Although the proof or the disproof of such theorems may not

appear to be of great consequence, yet the interdependence of
mathematical theorems is most marvelous, and the mathematical
investigator is attracted by such difficulties of long
standing
Although the proof or the disproof of such theorems may not
appear to be of great consequence, yet the interdependence of
mathematical theorems is most marvelous, and the mathematical
investigator is attracted by such difficulties of long
standing. These particular difficulties are mentioned here
mainly because they seem to be among the simplest illustrations
of the fact that mathematics is teeming with classic unknowns
as well as with knowns. By classic unknowns we mean here those
things which are not yet known to any one, but which have been
objects of study on the part of mathematicians for some time.
As our elementary mathematical text-books usually confine
themselves to an exposition of what has been fully established,
and hence is known, the average educated man is led to believe
too frequently that modern mathematical investigations relate
entirely to things which lie far beyond his training.


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