Benoit Mandelbrot Quotes

As one who has taught mathematics at all levels of university instruction, I am well aware of the negative attitude of so many students toward the subject. There are many reasons for this, one of them no doubt being the esoteric, dry way in which we teach the subject. We tend to overwhelm our students with formulas, definitions, theorems, and proofs, but we seldom mention the historical evolution of these facts, leaving the impression that these facts were handed to us, like the Ten Commandments, by some divine authority.

The great difficulty in education is to get experience out of ideas.

We in science are spoiled by the success of mathematics. Mathematics is the study of problems so simple that they have good solutions.

This is at the heart of all good education, where the teacher asks students to think and engages them in encouraging dialogues, constantly checking for understanding and growth.

It's my belief that you can take everyone down a logical path if you take them slowly enough, and the trouble is that mathematical brains can get scrambled a little bit on the way. You get a bad teacher, it messes you up for the rest of the journey.

The words printed here are concepts. You must go through the experiences.

The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.

[plaintiffs] cannot, by simply filing suit and crying ‘character assassination,” silence those who hold divergent views, no matter how divergent those views may be to plaintiffs’ interests. Scientific controversies must be settled by the methods of science rather than by the methods of litigation […] More papers, more discussion, better data, and more satisfactory models – not larger awards of damages – mark the path towards superior understanding of the world around us.

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

I was a terrible science student, and for a long time, I thought I just didn't understand science. It turned out that I didn't understand post-Newtonian science. I could actually understand how people thought scientifically about the world in the past.

My students may have dexterity with the equations they're required to know, but they lack the capacity to apply their knowledge to real-life problems. This critical shortcoming appears in high school and possibly in elementary grades - long before college.

Certainly to me it has been valuable to have to think through the basics of physics in order to present them in a halfway coherent form for a course. That has led me to ideas in research. Even freshman physics leads to thoughts that lead to other thoughts that are stimulating.

So you see that the process of education, taken in a large way, may be described as nothing but the process of acquiring ideas or conceptions, the best educated mind being the mind which has the largest stock of them, ready to meet the largest possible variety of the emergencies of life. The lack of education means only the failure to have acquired them, and the consequent liability to be 'floored' and 'rattled' in the vicissitudes of experience.

All knowledge is gained through an orderly loss of information.

Learning is more than the acquisition of the ability to think; it is the acquisition of many specialized abilities for thinking about a variety of things.

There are many words and definitions I have never lost. But some I am only just beginning to truly understand.

Once a day, especially in the early years of life and study, call yourselves to an account what new ideas, what new proposition or truth you have gained, what further confirmation of known truths, and what advances you have made in any part of knowledge.

If we trace the progress of our minds, and with attention observe how it repeats, adds together, and unites its simple ideas received from sensation or reflection, it will lead us farther than at first, perhaps, we should have imagined.

True learning must not be content with ideas, which are, in fact, signs, but must discover things in their individual truth.

I am convinced that it is of primordial importance to learn more every year than the year before. After all, what is education but a process by which a person begins to learn how to learn.

If there are lessons to be drawn from the sciences, then that should be the concern of everyone, including scientists to the extent that they can make a contribution.

But in the new (math) approach, the important thing is to understand what you're doing, rather than to get the right answer.

One always begins with the simple, then comes the complex, and by superior enlightenment one often reverts in the end to the simple. Such is the course of human intelligence.

The World requires at least ten years to understand a new idea, however important or simple it may be.