The future mathematician  should be a clever problem
solver; but to be a clever problem-solver is not enough.
In due time, he should solve significant mathematical
problems; and first he should find out for which kind of
problems his native gift is particularly suited.
    For him, the most important part of the work is to
look back at the completed solution. Surveying the
course of his work and the final shape of the solution,
he may find an unending variety of things to observe. He
may mediate upon the difficulty of the problem and
about the decisive idea; he may try to see what hampered
him and what helped him finally.  He may look out for
simple intuitive ideas; Can you see it at a glance? He
may compare and develop various methods; Can you 
derive the result differently?  He may try to clarify his
present problem by comparing it to problems formerly
solved; he may try to invent new problems which he can
solve on the basis of his just completed work.":Can you 
use the result, or the method, for some other problem?
Digesting the problems he solved as completely as he can,
he may acquired well ordered knowledge, ready to use.
    The future mathematician learns, as does everybody
else by imitation and practice.  He should look out for
the right model to imitate.  He should observe a stimulating
 teacher. He should complete with a capable friend.
Then, what may be more important, he should read
not only current textbooks but good authors till he finds
one whose ways he is naturally inclined to imitate. He
should enjoy and seek what seems to him simple or instructive
 or beautiful.  He should solve problems, chose
the problems which are in his line, meditate upon their
solution, and invent new problems.  By these means, and 
by all other means, he should endeavour to make his first
important discovery : he should discover his likes and his
dislikes, his taste, his own line.