in what way?
It is futile to try to make the universe add up. But I guess we must go on anyhow.
Most human problems can be solved by an appropriate charge of high explosive.
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