Your outdoor location for these interviews, while it may not always be ideal from an audio perspective, is absolutely lovely! I'd like to think the fresh air and bright green helps emphasize mathematics as the art/study of patterns for their beauty rather than their utility. Great stuff as always, I always enjoy seeing your math talks!! Keep up the good work!!
Outdoor audio should be very do-able - the low quality is a function of two varaibles, one being my poor hardware, and the other being my ignorance of cleaning up the audio afterwards. But I should improve upon... eventually...
@@knight3481 Yes! In order to see that the symmetric algebra of a vector space is Koszul dual to the antisymmetric algebra, one makes use of the Koszul complex.
This is an interesting perspective: e.g. on a mathematician preferring pure mathematics as opposed to physics. he has a background in physics, which he chose as, canonically, something thats more ‘interesting’ than pure mathematics. The ‘lower case’ pure mathematics is the definition for this particular bifurcation in global event: the career. He criticizes physics as - in terms of what the profession eventually forms into : as being too much - requiring proof-less belief. That’s him. For me, the nature of a criticism of physics that would result in this career ‘reversal’; reversal: as indeed mathematical concepts are understood before physics concepts. The cause of such a reversal, for me, is not necessarily his. There is in both fields of research a psychological necessity for believing things ‘in submission’ to what are perceived as people: Gauss, .. My exact preference for pure mathematics as opposed to physics is that the true intuitions one is granted in life are small in number: indeed, as one may recover a field of finite characteristic as a result of a more canonically natural one: For me, life has revealed that the feeling of infinitude associated to the possibilities of exploration in life is more seriously something that’s actually finite. In physics, the issue for me is that for certain kinds of basic intuitions: Relativity, for example. Are tortured into the mathematics that are far too arbitrary: in the sense of, what I observe, as weak: on the part of the theory. For the arrogance presented in its historical dominance. The mathematics of Grothendieck , And the topological ‘K-theory’, could be a considered truer study of relativity than any linear algebra in the name of Einstein. As I understand the fullest integrity of this intuition.
Your outdoor location for these interviews, while it may not always be ideal from an audio perspective, is absolutely lovely! I'd like to think the fresh air and bright green helps emphasize mathematics as the art/study of patterns for their beauty rather than their utility. Great stuff as always, I always enjoy seeing your math talks!! Keep up the good work!!
Outdoor audio should be very do-able - the low quality is a function of two varaibles, one being my poor hardware, and the other being my ignorance of cleaning up the audio afterwards. But I should improve upon... eventually...
Is it somehow related to Koszul sequences also.....Beautiful presentation.
@@knight3481 Yes! In order to see that the symmetric algebra of a vector space is Koszul dual to the antisymmetric algebra, one makes use of the Koszul complex.
@@k-theory8604 Yes! Of course. Thanks
This is an interesting perspective: e.g. on a mathematician preferring pure mathematics as opposed to physics.
he has a background in physics, which he chose as, canonically, something thats more ‘interesting’ than pure mathematics. The ‘lower case’ pure mathematics is the definition for this particular bifurcation in global event: the career.
He criticizes physics as - in terms of what the profession eventually forms into : as being too much - requiring proof-less belief.
That’s him.
For me, the nature of a criticism of physics that would result in this career ‘reversal’; reversal: as indeed mathematical concepts are understood before physics concepts.
The cause of such a reversal, for me, is not necessarily his.
There is in both fields of research a psychological necessity for believing things ‘in submission’ to what are perceived as people: Gauss, ..
My exact preference for pure mathematics as opposed to physics is that the true intuitions one is granted in life are small in number: indeed, as one may recover a field of finite characteristic as a result of a more canonically natural one:
For me, life has revealed that the feeling of infinitude associated to the possibilities of exploration in life is more seriously something that’s actually finite.
In physics, the issue for me is that for certain kinds of basic intuitions:
Relativity, for example.
Are tortured into the mathematics that are far too arbitrary: in the sense of, what I observe, as weak: on the part of the theory.
For the arrogance presented in its historical dominance.
The mathematics of Grothendieck ,
And the topological ‘K-theory’, could be a considered truer study of relativity than any linear algebra in the name of Einstein.
As I understand the fullest integrity of this intuition.