Mathematics consists in proving the most obvious thing in the least obvious way.
Instinct leads, logic does but follow.
In life two negatives don't make a positive. Double negatives turn positive only in math and formal logic. In life things just get worse and worse and worse.
Brevity is the soul of command. Too much talking suggests desperation on the part of the leader. Speak shortly, decisively and to the point–and couch your desires in such natural logic that no one can raise objections. Then move on.
The trouble with facts is that there are so many of them.
Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency.
Logic is invincible, because in order to combat logic it is necessary to use logic.
Only professional mathematicians learn anything from proofs. Other people learn from explanations.
Mathematics - this may surprise or shock some - is never deductive in creation.
Mathematics is a body of knowledge, but it contains no truths.
Government agents (and their allies) might enter chat rooms, online social networks, or even real-space groups and attempt to undermine percolating conspiracy theories by raising doubts about their factual premises, causal logic or implications for political action.
The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method.
What humans do with the language of mathematics is to describe patterns.
"Ganas is all you need."
Somehow, in painting I try to make some logic out of the world that has been given to me in chaos.
I do not believe in the gifted. If [the students] have ganas, I can make them do it.
"I see it, but I don't believe it."
I perceive the world in fragments. It is somewhat like being on a very fast train and getting glimpses of things in strange scales as you pass by. A person can be very, very tiny. And a billboard can make a person very large. You see the corner of a house or you see a bird fly by, and it's all fragmented. Somehow, in painting I try to make some logic out of the world that has been given to me in chaos. I have a very pretentious idea that I want to make life, I want to make sense out of it. The fact that I am doomed to failure - that doesn't deter me in the least.
The real universe is always one step beyond logic.
No daring is fatal. The whole logic of the universe is contained in daring, in creating from the flimsiest, slenderest support.
Ideas should be neutral. But man animates them with his passions and folly. Impure and turned into beliefs, they take on the appearance of reality. The passage from logic is consummated. Thus are born ideologies, doctrines, and bloody farce.
For once, I believe that PETA, at least on the level of logic, is correct. If the NCAA has to protect offended Native Americans ... by God, PETA ought to advocate for the protection of every organism in the animal kingdom.
Liberals state that many teenagers would rather sell crack for $100 an hour than to flip hamburgers for a minimum wage. Using the same liberal logic, you might think it would make more sense for the average middle-class worker to rob banks rather than work a forty-hour week? The reason why most people, rich and poor, do not commit crimes because they know it is wrong to do so.
When money, instead of man, is at the center of the system, when money becomes an idol, men and women are reduced to simple instruments of a social and economic system, which is characterized, better yet dominated, by profound inequalities. So we discard whatever is not useful to this logic; it is this attitude that discards children and older people, and is now affecting the young.
Every well-thought-out rebuttal to dogma, every scrap of intelligent logic, every absurdist reduction of some bullying stance is the antidote.
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