[FOM] FLT Decisive by Normal Math Standards

[tchow]

Bill Taylor wrote:
> Could you perhaps be more specific about this coming revolution
> especially regarding the nature of the "dam breaking", that is
> going to focus the attention of mathematicians with great force?

Friedman has spoken about this frequently, but let me give my paraphrase 
of his claim, in case that helps clarify.

One dominant attitude today among mathematicians is that it is not 
important to think about foundational issues when doing "core" 
mathematics.  If you stick to questions that are sufficiently concrete, 
then questions of undecidability, or of which axioms are needed to prove 
which theorems, will never arise.

Friedman thinks that after the "dam breaks," questions of which axioms 
are needed to prove which theorems will flood over all of mathematics.  
For example, questions that formerly were regarded to be extremely 
concrete and therefore "safe" will be shown to require large cardinal 
axioms (or at least their 1-consistency) to resolve.  Attention about 
which axioms are needed for which theorems will not be confined to an 
extremely small subset of arcane and exceptional results, but will 
pervade all of mathematics.

Tim