Mathematicians do not study objects, but the relations between objects.

Point set topology is a disease from which the human race will soon recover.

It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.

There are no solved problems; there are only problems that are more or less solved.

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.

Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.

If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living

It is through science that we prove, but through intuition that we discover.

Geometry is the art of correct reasoning from incorrectly drawn figures.

One geometry cannot be more true than another; it can only be more convenient.

It is far better to foresee even without certainty than not to foresee at all.

People are fascinating. Especially the ones who hate me.

Full minds create chaos.

It is pretty clear from Facebook we can enjoy entertaining each other as much as we enjoy surfing the experts' expressions.

I also know that every person faces adversity in life. Abraham Lincoln held this seat in Congress in one term. But few faced as many defeats in his personal, business and public life as he did.

People, chained by monotony, afraid to think, clinging to certainties... they live like ants.

Joy of living is sustainable; fear of dying is not.

I just felt that it was my responsibility, since so many people had taken the time to help me along, to do the same for others.

I think now because of this whole social media thing, people obviously felt these things [about cultural appropriation] before, and they comment on everything.

I know where he should have put his flag up, and he'd have got plenty of help. (said at Stamford Bridge)

No one ever got rich by studying poverty and thinking about poverty.