Now, as Mandelbrot points out, ... Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us.

The public has a distorted view of science because children are taught in school that science is a collection of firmly established truths. In fact, science is not a collection of truths. It is a continuing exploration of mysteries.

You ask: what is the meaning or purpose of life? I can only answer with another question: do you think we are wise enough to read God's mind?

The media always tries to make everything into a disaster, but it's mostly rubbish.

The average student emerges at the end of the Ph.D. program, already middle-aged, overspecialized, poorly prepared for the world outside, and almost unemployable except in a narrow area of specialization. Large numbers of students for whom the program is inappropriate are trapped in it, because the Ph.D. has become a union card required for entry into the scientific job market.

I think the biggest misconception about mathematics is that everybody has to learn it. That seems to be a complete mistake. All the time worrying about pushing the children and getting them to be mathematically literate and all that stuff. It's terribly hard on the kids. It's also hard on the teachers. And I think it's totally useless. To me, mathematics is like playing the violin. Some people can do it - others can't. If you don't have it, then there's no point in pretending.

That's the beautiful thing about science - that it's all about things we don't understand, not just the things we do understand.