Mathematical Problem Quotes

I tried to fit it in with some previous broad conceptual understanding of some part of mathematics that would clarify the particular problem I was thinking about.

The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. ... Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.

Courage is not a quality one normally associates with mathematicians. Yet it should apply to people who work in their attics in secret for seven years without cease on a problem that has eluded the greatest mathematical minds since first proposed in 1637.

The obvious mathematical breakthrough would be development of an easy way to factor large prime numbers.

A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution.

Some people focus more on sonics. Some people focus more on story. I focus on both sonics and story, but music sometimes, just music itself, can turn into more of a maths problem. I guess everything in life is a math problem, but it can be more about an empirical route to getting the symmetry that you want, and this vibe, sonically.

Fermat said he had a proof.

The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.

String theory has had a long and wonderful history. It originated as a technique to try to understand the strong force. It was a calculational mechanism, a way of approaching a mathematical problem that was too difficult, and it was a promising way, but it was only a technique. It was a mathematical technique rather than a theory in itself.

Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.

I approach an action sequence almost like a mathematical problem. Sometimes you get these action sequences that you read and go, 'Oh my God, this is huge, how do I do it?' and I go, 'Just a step at a time. Sit down and plot each piece of it out.'

There's a lot of science in it, and as Slartibartfast [in The Hitchhiker's Guide to the Galaxy] said: 'I am a great fan of science, but I cannot do a quadratic equation.' I've never, ever been able to do one. I remember one occasion at Warwick University, when Jack and Ian were at their wits' end because I couldn't get it. I felt totally ashamed.

Mathematicians come to the solution of a problem by the simple arrangement of the data, and reducing the reasoning to such simple operations, to judgments so brief, that they never lose sight of the evidence that serves as their guide.

As a single atom man is an enigma: as a whole he is a mathematical problem. As an individual he is a free agent, as a species the offspring of necessity.