If there is a problem you can't solve, then there is an easier problem you can't solve: find it.
A GREAT discovery solves a great problem but there is a grain of discovery in any problem.
The theory of high-intensity, anaerobic, bodybuilding exercise is not true because I or anyone else, no matter how many might agree, say it is true. It is the fact that the logic of the theory is unassailable which makes it true.
Logic is an old subject, and since 1879 it has been a great one.
Alan Rocke's Image and Reality does so many things vividly and convincingly: it shows how visual images led chemistry step by step to the reality of the microscopic world; how simple portrayals of the logic of substitution and combination were reified; brings to our attention the imaginative, neglected work of Williamson and Kopp; and takes a critical look at Kekule's daydream. And it beautifully delineates the essential place the imagination has in science. A rewarding, lively picture of chemistry in formation.
I'm supposed to be a scientific person but I use intuition more than logic in making basic decisions.
Eventually, Aristotle appeared among the Greeks. He improved the methods of logic and systematized its problems and details. He assigned to logic its proper place as the first philosophical discipline and the introduction to philosophy. Therefore he is called the First Teacher.
There's a logic to dreams that doesn't necessarily follow linear narrative. You don't know why things happen, it's your subconscious pushing you, to give you information.
Mathematics consists in proving the most obvious thing in the least obvious way.
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.
At the moment, every country arrives at climate negotiations seeking to keep their own emissions as high as possible. This is the logic of the madhouse, a recipe for collective suicide. We dont want a global suicide pact. We want a global survival pact
To make music means to express human intelligence by sonic means. This is intelligence in its broadest sense, which includes not only the peregrinations of pure logic but also the "logic" of emotions and intuition. My musical techniques, although often rigorous in their internal structure, leave many openings through which the most complex and mysterious factors of the intelligence may penetrate.
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.
Mathematicians create by acts of insights and intuition. Logic then sanctions the conquests of intuition.
Mathematics is a body of knowledge, but it contains no truths.
Proof is an idol before which the mathematician tortures himself.
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.
Calculators can only calculate - they cannot do mathematics.
Logic doesn't apply to the real world.
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