A Quote by Paul Halmos

The author discusses valueless measures in pointless spaces.

Paul Halmos

Quote Topics

Author Measures Pointless Spaces Valueless

Quote Author

Paul Halmos
American - Mathematician
March 3, 1916 - October 2, 2006

I remember one occasion when I tried to add a little seasoning to a review, but I wasn't allowed to. The paper was by Dorothy Maharam, and it was a perfectly sound contribution to abstract measure theory. The domains of the underlying measures were not sets but elements of more general Boolean algebras, and their range consisted not of positive numbers but of certain abstract equivalence classes. My proposed first sentence was: "The author discusses valueless measures in pointless spaces."

Paul Halmos

You imagine a reader and try to keep the reader interested. That's storytelling. You also hope to reward the reader with a sense of a completed design, that somebody is in charge, and that while life is pointless, the book isn't pointless. The author knows where he is going. That's form.

John Updike

Everything useful in mathematics has been devised for a purpose. Even if you don't know it, the guy who did it first, he knew what he was doing. Banach didn't just develop Banach spaces for the sake of it. He wanted to put many spaces under one heading. Without knowing the examples, the whole thing is pointless.

Michael Atiyah

One never discusses anything with anybody who can understand one discusses things with people who cannot understand.

Gertrude Stein

Don't pointless things have a place, too, in this far-from-perfect world? Remove everything pointless from an imperfect life, and it'd lose even its imperfection.

Haruki Murakami

In New York there's a lot of interstitial spaces; spaces in between spaces, where you're changing, and New York gives you the anonymity to be who you want to be.

Dee Rees

Web publishing can create common spaces; it all depends on how we, the readers and sometimes the producers, react to technological change. If we sort ourselves into narrow groups, common spaces will be in big trouble. But there's no reason not to have common spaces on the Internet. There are lots of them out there.

Cass Sunstein

Art is so wonderfully irrational, exuberantly pointless, but necessary all the same. Pointless and yet necessary, that's hard for a puritan to understand.

Gunter Grass

It's the pointless things that give your life meaning. Friendship, compassion, art, love. All of them pointless. But they're what keeps life from being meaningless.

Tim Winton

Oftentimes, secrecy involves creating spaces that are outside of the law but are outside the normal channels of oversight. And I think it's pretty easy to see that if you create spaces that are essentially outside the law, then you're creating spaces where anything can happen.