"Yeah, that’s another difficult question. I suppose it has to do with… My mathematical style, my style as a mathematician, is that I don’t really like difficult mathematics. What I love is simple, clear, easy-to-understand arguments that prove a surprising result. That’s my favorite situation. And actually, the question of whether it’s a new result or not is somehow less important to me. And so that has to do with this question of the greats and so on, whoever does it first. Because I think, for example, if you prove a new result with a bad argument or a complicated argument, that’s great because you proved something new. But I still want to see the beautiful, simple, because that’s what I can understand."

"Well, the mathematical Platonic realm is… I’m not sure I would say it’s more real, but I’m saying we understand the reality of it in a much deeper and more— …a more convincing way. I don’t think we understand the nature of physical reality very well at all, and I think most people aren’t even scratching the surface of the question as I intend to be asking it. So, you know, obviously we understand physical reality. I mean, I knock on the table— …and so on, and we know all about what it’s like to, you know, have a birthday party or to drink a martini or whatever. And so we have a deep understanding of existing in the physical world. But maybe understanding is the wrong word. We have an experience of living in the world—"

"And so for small values of inputs, then it doesn’t make sense to talk about this polynomial time feasibility with respect to, say, the range of problem inputs that we will ever give it in our lifetime or in the span of human civilization or whatever. I mean, because it’s an asymptotic property, it’s really in the limit as the size of the inputs goes to infinity, that’s the only time that polynomial or NP becomes relevant. And so maybe it’s important to keep that in mind when… Sometimes you find kind of overblown remarks made about, you know, if P equals NP, then this will be incredibly important for human civilization because it means that we’ll have feasible algorithms for solving these incredibly important…"