Ibn Khaldun Quotes

Geometry enlightlens the intellect and sets one's mind right

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.

The investigation of mathematical truths accustoms the mind to method and correctness in reasoning, and is an employment peculiarly worthy of rational beings.

I approached the bulk of my schoolwork as a chore rather than an intellectual adventure. The tedium was relieved by a few courses that seem to be qualitatively different. Geometry was the first exciting course I remember. Instead of memorizing facts, we were asked to think in clear, logical steps. Beginning from a few intuitive postulates, far reaching consequences could be derived, and I took immediately to the sport of proving theorems.

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

Math is like going to the gym for your brain. It sharpens your mind.

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

What I knew was I liked math and science, and I never wanted to memorize everything. I wanted to understand where it came from.

To solve the Cube, you need special skills and understanding. For example, pattern recognition is very important to solve the Cube.

Science and math are hard for everybody, and it's usually not a matter or being born gifted at it or not. It's hard work, but it can be a lot of fun!

The student of mathematics must get rid of all arbitrary thinking and follow purely the demands of thought. In thinking in this way, the laws of the spiritual world flow into him. This regulated thinking leads to the most spiritual truths.

When I was in school, my favorite subject was math. I took algebra and calculus. At an early age I grasped it and understood it quickly. I just enjoyed breaking the codes and solving problems.

I think that great programming is not all that dissimilar to great art. Once you start thinking in concepts of programming it makes you a better person...as does learning a foreign language, as does learning math, as does learning how to read.

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

Geometry is the art of correct reasoning from incorrectly drawn figures.

Learning to write programs stretches your mind, and helps you think better, creates a way of thinking about things that I think is helpful in all domains.

If a man's wit be wandering, let him study the mathematics; for in demonstrations, if his wit be called away never so little, he must begin again.

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.

Of all the intellectual faculties, judgment is the last to mature. A child under the age of fifteen should confine its attention either to subjects like mathematics, in which errors of judgment are impossible, or to subjects in which they are not very dangerous, like languages, natural science, history, etc.

The advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil.

I take a dose of mathematics every day to prevent my brain from becoming quite soft.

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.

Reading aloud and talking about what we're reading sharpens children's brains. It helps develop their ability to concentrate at length, to solve problems logically, and to express themselves more easily and clearly.

Thinking. A process by which I use my brain to make a rational decision.

Always it is thus with my new students, and especially with the human ones; the mind is the last muscle they train or use, and the one that they regard the least. Ask them about swordplay and they can list every blow from a duel a month old, but ask them to solve a problem or make a coherent statement and... well, I would be lucky to get more than a blank stare in return.