Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.
The main foundations of every state, new states as well as ancient or composite ones, are good laws and good arms you cannot have good laws without good arms, and where there are good arms, good laws inevitably follow.
I wanted a perfect ending. Now I've learned, the hard way, that some poems don't rhyme, and some stories don't have a clear beginning, middle, and end.
In my mind's eye, I visualize how a particular... sight and feeling will appear on a print. If it excites me, there is a good chance it will make a good photograph. It is an intuitive sense, an ability that comes from a lot of practice.
Accordingly, since nothing prevents the earth from moving, I suggest that we should now consider also whether several motions suit it, so that it can be regarded as one of the planets. For, it is not the center of all the revolutions.
It is my intention to present - through the medium of photography - intuitive observations of the natural world which may have meaning to the spectators.
Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.
A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.
No single man can be taken as a model for a perfect figure, for no man lives on earth who is endowed with the whole of beauty.
When you start with a portrait and search for a pure form, a clear volume, through successive eliminations, you arrive inevitably at the egg. Likewise, starting with the egg and following the same process in reverse, one finishes with the portrait.
Those who know that the consensus of many centuries has sanctioned the conception that the earth remains at rest in the middle of the heavens as its center, would, I reflected, regard it as an insane pronouncement if I made the opposite assertion that the earth moves.
March on. Do not tarry. To go forward is to move toward perfection. March on, and fear not the thorns, or the sharp stones on life's path.
The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.
He was thinking alone, and seriously racking his brain to find a direction for this single force four times multiplied, with which he did not doubt, as with the lever for which Archimedes sought, they should succeed in moving the world, when some one tapped gently at his door.
Truth happens in a state of not knowing, truth happens in innocence. Truth happens where there are no clouds of thoughts moving in your consciousness,when the sky is absolutely clear.
If you cry "Forward" you must be sure to make clear the direction in which to go. Don't you see that if you fail to do that and simply call out the word to a monk and a revolutionary, they will go in precisely opposite directions?
On the basis of Lorentz's theory, if we limit ourselves to a single spectral line, it suffices to assume that each atom (or molecule) contains a single moving electron.
The important work of moving the world forward does not wait to be done by perfect men.
I have stepped off the relationship scene to come to terms with myself. I have spent most of my adult life being 'someone's girlfriend', and now I am happy being single.
The computer offers another kind of creativity. You cannot ignore the creativity that computer technology can bring. But you need to be able to move between those two different worlds.
The rule is perfect: in all matters of opinion our adversaries are insane.
Beware of missing chances; otherwise it may be altogether too late some day.
This is the first time in 10 years I don't know what I'm doing next, and I'm rather enjoying it. Soon I'll be climbing the walls no doubt, but right now, it's not clear, I'm just enjoying the freedom.
The plain man is familiar with blindness and deafness, and knows from his everyday experience that the look of things is influenced by his senses; but it never occurs to him to regard the whole world as the creation of his senses.
When you say you agree to a thing in principle you mean that you have not the slightest intention of carrying it out in practice.