The greatest reward lies in making the discovery; recognition can add little or nothing to that.
Such is the advantage of a well constructed language that its simplified notation often becomes the source of profound theories.
Prayers for the condemned man will be offered on an adding machine. Numbers constitute the only universal language.
Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghostlike character of the real variable.
Just as the introduction of the irrational numbers ... is a convenient myth [which] simplifies the laws of arithmetic ... so physical objects are postulated entities which round out and simplify our account of the flux of existence... The conceptional scheme of physical objects is [likewise] a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part.
[Math] curriculum is obsessed with jargon and nomenclature seemingly for no other purpose than to provide teachers with something to test the students on.
The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was "out there" all along I just couldn't see it. And now I can! This is really what keeps me in the math game- the chance that I might glimpse some kind of secret underlying truth, some sort of message from the gods.
Sometimes in studying Ramanujan's work, [George Andrews] said at another time, "I have wondered how much Ramanujan could have done if he had had MACSYMA or SCRATCHPAD or some other symbolic algebra package."
Later in the fifties I got involved in kinetic studies using my long forgotten math background.
... that, in a few years, all great physical constants will have been approximately estimated, and that the only occupation which will be left to men of science will be to carry these measurements to another place of decimals.
The errors of definitions multiply themselves according as the reckoning proceeds; and lead men into absurdities, which at last they see but cannot avoid, without reckoning anew from the beginning.
I was an undergraduate at Princeton, and I was pressed by the math department to go on to graduate school. Actually they gave me fellowships that paid my way, otherwise I would not have been able to continue.
We can either save the planet from catastrophic warming, or protect fossil fuel CEOs. Not both. Do the math(s)
Once you hit 40, you start reexamining the math of it all. I'll trade wisdom for youth any day.
Those who write against vanity want the glory of having written well, and their readers the glory of reading well, and I who write this have the same desire, as perhaps those who read this have also.
The surprising thing about this paper is that a man who could write it would.
Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence.... The two propositions: "The earth turns round" and "it is more convenient to suppose the earth turns round" have the same meaning; there is nothing more in the one than in the other.
. . . we have overcome the notion that mathematical truths have an existence independent and apart from our own minds. It is even strange to us that such a notion could ever have existed.
So far as the mere imparting of information is concerned, no university has had any justification for existence since the popularization of printing in the fifteenth century.
Remember, a negative multiplied by a negative is only positive in maths, not in the real world
Religion is so great a thing that it is right that those who will not take the trouble to seek it if it be obscure, should be deprived of it.
Skibbereen have a hard time at [math]; the best that the smartest of them can do with adding two plus two is guessing: three plus one. Correct, sort of, but not always useful.
College was an experience I'll always cherish. Now I fund a scholarship at my alma mater in my late father's name-he'd laugh to know that it's a science scholarship, when I can barely do math! I also fund a nursing scholarship at the Oglala Lakota College in Kyle, South Dakota, in the name of my mother, who was a nurse.
I take great solace that Einstein failed math. I failed math. I also failed English and home economics. Einstein was an underachiever.
A proof tells us where to concentrate our doubts.
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