Mathematical Challenges Quotes

God does not care about our mathematical difficulties. He integrates empirically.

I suppose you are two fathoms deep in mathematics, and if you are, then God help you. For so am I, only with this difference: I stick fast in the mud at the bottom, and there I shall remain.

Mathematicians always like a deceptively difficult problem.

Mathematics is not yet ready for such problems.

I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future.

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.

In mathematics we have long since drawn the rein, and given over a hopeless race.

[A mathematician is a] scientist who can figure out anything except such simple things as squaring the circle and trisecting an angle.

It is hard to convince a high-school student that he will encounter a lot of problems more difficult than those of algebra and geometry.

Abel has left mathematicians enough to keep them busy for 500 years.

Well, 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.

If some day you're struggling with math, and you think, 'I don't think I can do this,' you can - you actually can. Everybody has their hard days - I definitely had mine - and you get through them, and you learn from that stumble, and then you're onto the next problem.

And by the same token, I appreciate math, because I can't do math. If I have to read a map or figure out the tip on a restaurant bill, I might start to tear up a little bit.

How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!

Increasingly, the mathematics will demand the courage to face its implications.

The book Dynamic Programming by Richard Bellman is an important, pioneering work in which a group of problems is collected together at the end of some chapters under the heading "Exercises and Research Problems," with extremely trivial questions appearing in the midst of deep, unsolved problems. It is rumored that someone once asked Dr. Bellman how to tell the exercises apart from the research problems, and he replied: "If you can solve it, it is an exercise; otherwise it's a research problem."

The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.

Let's face it; by and large math is not easy, but that's what makes it so rewarding when you conquer a problem, and reach new heights of understanding.