Benoit Mandelbrot Quotes

Strange! I don't understand how it is that we can write mathematical expressions and calculate what the thing is going to do without being able to picture it.

In the future, as in the past, the great ideas [of mathematics] must be simplifying ideas, the creator must always be one who clarifies, for himself, and for others, the most complicated issues of formulas and concepts.

It is here [in mathematics] that the artist has the fullest scope of his imagination.

Without the concepts, methods and results found and developed by previous generations right down to Greek antiquity one cannot understand either the aims or achievements of mathematics in the last 50 years. [Said in 1950]

With an absurd oversimplification, the 'invention' of the calculus is sometimes ascribed to two men, Newton and Leibniz. In reality, the calculus is the product of a long evolution that was neither initiated nor terminated by Newton and Leibniz, but in which both played a decisive part.

For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.

The introduction of the cipher 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps.

Your ideas need not have anything to do with reality. Making conclusions is a sure way of not enhancing our perception.

Why is the human skull as dense as it is? Nowadays we can send a message around the world in one-seventh of a second, but it takes years to drive an idea through a quarter-inch of human skull.

I'm not nervous if I think about something for nine years and then I don't write it. Even if it fades it doesn't concern me. It'll come back if it's worth it.

Mathematics deals exclusively with the relations of concepts to each other without consideration of their relation to experience.

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

In 15 years or something - I like the idea of just one paparazzo coming out and trying to get a picture, and I just beat the shit out of him. I mean - out of nowhere - when my picture's not even worth...and I've spent all my money, so you can't sue me!

Paint ideas, paint thought.

It was among the ruins of the capitol that I first conceived the idea of a work which has amused and exercised nearly twenty years of my life.

It is a good deal easier for most people to state an abstract idea than to describe and thus re-create some object they actually see.

I plan years in advance, but I like to leave enough space in the narrative scheme to change things, because I always get my best ideas the closer I come to the end of a project, after I've lived with it for a while.

If you don't generalize you don't philosophize.

They called it the Terminal Bar but they had no idea that like twenty years later the place'd be filling up with terminal cases.

Though determinants and matrices received a great deal of attention in the nineteenth century and thousands of papers were written on these subjects, they do not constitute great innovations in mathematics.... Neither determinants nor matrices have influenced deeply the course of mathematics despite their utility as compact expressions and despite the suggestiveness of matrices as concrete groups for the discernment of general theorems of group theory.

As I say, I have never in all these years thought of the matter in quite this way; but then it is perhaps in the nature of coming away on a trip such as this that one is prompted towards such surprising new perspectives on topics one imagined one had long ago thought throughly.

I've got at least two major project ideas that I've been chewing on for several years in my head and I've been trying to resist them both. But I have learned over the years that when they don't go away and they're still in there, you probably have to resign yourself to the fact that you're going to do something about them.

Time is but the measure of the difficulty of a conception. Pure thought has scarcely any need of time, since it perceives the two ends of an idea almost at the same moment.

A lot of different things had to come together over the years, accumulated experiences of a general and personal nature, before the idea and the decision were developed and then carried out.