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[Xmca-l] Re: grosholz



I just finished the Grosholz article (“Phil of Math & Phil of History”). 

I was thinking about conjectures regarding things that have not been proven) and discoveries of things that have may not even been imagined. Fermat’s theorem was a conjecture until Wylie proved it. I would contrast Wylie’s proof with the year of “pure math” I did at U of Texas at Austin in the program set up by E.T. Moore. I tried very hard to prove that such a thing as a Cantor set existed. I was not able to beat another student in the program to the punch, in fact made a fool of myself in front of a class thinking I DID have a proof when I didn’t. But that failure, and the struggle that went into it, made it possible for me to understand the other guy’s proof. So, on that occasion, he was better at math than me. But by the time the two of us worked on the problem it was neither a conjecture, nor a discovery. Somebody else had done it for the first time. Our job was not trivial, to trace the steps to the proof, but it was very different from what Wylie did. Cantor’s story, I think, ups the ante. The set in question may have been only a conjecture to Cantor at the time. His ideas on transfinite numbers were ridiculed and he was hounded much like Vygotsky by the cogniscenti at the time. In fact the It was a discovery of that set that has become the foundations of fractal mathematics (which I think is worth talking about in this thread). In analogous fashion, Vygotsky’s work was epic in analogous fashion and equally tragic. I sort of see us here today, with our crisis, working with LSV’s conjectures, finding the solution to the problems. I think it’s worth adding these kinds of narratives to the history of math and the history of philosophy, as Grosholz has construed it. And maybe it’s sort of what she was getting at on page 16:
“…[T]his is the logical texture of everyday life, where the unforeseen constantly puts to the test our intellectual and moral resources, and where our ability to rise to the occasion must always remain in question: the insight of tragedy is that anyone can be destroyed by some unfortunate combination of events and a lapse in fortitude or sympathy.
 Clearly my little piece of it amounts to very little. Still... 
Henry



> On Nov 9, 2014, at 5:05 PM, Ed Wall <ewall@umich.edu> wrote:
> 
> Thanks
> 
> Yes, Wiles is a nice example of doing mathematics within a historical dimension.One part of the article bothered me when the author averred that Fermat would need to pick up the centuries between. Interestingly that is not what a student of mathematics who was born today would 'need' to do to enter the conversation. 
> 
> I was listening to a presentation, you might say, on the 'true but unprovable'  (in the sense of Godel) by John Conway and he kept saying "I don't know if this is true, but …"; "I don't have a proof, but …" It was a serious mathematical presentation.
> 
> Ed Wall
> 
> On Nov 9, 2014, at  5:26 PM, Vera John-Steiner wrote:
> 
>> Hi,
>> 
>> I am forwarding an article by a philosopher of mathematics who addresses issues of narrative and logic as well as the role of history
>> 
>> in mathematics. Some of the article requires a familiarity with concepts in the field which are above my head, nevertheless it was a valuable
>> 
>> piece in the context of the current thread. 
>> 
>> Vera
>> 
>> 
>> 
>> From: reuben hersh [mailto:rhersh@gmail.com] 
>> Sent: Friday, November 07, 2014 7:44 AM
>> To: Vera John-Steiner
>> Subject: grosholz
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> <Grosholz_Maths & History.pdf>
> 
>