[FOM] translations of quotes from Karlis Podnieks' recentposting

[Martin Davis]

Rough and ready translations from the moderator:

"Ce qu'il faut admirer, c'est la puissance de l'analyse mathematique qui
arrive ainsi, dans tant de cas, a reduire une infinite de verifications a un
raisonnement unique. Qui peut s'etonner qu'elle n'y soit pas parvenue dans
tous les cas? Non seulement cela n'a rien d'etonnant, mais il est a priory
assez probable qu'il existe certains enonces, qui resument ainsi en une
formule unique une infinite de cas particuliers, et pour lesquels il est
impossible de jamais reduire toutes les verifications necessaires a un
nombre fini d'operations..."

What it is necessary to admire is the power of mathematical analysis which 
thus achieves a reduction of an infinity of verifications in a single piece 
of reasoning. What is it that is astonishing in such situations? Not only 
that which is in itself not surprising [??], but also that a priori just as 
possible that there exist propositions which consist of an infinite number 
of special cases and for which it is impossible to ever reduce all of the 
necessary verifications to a finite number of operations.

"... il est possible que le theoreme de Fermat soit indemontrable, mais on
ne demontrera jamais qu'il est indemontrable. Au contraire, il n'est pas
absurde d'imaginer qu'on demontre qu'on ne soura jamais si la constante
d'Euler est algebrique ou transcendente."

... it is possible that Fermat's last theorem should be unprovable but that 
one will never prove that it is unprovable. On the contrary, it isn't 
absurd to imagine that on could prove that one will never know whether 
Euler's constant is algebraic or transcendental.

[For FOMers who may not know, Euler's constant is the limit of the sequence
1 + 1/2 + 1/3 + ... + 1/n - log n
Its value (if I remember correctly) is about .577 and the question raised 
remains unanswered.]

-Martin