Browsing Topic Best Mathematical Problems Quotes

There are problems to whose solution I would attach an infinitely greater importance than to those of mathematics, for example touching ethics, or our relation to God, or concerning our destiny and our future; but their solution lies wholly beyond us and completely outside the province of science.

Before a kid learns how to use a computer that can solve mathematical problems, he or she should know how to do arithmetic without a computer.

In fact, I barely missed being number one in France in both schools. In particular I did very well in mathematical problems.

By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.

If you think it’s simple, then you have misunderstood the problem.

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

Theorems are fun especially when you are the prover, but then the pleasure fades. What keeps us going are the unsolved problems.

Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and conformed. They are no exceptions to the rule that God always geometrizes. Their problems of form are in the first instance mathematical problems, their problems of growth are essentially physical problems, and the morphologist is, ipso facto, a student of physical science.

This paper gives wrong solutions to trivial problems. The basic error,however, is not new.

The measure of our intellectual capacity is the capacity to feel less and less satisfied with our answers to better and better problems.

If there is a problem you can’t solve, then there is an easier problem you can’t solve: find it.

Since you are now studying geometry and trigonometry, I will give you a problem. A ship sails the ocean. It left Boston with a cargo of wool. It grosses 200 tons. It is bound for Le Havre. The mainmast is broken, the cabin boy is on deck, there are 12 passengers aboard, the wind is blowing East-North-East, the clock points to a quarter past three in the afternoon. It is the month of May. How old is the captain?

The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It’s like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.

Music is a secret and unconscious mathematical problem of the soul.

Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. … A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.

It isn’t that they can’t see the solution. It is that they can’t see the problem.

The older I get, the more I believe that at the bottom of most deep mathematical problems there is a combinatorial problem.

One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.

I combat the errors of ages; I meet the violence of mobs; I cope with illegal proceedings from executive authority; I cut the gordian knot of powers, and I solve mathematical problems of universities, with truth-diamond truth; and God is my ‘right hand man’.