Timeline for What is the significance of non-commutative geometry in mathematics?
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14 events
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| Dec 18, 2021 at 23:49 | comment | added | Mozibur Ullah | @Yemon Choi: You can also see that in my post I quote an AMS reviewer who looking at Connes programme, calls it a "what a wild, wild ride!" Now that's what I call breathless excitement and from a professional research mathematician who isn't afraid to express his emotions in a publically available journal and not just down in the pub with his mates. So if him, then why not the poster? | |
| Dec 18, 2021 at 17:25 | comment | added | Mozibur Ullah | @Yemon Choi: Like I already said, the post was by someone who admitted quite freely that he was not a professional mathematician or physicist. I daresay he was excited because he had understood something which hadn't before - whichbis that the standard model can be written in an elegant manner unlike the warts and all description in Veltman's Diagramaticca which had over a hundred terms and which Connes said took him around four hours to typeset properly. | |
| Dec 18, 2021 at 16:47 | comment | added | Yemon Choi | The original post asked particular questions, presumably hoping for informed answers. MO is not a general discussion board, and I don't think this particular answer adds anything, especially given the other detailed older answers | |
| Dec 18, 2021 at 16:45 | comment | added | Yemon Choi | @MoziburUllah MO, and dare I say i mathematics, is not about generating breathless excitement but about increasing understanding. MO is a site for those of us in the business of mathematical research; and my local pub is a site (COVID permitting) for breathless discussion with my friends. | |
| Dec 18, 2021 at 5:48 | comment | added | Mozibur Ullah | @Yemon Choi: He also says, "he explains all this starting from Heisenberg's matrix mechanics". So the poster is acknowledging prior work on non-commutativity (or at least matrix mechanics - the poster might not appreciate that matices are inherently non-commutative) and also prior work on QM. I think he understands that QM was already around before Connes got to work on it. And his breathless tone only betrays excitement. | |
| Dec 18, 2021 at 5:43 | comment | added | Mozibur Ullah | @Yemon Choi: And nor is his tone vastly different to much of popular writing on QM which even after a century has passed is still trying to astonish us with just how bizarre, anti-intuitive and strange the quantum world is. | |
| Dec 18, 2021 at 5:40 | comment | added | Mozibur Ullah | @Yemon Choi: Given that the poster has said that he isn't a professional mathematician or physicist, I don't quite see the point of your criticisms. That as a non-mathematician and physicist he has heard of NCG to me is already a thing of wonder. | |
| Dec 18, 2021 at 4:02 | comment | added | Yemon Choi | Wonderful as Connes's NCG book is, I don't think it ever claimed to supersede or render obsolete all the work done before it | |
| Dec 18, 2021 at 4:00 | comment | added | Yemon Choi | "Although many say Heisenberg's and Schrodinger's pictures are the same, he introduces the basic notion of non-commutativity with this matrix mechanics and uncertainty principle" -- once again, QM existed before Connes. | |
| Dec 18, 2021 at 4:00 | comment | added | Yemon Choi | "He has reproduced the Standard Model of physics from purely mathematical work which is worthy of history books." Even if one believes one can get physics purely from mathematics, the breathless tone of this praise gives the impression that no one else has worked on the mathematics of the Standard Model | |
| Dec 17, 2021 at 8:58 | history | edited | Glorfindel | CC BY-SA 4.0 |
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| Dec 17, 2021 at 8:40 | review | Late answers | |||
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| S Dec 17, 2021 at 8:23 | review | First answers | |||
| Dec 17, 2021 at 8:59 | |||||
| S Dec 17, 2021 at 8:23 | history | answered | G P S | CC BY-SA 4.0 |