Conrad Wolfram Quotes

A dozen more questions occurred to me. Not to mention twenty-two possible solutions to each one, sixteen resulting hypotheses and counter-theorems, eight abstract speculations, a quadrilateral equation, two axioms, and a limerick. That's raw intelligence for you.

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning. The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.

A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.

Math has a lot of negative stereotypes, but it can actually be fun and incredibly empowering.

Being exposed to theory, stimulated by a basic love of concepts and mathematics, was a marvelous experience.

Simple ideas lie within the reach only of complex minds.

Mathematical discoveries, small or great are never born of spontaneous generation.

Thinking - in particular abstract thinking, which most of us are introduced to through the study of mathematics and literature - helps us learn that we can become problem solvers.

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.

I like to figure things out and solve problems.

Mathematics seems to endow one with something like a new sense.

Math makes sense when you apply it to projects.

On 'MythBusters,' a lot of what we do does not fall into any category of things we have ever done before. There's a lot of problem solving to figure out how to even approach a given problem. A background in science or engineering helps a lot.

As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention.

We've taught you that the earth is round, That red and white make pink, And something else that matters more - We've taught you how to think.

In their field they [mathematicians] do what we ought to be doing in ours. Therein lies the significant lesson ... of their existence. They are an analogy for the intellectual of the future.

Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning.

A Vulgar Mechanick can practice what he has been taught or seen done, but if he is in an error he knows not how to find it out and correct it, and if you put him out of his road he is at a stand. Whereas he that is able to reason nimbly and judiciously about figure, force, and motion, is never at rest till he gets over every rub. (from a letter dated 25 May, 1694)

... mathematics is the science of skillful operations with concepts and rules invented just for this purpose.

Mathematics ... is indispensable as an intellectual technique. In many subjects, to think at all is to think like a mathematician.

The number of people that can reason well is much smaller than those that can reason badly. If reasoning were like hauling rocks, then several reasoners might be better than one. But reasoning isn't like hauling rocks, it's like, it's like racing, where a single, galloping Barbary steed easily outruns a hundred wagon-pulling horses.

Mathematics is not a contemplative but a creative subject.

Children must be taught how to think, not what to think.

Learn to use your brain power. Critical thinking is the key to creative problem solving in business.

The grand thing is to be able to reason backwards.