[FOM] Clarity in fom and problem solving

[Zachary J. Purvis]

In his Gibbs lecture, Goedel remarks that clarity in the foundations of
mathematics has not helped much in deciding mathematical problems.  This
would be impossible if mathematics were our creation, because then our
difficulties would be due only to a failure to understand what we have
created; with perfect clarity our mathematical ignorance would disappear.

 

I'm not quite sure what to think about his first statement, that clarity in
foundations has not helped with solving problems.  Are there any examples or
suggests at what Goedel is getting at here?

 

Thanks,

 

Zack Purvis

WSU mathematics

zackpurvis at comcast.net

 

 

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