A Quote by Paul Halmos

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.

Paul Halmos

Quote Topics

Error Experimentation Guesswork Hypotheses Just List Mathematics Prove Reason Science Start Then Theorem Trial Trial And Error Try

Quote Author

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

Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.

Paul Halmos

If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it.

George Polya

Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.

George Polya

In order to predict effectively, we need to use science. And the reason that we need to use science is because then we can reproduce what we're doing; it's not just wisdom or guesswork. And if we can predict, then we can engineer the future.

Bruce Bueno de Mesquita

For me, form is something I locate in the process of writing the poems. What I mean is, I start scribbling, and then try to form the poem - on a typewriter or on my computer - and, by trial and error, try to find the right shape. I just try to keep forming the poem in different ways until it feels right to me.

Matthew Zapruder

Creativity is the process of sensing problems or gaps in information, then identifying the difficulties and seeking solutions through trial and error or through forming hypotheses.

Ellis Paul Torrance

Music is really all about experimentation and lots of trial and error. It's just mind-numbingly boring until you hit on something that works well.

Martin Gore

Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. Fermat's Last Theorem is the most beautiful example of this.

Andrew Wiles

Every great idea emerges out of a process of trial-and-error experimentation.

Scott D. Anthony

Survival in the demand economy depends on and requires experimentation, risk taking, and trial and error.

Kevin Allen

Educated guesswork' is what science is. You form hypotheses, test them against the evidence, and if they fit the evidence, you can assume you've got close to the truth.

Alice Roberts

You still want to be thoughtful about what you do, no doubt, but you have to learn through trial-and-error experimentation as well.

Scott D. Anthony

science progresses by trial and error, and when it is forbidden to admit error there can be no progress.

Joan Robinson

Many 'hard' scientists regard the term 'social science' as an oxymoron. Science means hypotheses you can test, and prove or disprove. Social science is little more than observation putting on airs.

Michael Kinsley

Through a process of trial and error and experimentation, I discovered the simplest method - using only black - produced work with the strongest visual impact installed.