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Mathematics is not a spectator sport. You have to get involved.
The most exciting moments in mathematics are when you see connections between things that seemed unrelated before.
Don't be afraid to ask questions. That's how you learn.
I always tell my students that it's okay to make mistakes, as long as you learn from them.
You have to be comfortable with being uncomfortable if you want to make progress in mathematics.
I think that in mathematics, and maybe in life, you have to be willing to be a little bit lost.
The most important thing is to have a vision of what you want to do and then to have the persistence to carry it out.
The most exciting moments in mathematics are when you discover something that was hidden in plain sight.
The best mathematics is that which you do not understand at first glance.
The most exciting thing is when you suddenly see the solution to a problem that has been puzzling you for a long time.
When you solve a mathematical problem, you don't just get the answer - you understand why it's the answer.
I think that the thing that makes mathematics worthwhile is the fact that it has this incredible structure that you can explore and discover.
The only way to do great work is to love what you do.
You don't have to be a mathematician to have a feel for numbers.
The deepest theorems often have the simplest proofs - if you look at them from the right angle.
In mathematics, truth is always relative to the system you're working in.
The most exciting moments in mathematics are when you discover that two seemingly unrelated areas are deeply connected.
In mathematics, you don't understand things. You just get used to them.
Mathematics is not a deductive science—that's a cliché. When you try to prove a theorem, you don't just list the hypotheses and then start to reason. What you do is trial and error, experimentation, guesswork.
To do mathematics is to explore a universe of ideas, where the only limit is your imagination.
