Mathematician Quotes

I am accustomed to sleep and in my dreams to imagine the same things that lunatics imagine when awake.

If you would be a real seeker after truth, it is necessary that at least once in your life you doubt, as far as possible, all things.

You just keep pushing. You just keep pushing. I made every mistake that could be made. But I just kept pushing.

I think; therefore I am.

The senses deceive from time to time, and it is prudent never to trust wholly those who have deceived us even once.

An optimist may see a light where there is none, but why must the pessimist always run to blow it out?

Divide each difficulty into as many parts as is feasible and necessary to resolve it.

It is not enough to have a good mind; the main thing is to use it well.

The dark outside world of Paris under German occupation exerted a strong containing pressure.

The Cowles Commission was the optimal environment for the type of research that I wanted to do.

In the mid-'60s in Berkeley, the theory of measure spaces of economic agents became one of my main interests.

I had become interested in economics, an interest that was transformed into a lifetime dedication when I met with the mathematical theory of general economic equilibrium.

The numbers are a catalyst that can help turn raving madmen into polite humans.

So much the worse, it may be, for a particular meeting: but the meeting is the individual, which on evolution principles, must be sacrificed for the development of the race.

Projective geometry is all geometry.

Not that the propositions of geometry are only approximately true, but that they remain absolutely true in regard to that Euclidean space which has been so long regarded as being the physical space of our experience.

But be that as it may, I think it is more respectful to you that I should speak to you upon and do my best to interest you in the subject which has occupied me, and in which I am myself most interested.

And in another point of view, I think it is right that the address of a president should be on his own subject, and that different subjects should be thus brought in turn before the meetings.

As for everything else, so for a mathematical theory: beauty can be perceived but not explained.

The essence of mathematics lies in its freedom.

A set is a Many that allows itself to be thought of as a One.

I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.

In mathematics the art of proposing a question must be held of higher value than solving it.

Wherefore for the public interest and benefit of human society it is requisite that the highest obligations possible should be laid upon the consciences of men.

Whence it is somewhat strange that any men from so mean and silly a practice should expect commendation, or that any should afford regard thereto; the which it is so far from meriting, that indeed contempt and abhorrence are due to it.

That men should live honestly, quietly, and comfortably together, it is needful that they should live under a sense of God's will, and in awe of the divine power, hoping to please God, and fearing to offend Him, by their behaviour respectively.

That justice should be administered between men, it is necessary that testimonies of fact be alleged; and that witnesses should apprehend themselves greatly obliged to discover the truth, according to their conscience, in dark and doubtful cases.

That in affairs of very considerable importance men should deal with one another with satisfaction of mind, and mutual confidence, they must receive competent assurances concerning the integrity, fidelity, and constancy each of other.

No man speaketh, or should speak, of his prince, that which he hath not weighed whether it will consist with that veneration which should be preserved inviolate to him.

It is safe to make a choice of your thoughts, scarcely ever safe to express them all.