[FOM] 31st Novembertagung 2020

Timothy Y. Chow tchow at math.princeton.edu
Thu Apr 23 18:49:23 EDT 2020

On Thu, 23 Apr 2020, Joe Shipman wrote:
> I have been trying to ask a specific question here, and I keep getting 
> off-point answers. My question is how the axiomatic method is “harmful” 
> to MATHEMATICS. In what ways have mathematicians been harmed, not by 
> having the axiomatic method available as a tool which they may or may 
> not choose to use, but by being either hampered in their regular work by 
> an insistence upon axiomatics, or denied insight or blocked from 
> progress due to a subject having been axiomatised in an unfortunate way?

I'm not sure what you would count as an example, so let me ask whether the 
following sort of thing counts.  It was physicists, rather than 
mathematicians, who first stumbled across mirror symmetry.  As Brian 
Greene tells the story, Shing-Tung Yau at first couldn't believe that such 
a thing could be possible.

Could one argue that mathematicians' reluctance to trust physicists' 
"non-axiomatic approach" hampered them from making this major discovery?

Here's a different kind of possible example.  Bourbaki could perhaps be 
considered an exemplar of "the axiomatic method."  Bourbaki has been 
criticized (rightly or wrongly) for certain detrimental influences on 
mathematical pedagogy and mathematical culture.



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