[FOM] Peano (1912) on generalized functions?

katzmik at macs.biu.ac.il katzmik at macs.biu.ac.il
Sun Nov 30 11:12:15 EST 2014

If it were anybody other than the purported inventor of distributions, I would
not have said that Schwartz made it up to boost his own image. MK

On Thu, November 27, 2014 20:52, Richard Zach wrote:
> 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
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