Charles Darwin Quotes

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

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.

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

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.

if you do not appreciate the mathematics, you cannot see, among the great variety of facts, that logic permits you to go from one to the other

You must acquire something of that industrious habit of mind which the study of natural science gives,—the art of comparing, of perceiving true likenesses and true differences, and so of classifying and arranging what you see; the art of connecting facts together in your mind in cause and effect

I'm a natural puzzle solver.

I think you have to be left-brained, to a certain extent, to understand science. I can talk about it, but I can't do it.

It's strange how few of the world's great problems are solved by people who remember their algebra.

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.

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

Many who have had an opportunity of knowing any more about mathematics confuse it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination.

If you are truly serious abut preparing your child for the future, don't teach him to subtract teach him to deduct.

I don't like to be negative about math because it really teaches you a lot of great things. You kind of use math every day.

I have hardly ever known a mathematician who was capable of reasoning.

Mathematical Knowledge adds a manly Vigour to the Mind, frees it from Prejudice, Credulity, and Superstition.

I think I still like science and art better, but geometry is a big improvement over algebra.

I think philosophy is extremely good training for anyone who wants to do anything. Although that is an idea which people may speak scornfully of now, I think it does teach one to

I am convinced that the act of thinking logically cannot possibly be natural to the human mind. If it were, then mathematics would be everybody's easiest course at school and our species would not have taken several millennia to figure out the scientific method.

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.

The math helps you have better understanding and helps you have more creative ideas, but you can't replace the creative ideas

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.

Geometry is beautifully logical, and it teaches you how to think and prove that things are so, step by step by step. Proofs are excellent lessons in reasoning. Without logic and reasoning, you are dependent on jumping to conclusions or - worse - having empty opinions.

Perhaps the best test of a man's intelligence is his capacity for making a summary.

Problems may be solved in the study which have baffled all those who have sought a solution by the aid of their senses. To carry the art, however, to its highest pitch, it is necessary that the reasoner should be able to use all the facts which have come to his knowledge; and this in itself implies, as you will readily see, a possession of all knowledge, which, even in these days of free education and encyclopaedias, is a somewhat rare accomplishment.