The real work of us mathematicians, from now until, roughly, fifty years from now, when computers won't need us anymore, is to make the transition from human-centric math to machine-centric math as smooth and efficient as possible.

No Victor, you got it backwards, you should evaluate these integrals non-rigorously if you can, and rigorously if you must.

Programming is much much harder than doing mathematics.

When a problem seems intractable, it is often a good idea to try to study "toy" versions of it in the hope that as the toys become increasingly larger and more sophisticated, they would metamorphose, in the limit, to the real thing.

Regardless of whether or not God exists, God has no place in mathematics, at least in my book.

The real work of us mathematicians, from now until, roughly, fifty years from now, when computers won't need us anymore, is to make the transition from human-centric math to machine-centric math as smooth and efficient as possible.

You can keep counting forever. The answer is infinity. But, quite frankly, I don't think I ever liked it. I always found something repulsive about it. I prefer finite mathematics much more than infinite mathematics. I think that it is much more natural, much more appealing and the theory is much more beautiful. It is very concrete. It is something that you can touch and something you can feel and something to relate to. Infinity mathematics, to me, is something that is meaningless, because it is abstract nonsense.