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I don't have any particular recipe [for developing new proofs] ... It is the reason why doing research is challenging as well as attractive. It's like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out.
My goal is simple. It is a complete understanding of the universe, why it is as it is and why it exists at all.
Look up at the stars and not down at your feet. Try to make sense of what you see, and wonder about what makes the universe exist. Be curious.
I have a different understanding of what is important and what is not.
I am not a hero of mathematics. I'm not even that successful; that is why I don't want to have everybody looking at me.
I have already carried out my duty. I have proved the Poincaré conjecture and I have nothing more to do in mathematics.
In quantum computing, we are not just pushing the boundaries of technology, but also exploring the fundamental limits of what is computable.
The sense of smell is directly connected to the emotional centers of the brain, which is why smells can evoke such strong memories.
The thing about life is that you never know what's going to happen next.
The most important thing in filmmaking is the story. Without a good story, you have nothing.
A good director is like a good conductor; you have to know when to lead and when to let go.