It's as great a part of the human adventure to invent things as to understand them. John Randall wasn't a great scientist, but he was a great inventor. There's been lots more like him, and it's a shame they don't get Nobel Prizes.

The question that will decide our destiny is not whether we shall expand into space. It is: shall we be one species or a million? A million species will not exhaust the ecological niches that are awaiting the arrival of intelligence.

We simply don't know yet what's going to happen to the carbon in the atmosphere.

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.

When the great innovation appears, it will almost certainly be in muddled, incomplete and confusing form. ... For any speculation which does not at first glance look crazy, there is no hope.

The important thing is that we now have the tools to sequence all kinds of animals and plants and microbes - as well as humans. It is not important that we didn't actually finish the human sequence yet.

The PhD system is the real root of the evil of academic snobbery. People who have PhDs consider themselves a priesthood, and inventors generally don't have PhDs.