Timeline for What does Mellin inversion "really mean"?
Current License: CC BY-SA 3.0
15 events
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| Apr 24, 2018 at 20:04 | history | edited | Qfwfq | CC BY-SA 3.0 |
(Latin) grammar
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| Nov 14, 2011 at 14:33 | comment | added | paul garrett | @KConrad: About elementary number theory... of course, it can be a very nice entry point into mathematics other than calculus. But I have witnessed many instances in which deliberate suppression of the notions of group and ring made a mess. Discussing "congruences" in a "null context" is gruesome, I think. Also distressing to me are "elementary" arguments for quadratic reciprocity. In general, making an argument (much) more complicated while making it seemingly "elementary" seems to me to dis-serve everyone. (I'll save my rant about contrived "exercises" for another time...) | |
| Nov 14, 2011 at 14:25 | comment | added | paul garrett | @daniel litt: I am not opposed to rigor itself, but to (what seems to me) a disproportionate interest in prohibition, rather than facilitation. A caricature of this is a scenario in which one proves that there is no Dirac delta "function", rather than the more useful building-up of a situation in which it is perfectly legitimate. Related to this (example and notion) is/are provocative examples (e.g., the first volume of Gelfand-et-alia on Generalized Functions, which I accidentally encountered before having any general understanding of distributions) compelling work to legitimize it. | |
| Nov 14, 2011 at 2:31 | comment | added | KConrad | Paul: What do you mean about elementary number theory being made senselessly difficult? | |
| Nov 13, 2011 at 23:18 | comment | added | Daniel Litt | (cont.) think there's no question that Pontrjagin duality truly clears up a lot of what is mysterious about Fourier analysis. | |
| Nov 13, 2011 at 23:18 | comment | added | Daniel Litt | Yeesh. Paul, I agree with you that mathematics would be better off if the poetic and intuitive aspects of our work was not excised from our writings. But the claim that an emphasis on rigor is if I may paraphrase you, the enemy of understanding, is I think wrong on its face. Rigor is really the act of undressing our intuitions; perhaps without it, one can get a feeling for a subject, but it is the detailed analysis of those feelings that transmutes them into true understanding. To give a topical example, can imagine a serious investigation of Pontrjagin duality without rigor? And I... | |
| Nov 13, 2011 at 20:58 | comment | added | Suvrit | But on the other hand, I found the flourish enjoyable to read; indeed, the imprecise and imperfect, but iconoclastic is as worthy of attention as its counterparts. best regards-- | |
| Nov 4, 2011 at 23:12 | history | edited | paul garrett | CC BY-SA 3.0 |
added 3877 characters in body
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| Nov 4, 2011 at 3:32 | comment | added | Yemon Choi | @paul garrett: I would be interested to read a write-up of your views on putting the "Fourier" back in "Fourier analysis"; but I don't think the cramped comment boxes of MathOverflow are an optimal place :) Certainly these boxes aren't a good place for discussion. | |
| Nov 4, 2011 at 2:37 | comment | added | Yemon Choi | Is this called "analysts' pedantry strikes me as misguided", by any chance? | |
| Nov 4, 2011 at 1:45 | comment | added | Mariano Suárez-Álvarez | ...I do have problems with obscurity. | |
| Nov 4, 2011 at 1:45 | comment | added | Mariano Suárez-Álvarez | I can't even tell what most of your answer and essentially all of your comment have to do with the question, really. «They only relieve us of some of the burden of misguided fussiness of some self-appointed guardians of a misunderstanding of the Cauchy-Weierstrass tradition.» is a circumlocution for an demeaning comment at who/what, exactly? I have absolutely no problem with opinions or tastes —despite my school-math mind-set and my characteristic conformity, which you very perspicaciously managed to put to the fore, even I have been known to have a couple of both— but... | |
| Nov 4, 2011 at 1:23 | comment | added | paul garrett | @Mariano S-A... Hahaha! Your "criticism" does gratify me, of course, ... tho' with a small worry in the back of my mind. :) As you/one may imagine, I was sincere. At the same time, yes, the school-math mind-set does prohibit having opinions/tastes. My real worry is that beginners accidentally alienate potential employers by being "too honest". That is, it is often the case that conformity is the implicitly-valued trait, despite other things being the advertised desiderata. I am glad (!?) I did not understand the state of things when I was younger... it would have been ... impossible. (Thx) | |
| Nov 4, 2011 at 1:04 | comment | added | Mariano Suárez-Álvarez | It is probably just me but... your answer strikes me a slightly too poetical. | |
| Nov 4, 2011 at 0:40 | history | answered | paul garrett | CC BY-SA 3.0 |