We shall find in our troubled hearts, where discord reigns, two needs which seem at variance, but which merge, as I think, in a common source - the love of the true, and the love of the fabulous.
Each of us seems to have a main focus, a particular idea of practicality - a concept of 'what we want out of life' against which we judge our experiences.
There's something about [cyclically] doing something over and over and over that seems to be particularly demotivating.
Sometimes when an idea flashes, you distrust it because it seems too easy. You qualify it with all kinds of evasive phrases because you’re timid about it. But often, this turns out to be the best idea of all.
I had no idea what I was doing, I had no idea where I was going, but at some point I stopped — when to keep going would seem like I was going too far.
Oak trees come out of acorns, no matter how unlikely that seems. An acorn is just a tree's way back into the ground. For another try. Another trip through. One life for another.
All that was required to measure the planet was a man with a stick and a brain. In other words, couple an intellect with some experimental apparatus and almost anything seems achievable.
The Law of Diminishing Returns is true of everything in life, except sex, which seems endlessly repeatable with effect.
It is not only visitors to the zoo who are fascinated but uneasy in the presence of chimpanzees; the same is true of scientists. The more they learn about these great apes, the deeper our identity crisis seems to become. The resemblance between humans and chimpanzees is not only external. If we look straight and deep into a chimpanzee’s eyes, an intelligent, self-assured personality looks back at us. If they are animals, what must we be?
Paleontologist Niles Eldredge, a prominent evolutionist, said: 'The doubt that has infiltrated the previous, smugly confident certitude of evolutionary biology’s last twenty years has inflamed passions.' He spoke of the 'lack of total agreement even within the warring camps,' and added, 'things really are in an uproar these days . . . Sometimes it seems as though there are as many variations on each [evolutionary] theme as there are individual biologists.'
When discussing organic evolution the only point of agreement seems to be: ‘It happened.’ Thereafter, there is little consensus, which at first sight must seem rather odd.
Mankind is advanced technically. Man can build space stations, can assemble them in space, and ponders about landing on Mars, but the development of mankind itself seems to stagnate on stone age level.
When the rate of return on capital exceeds the rate of growth of output and income, as it did in the nineteenth century and seems quite likely to do again in the twenty-first, capitalism automatically generates arbitrary and unsustainable inequalities that radically undermine the meritocratic values on which democratic societies are based.
The footnote would seem to be the smallest detail in a work of history. Yet it carries a large burden of responsibility, testifying to the validity of the work, the integrity (and the humility) of the historian, and to the dignity of the discipline.
Mathematics seems to endow one with something like a new sense.
I would like to make a confession which may seem immoral: I do not believe absolutely in Hilbert space any more.
Mathematics, however, is, as it were, its own explanation; this, although it may seem hard to accept, is nevertheless true, for the recognition that a fact is so is the cause upon which we base the proof.
One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That's so unlike the true nature of mathematics.
There is no study in the world which brings into more harmonious action all the faculties of the mind than [mathematics], ... or, like this, seems to raise them, by successive steps of initiation, to higher and higher states of conscious intellectual being.
Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable, but it is impossible to foresee their consequences. These have only been found out by long study, extending over many centuries. Much of our knowledge is due to a comparatively few great mathematicians such as Newton, Euler, Gauss, or Riemann; few careers can have been more satisfying than theirs. They have contributed something to human thought even more lasting than great literature, since it is independent of language.
Mathematics is a world created by the mind of men, and mathematicians are people who devote their lives to what seems to me a wonderful kind of play!
Like a bird she seems to wear gay plumage unconsciously, as if it grew upon her.
It seems we are capable of immense love and loyalty, and as capable of deceit and atrocity. It's probably this shocking ambivalence that makes us unique.
Men, like musical instruments, seem made to be played upon.
Now the peak of summer's past, the sky is overcast And the love we swore would last for an age seems deceit.
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