A Quote by Norbert Wiener
The advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil.
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The Advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil. It is a field which has often been compared with chess, but differs from the latter in that it is only one's best moments that count and not one's worst. A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician's reputation.
The tools of the academic designer are a piece of paper and a pencil with an eraser. If a mistake is made, it can always be erased and changed. If the practical-reactor designer errs, he wears the mistake around his neck; it cannot be erased. Everyone sees it.
Ay! says the Vedanta, it is not the fault of God that this partiality exists, that this competition exists. Who makes it? We ourselves. There is a cloud shedding its rain on all fields alike. But it is only the field that is well cultivated, which gets the advantage of the shower; another field, which has not been tilled or taken care of cannot get that advantage. It is not the fault of the cloud.
Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.
A computer does not substitute for judgment any more than a pencil substitutes for literacy. But writing without a pencil is no particular advantage.
Mathematics is much more than computation with pencil and a paper and getting answers to routine exercises. In fact, it can easily be argued that computation, such as doing long division, is not mathematics at all. Calculators can do the same thing and calculators can only calculate they cannot do mathematics.
I learned very quickly that when you emigrate, you lose the crutches that have been your support; you must begin from zero, because the past is erased with a single stroke and no one cares where you’re from or what you did before.
The Stroke Association has produced leaflets that set out clearly the health risks associated with stroke that African-Caribbean people face.
History written in pencil is easily erased, but crayon is forever.
Learn to self-conquest, persevere thus for a time, and you will perceive very clearly the advantage which you gain from it.
In the field of Egyptian mathematics Professor Karpinski of the University of Michigan has long insisted that surviving mathematical papyri clearly demonstrate the Egyptians' scientific interest in pure mathematics for its own sake. I have now no doubt that Professor Karpinski is right, for the evidence of interest in pure science, as such, is perfectly conclusive in the Edwin Smith Surgical Papyrus.
The pencil-stroke is like cutting into the heart.
Home field advantage can be overrated in the NFL because veteran players aren't bothered by it. Home-field advantage is a bigger deal in college.
Ever since high school I've been writing in a spiral notebook, in pencil. Everything looks too polished on a computer when you start writing, and I can't really see it. I feel like the words are much more naked in pencil, on a notebook. I feel that my brain works differently, and words come out differently, if I have a pencil in my hand, rather than if I have a keyboard. I tend to add more in the margins. I tend to elongate the sentences as I'm writing and editing, and there is just something about the feeling of writing longhand that I really love.
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.
Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.
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