> > When we presented Tao with our result, he cheerfully declared that it was, in fact, the discovery of a new identity, and he provided several mathematical proofs, which have now been published online
"There is nothing new under the sun." One cannot be too careful when claiming novelty... 18 November, 2019 at 5:07 am Carlo Beenakker I may have found a 1993 appearance of this formula, https://mathoverflow.net/a/346313/11260 18 November, 2019 at 10:41 am Terence Tao Thanks for this! We are in the process of completely rewriting the paper; at this point it seems more appropriate to present a historical survey of the various places in the literature the identity has appeared (the earliest relevant reference we have currently is a 1934 paper of Loewner, and there are at least 18 other appearances in the literature to our knowledge), and describe the various proofs, generalisations, and applications that we are now aware of. There is also an interesting sociology-of-science aspect to this story which is also worth recording, in particular how it seems that it was not feasible to integrate all the disparate references to this identity in the literature until a popular science article reporting on the identity created enough “common knowledge” to kick off what was effectively a crowdsourced effort to locate all these prior references. On Mon, Nov 18, 2019 at 3:05 PM Donna Y <[email protected]> wrote: > > Theorists discover the 'Rosetta Stone' for neutrino physics > https://phys.org/news/2019-09-theorists-rosetta-stone-neutrino-physics.html <https://phys.org/news/2019-09-theorists-rosetta-stone-neutrino-physics.html > > > > When we presented Tao with our result, he cheerfully declared that it was, in fact, the discovery of a new identity, and he provided several mathematical proofs, which have now been published online < https://arxiv.org/abs/1908.03795>. Tao also discussed the new identity in his math blog < https://terrytao.wordpress.com/2019/08/13/eigenvectors-from-eigenvalues/>. > > https://terrytao.wordpress.com/2019/08/13/eigenvectors-from-eigenvalues/ < https://terrytao.wordpress.com/2019/08/13/eigenvectors-from-eigenvalues/> > > > > we called the eigenvalues "the Rosetta Stone" for neutrino oscillations in our original publication <https://arxiv.org/abs/1907.02534>—once you have them, you know everything you want to know. > > > Donna Y > [email protected] > > > > On Nov 16, 2019, at 7:04 AM, Vijay Lulla <[email protected]> wrote: > > > > I think Richard Hamming's n-Dimensional Space lecture > > https://www.youtube.com/watch?v=uU_Q2a0S0zI might be pertinent. I hope > > some of you will enjoy watching this lecture. > > Cordially, > > Vijay. > > > > On Fri, Nov 15, 2019 at 2:40 PM R.E. Boss <[email protected]> wrote: > > > >> Or here https://arxiv.org/pdf/1908.03795 > >> > >> > >> R.E. Boss > >> > >> > >>> -----Oorspronkelijk bericht----- > >>> Van: Chat <[email protected]> Namens Roger Hui > >>> Verzonden: vrijdag 15 november 2019 17:22 > >>> Aan: [email protected] > >>> Onderwerp: Re: [Jchat] geometric intuition > >>> > >>> The actual theorem and proofs: > >>> https://terrytao.wordpress.com/tag/xining-zhang/ > >>> > >>> > >>> > >>> On Fri, Nov 15, 2019 at 2:13 AM R.E. Boss <[email protected]> wrote: > >>> > >>>> Well, what about this > >>>> https://www.quantamagazine.org/neutrinos-lead-to-unexpected- > >>> discovery- > >>>> in-basic-math-20191113/ > >>>> ? > >>>> > >>>> > >>>> R.E. Boss > >>>> > >>>> > >>>>> -----Oorspronkelijk bericht----- > >>>>> Van: Chat <[email protected]> Namens Raul Miller > >>>>> Verzonden: donderdag 14 november 2019 17:16 > >>>>> Aan: Chat forum <[email protected]> > >>>>> Onderwerp: [Jchat] geometric intuition > >>>>> > >>>>> I stumbled across this today: > >>>>> https://github.com/leopd/geometric-intuition accompanied by an > >>>>> assertion that you can find the eigenvectors for a hermitian matrix > >>>>> from its > >>>> eigenvalues > >>>>> and the eigenvalues of its submatrices. I have not yet worked > >>>>> through > >>>> the > >>>>> details of that, but it sounds plausible and might be of interest to > >>>> some of > >>>>> you, here. > >>>>> > >>>>> But the repository itself covers a lot more ground than that. > >>>>> > >>>>> Anyways, the code is python, but a lot of it is fairly > >>>>> straightforward > >>>> to re- > >>>>> implement, and there's good english descriptions and illustrations, > >>>> also. So > >>>>> this looks like fun. > >>>>> > >>>>> FYI, > >>>>> -- > >>>>> Raul > >>>>> -------------------------------------------------------------------- > >>>>> -- For information about J forums see > >>>>> http://www.jsoftware.com/forums.htm > >>>> ---------------------------------------------------------------------- > >>>> For information about J forums see > >>> http://www.jsoftware.com/forums.htm > >>>> > >>> ---------------------------------------------------------------------- > >>> For information about J forums see http://www.jsoftware.com/forums.htm > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > >> > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
