In every way at every turn, the question we ask ourselves is not what can we do, but what should we do?.”

To get the most out of the world around you you’ve got to really look hard. Most people out walking in the woods don’t really look. They just glance around. They scan. Before I start a painting I spend a lot of time looking and thinking, I go out in the car and pull a chair out of the boot and sit in the woods. I sit there and smoke and just look.

I have now come down to a topic which is very distasteful; it is not sufficient to do a job, you have to sell it. 'Selling' to a scientist is an awkward thing to do. It's very ugly; you shouldn't have to do it. The world is supposed to be waiting, and when you do something great, they should rush out and welcome it. But the fact is everyone is busy with their own work. You must present it so well that they will set aside what they are doing, look at what you've done, read it, and come back and say, "Yes, that was good."

Of course, the most rewarding part is the "Aha" moment, the excitement of discovery and enjoyment of understanding something new, the feeling of being on top of a hill, and having a clear view. But most of the time, doing mathematics for me is like being on a long hike with no trail and no end in sight! I find discussing mathematics with colleagues of different backgrounds one of the most productive ways of making progress.

Curiosity is a form of humility — acknowledging that you don't know everything. Responding to curiosity allows other people to speak freely. Facts and details matter and inform a deeper and deeper analysis that allows you to continually revise and update your plans. This, of course, also means that you are constantly admitting prior mistakes. You need to shed sacred cows, seek out blind spots and challenge the status quo.