The few mathematical unknowns explicitly noted above may
suffice to illustrate the fact that the path of the
mathematical student often leads around difficulties which are
left behind. Sometimes the later developments have enabled the
mathematicians to overcome some of these difficulties which had
stood in the way for more than a thousand years. This was done,
for instance, by Gauss when he found a necessary and sufficient
condition that a regular polygon of a prime number of sides can
be constructed by elementary methods. It was also done by
Hermite, Lindemann and others by proving that epsilon and rho
are transcendental numbers. While such obstructions are thus
being gradually removed some of the most ancient ones still
remain, and new ones are rising rapidly in view of modern
developments along the lines of least resistance.

These obstructions have different effects on different people.
Some fix their attention almost wholly on them and are thus
impressed by the lack of progress in mathematics, while others
overlook them almost entirely and fix their attention on the
routes into new fields which avoid these difficulties. A
correct view of mathematics seems to be the one which looks at
both, receiving inspiration from the real advances but not
forgetting the desirability of making the developments as
continuous as possible. At any rate the average educated man
ought to know that there is no mathematician who is able to
solve all the mathematical questions which could be proposed
even by those having only slight attainments along this line.