[FOM] Peano (1912) on generalized functions?

[Richard Zach]

Hi,

Have you asked some Peano experts?  Eg Hubert Kennedy, who wrote a 
biography of him, http://hubertkennedy.angelfire.com/
any of the authors in this book:
http://books.google.ca/books?id=ulUM2GagwacC
eg Ivor Grattan-Guinness?

Also, another option is that Schwartz was mistaken about the year.

Best
Richard

On 2014-11-26 02:51 PM, Michael Barany wrote:
> Vladik,
>
> Naturally, the 1912 article you mention was the first place I looked.
> I am certainly not an infallible speed-reader of Italian, so it is
> possible I missed the phrase in question, but I did not see anything
> looking like the quote in Schwartz's autobiography in that article or
> in the handful on related themes Peano published over the few years in
> either direction of 1912. The 1912 article does treat many themes one
> would retrospectively associate with Schwartz's quote.
>
> Since a few have asked about this off-list, I can spell out what I
> currently suspect are the most likely explanations for the quote:
> 1) Schwartz was better at reading Italian than I am (true, as far as I
> know) and the quote is hidden in a usage I didn't pick up (less
> likely, I hope).
> 2) The quote is contained in some correspondence from around the time
> of that 1912 article, possibly related to the article itself.
> 3) Peano said or wrote something like that quote elsewhere and because
> of the thematic relevance to the 1912 article Schwartz attributed it
> to that.
> 4) The quote is from someone else, and Schwartz mis-remembered it as
> coming from Peano.
> 5) The quote is the product of a rumor mill, without an identifiable
> origin but leaving a strong enough impression that Schwartz could
> assume his rumor-inflected recollection was accurate without checking
> it up for his manuscript.
>
> As part of my broader project, which has required me to fact-check a
> fair number of claims from Schwartz's autobiography, I've encountered
> situations resembling each of those 5 (with #1 here being a case of a
> suspicious memory of an obscure document turning out to have been
> accurate).
>
> At the start my best guess was #2 or #3, which are both cases where I
> think an FOM query would have had a high probability of success (as
> with #1). Since it doesn't seem like those on the list recognize the
> quote however, that points me more toward #4 and #5.
>
> Thanks to everyone for your help on this, and I'll try not to clog
> your inboxes further on this bit of philosophy-of-math-themed
> philology.
>
> Sincerely,
>
> Michael
> Princeton University
> Program in History of Science
> http://mbarany.com
>
>> Date: Mon, 24 Nov 2014 23:16:05 +0000
>> From: "Kreinovich, Vladik" <vladik at utep.edu>
>> To: Foundations of Mathematics <fom at cs.nyu.edu>
>> Subject: Re: [FOM] Peano (1912) on generalized functions?
>> Message-ID:
>>          <49A1861CB3A6E84A95F43B695D2B5C381A2A796D at ITDSRVMAIL011.utep.edu>
>> Content-Type: text/plain; charset=tf-8"
>>
>> Most probably, it is from Peano, G. 1912 "Derivata e differenziale," Atti Accad. sci. Torino 48: 47?69 since this is a paper he wrote in 1912 about difficulties of diffentiation
>>
>> From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf Of Michael Barany
>> Sent: Monday, November 24, 2014 8:12 AM
>> To: Foundations of Mathematics
>> Subject: [FOM] Peano (1912) on generalized functions?
>>
>> Dear FOMers,
>> In Laurent Schwartz's autobiography, he writes the following:
>> The mathematician Peano wrote in 1912 on the difficulties of differentiation: "I am sure that something must be found. There must exist a notion of generalized functions which are to functions what the real numbers are to the rationals."
>> I haven't been able to find the source of this quote in articles circa 1912 in Peano's collected works, and Schwartz does occasionally take liberties with these sorts of attributions, but I was hoping someone on this list might recognize the quote or have a quick way of knowing where it's from, if it is indeed genuine.
>> Many thanks,
>>
>> Michael
>> Princeton University
>> Program in History of Science
>> http://mbarany.com

-- 
Richard Zach ...... http://www.ucalgary.ca/rzach/
Professor,             Department  of  Philosophy
University of Calgary, Calgary AB T2N 1N4, Canada