About the question asked by Ed,
Perhaps the book "Philosophy of mathematics" writen by Herman Weyl it will
be helpfull. Also Piaget wrote about it.
Sincerely
At 08:59 PM 6/2/99 -0400, you wrote:
>Julio,
>
> I will try to elaborate somewhat although I am only giving my thoughts
>and impressions. I find it interesting that you mention seeing no
>historical content whatsoever. You are quite posssibly correct although I
>must admit having thought about adding a slight postscript to this
>forwarded request which roughly said that I thought perhaps some possible
>essays of the sort being asked for might lie somewhat near the intersection
>of the work done in the history of mathematics and the philosophy of
>mathematics (actually I thought I had added it, but perhaps I left it off
>thinking that it would be interesting to see what responses I received).
> Why did I think that? First in both these areas *serious writing* is
>done, at least in my opinion, on mathematics which, if one is to believe
>Louis Mink (the view of a historian about the writing of history), for a
>"potentially universal audience." Secondly, I have found previously that an
>interesting piece on number with perhaps a historical flavor (although
>perhaps not an appropriate one in this instance), again from my point of
>view, was the Introductio Arithmetica of Nicomachus. And thirdly it seemed
>that if anything was especially well-written on number in the present or in
>the past, members of this group were likely to know. Finally, I admit to
>thinking that some historical perspective on number should be part of the
>basis of this essay.
>
> What was actually requested? After discussing the received messages
>briefly with my colleague, it was clear that suggestions from this group
>together with some other thoughts of mine and suggestions from others still
>were all gratefully received. So my impression is that a historical
>perspective on number will be factored in. Perhaps it would be useful if I
>noted that when this person says well-written she means scholarly, and the
>word educated is also used in its *strong* sense. It, of course, remains to
>be seen how successful she is in getting some capable research
>mathematicans to convey their thoughts about number in a substantial yet
>somewhat symbol free and readable manner. Some models from the past and
>present would seem to be most welcome.
>
>Hopefully this clarifies things somewhat
>
>Ed Wall
>
>
>At 3:13 PM -0300 6/2/99, Julio Gonzalez Cabillon wrote:
>>At 10:09 PM 27/05/1999 -0400, Ed Wall <ewall@umich.edu> wrote:
>>>
>>> I was asked the following question by a colleague:
>>>
>>> ******
>>> Do you know of any very good essays or other treatments of domain of
number
>>> (e.g., the major objects , operations, etc, of the whole, integer,
>>> rational, and real number systems) that would be serious and yet
accessible?
>>> I'd like help in assembling a small number of very good pieces that
>>> would serve as a resource for a group of mathematicians with whom I am
>>> working to write an essay on number. In part, I want them to see some
>>> other people's takes on this domain, and in part, I also want them to see
>>> what examples of serious writing that is accessible to an educated, but
not
>>> mathematically trained, reader might look like.
>>> ******
>>>
>>
>>Dear Ed,
>>
>>Please, excuse my lack of understanding of what is being asked for above.
>>Whereas I see no historical content whatsoever I would much appreciate to
>>grasp what precisely your colleague is looking for. Would you be kind
>>enough as to elaborate a bit on this issue?
>>
>>Many thanks.
>>
>>Regards, JGC
>
>
>
>
>
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