At the age of 12 I experienced a second wonder of a totally different nature:
in a little book dealing with Euclidean plane geometry, which came into my
hands at the beginning of a schoolyear.  
Here were assertions, as for
example the intersection of the three altitudes of a triangle in one point,
which --- though by no means evident --- could nevertheless be proved with
such certainty that any doubt appeared to be out of the question.  This lucidity and certainty made an indescribable impression
upon me.  That the axiom had to be accepted unproved did 
not disturb me.  In any case it was
quite sufficient for me if I could peg proofs upon propositions
the validity of which did not seem to me to be
dubious.  
For example I remember that an uncle 
told me the Pythagorean theorem before the 
holy geometry booklet had come into my hands.  
After much effort I succeeded
in ``proving'' this theorem on the 
basis of the similarity of triangles; in doing so it seemed to me
``evident'' that the relations 
of the sides of the right-angled triangles
would have to be determined by
one of the acute
angles.  Only something which did not in
similar fashion seem to be ``evident'' 
appeared to me to be in need of any proof at all.

... for anyone who experiences it for the first time, it is marvellous
enough that man is capable at all to reach such a degree
of certainty and purity in pure thinking as the
Greeks showed us for the first time to be
possible in geometry.


Albert Einstein:
Philosopher-Scientist

New York, Tudor Publishing Company, 1949 (first edition)
and 1951 (second)

edited by Paul Arthur Schilpp
translated by Paul Arthur Schilpp


pp. 9--11