“The straight line has a property of self-similarity. Each piece of the straight line is the same as the whole line when used to a big or small extent.”

Nobody will deny that there is at least some roughness everywhere

The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.

A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…

I don’t seek power and do not run around

I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.

A formula can be very simple, and create a universe of bottomless complexity.

In mathematics and science definition are simple, but bare-bones. Until you get to a problem which you understand it takes hundreds and hundreds of pages and years and years of learning.

Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree.

Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics

I’ve been a professor of mathematics at Harvard and at Yale. At Yale for a long time. But I’m not a mathematician only. I’m a professor of physics, of economics, a long list. Each element of this list is normal. The combination of these elements is very rare at best.

There is a saying that every nice piece of work needs the right person in the right place at the right time.

I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes. And the two are extraordinarily close; in one way both are fractal.

Engineering is too important to wait for science.

The most complex object in mathematics, the Mandelbrot Set … is so complex as to be uncontrollable by mankind and describable as ‘chaos’.

Although computer memory is no longer expensive, there’s always a finite size buffer somewhere. When a big piece of news arrives, everybody sends a message to everybody else, and the buffer fills

Bottomless wonders spring from simple rules, which are repeated without end.

I sat down one night and wrote the line rock, rock, rock everybody.

In the marathon of life, there is no finish line.

If you look at a shape like a straight line, what’s remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.

I remember, the players have often mentioned it as an honour to Shakespeare, that in his writing (whatsoever he penned) he never plotted out a line. My answer hath been, would he had blotted a thousand.

Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated.

I always have problems with seeing how our new stuff relates to our old stuff – I’m better at seeing long lines in other people’s music than in my own.

I loved English literature – if didn’t it would have been hard – but I had to learn it myself. I remembered ways to repeat words, to put more emphasis on certain lines.

I always assumed scientists were free to ask any question, pursue any line of inquiry without fear or reprisal.