Mathematicians aren't satisfied because they know there are no solutions up to four million or four billion, they really want to know that there are no solutions up to infinity.
Sentiment: NEGATIVE
Pure mathematicians just love to try unsolved problems - they love a challenge.
Need we add that mathematicians themselves are not infallible?
Even the greatest mathematicians, the ones that we would put into our mythology of great mathematicians, had to do a great deal of leg work in order to get to the solution in the end.
To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.
Just because we can't find a solution it doesn't mean that there isn't one.
We in science are spoiled by the success of mathematics. Mathematics is the study of problems so simple that they have good solutions.
The infinite in mathematics is alway unruly unless it is properly treated.
As far as I know, only a small minority of mathematicians, even of those with Platonist views, accept the idea that there may be mathematical facts which are true but unknowable.
Mathematics cannot handle physical quantities like density that literally go to infinity.
I am incapable of conceiving infinity, and yet I do not accept finity.
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