[FOM] Gabriel's ruminations

Martin Davis martin at eipye.com
Tue Apr 18 14:40:20 EDT 2006

Gabriel Stolzenberg has favored FOM with his ruminations which frequently 
take a subjective turn. He assures us that he can be in one of two clearly 
distinct states or "mindsets" when thinking mathematically: classical and 
constructive. We who haven't had this experience should just accept 
Gabriel's assurance. We can't know until we experience it ourselves. This 
does remind one of things one is more likely to hear in a Church sermon 
than in a Mathematics colloquium talk - but no matter.

On the other hand he's quite unaccepting of other's subjectivity insisting 
on explicit explanations of just when a number theorist will find a bound 
interesting and even more asking for the "reason" why a particular result 
is of interest. Of course this is not only highly subjective, it varies 
greatly from one mathematician to another, which is as it should be. My 
good friend may be overjoyed to manage to improve an n log n to n (loglog 
n)^3.7 while I wonder why he cares.

In addition to insisting on the validity of his own subjective categories, 
Gabriel feels free to objectivize the subjective remarks of others. Thus he 

"Harvey believes that, at least for bounds and algorithms, increased 
knowledge, no matter what, is desirable."

No matter what? What does this even mean? But in any case, of course Harvey 
believes no such thing.



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