Very enjoyable talk.

13:41 "There's gonna be two, you can see what to do..." I thought he was going for a little rhyme there. That would've been nice. In all seriousness though, great talk, I enjoyed it very much. Amazing channel.

Authorship what does it mean

So... if the two pillars are 'motives' (from Algebraic Geometry) and 'Automorphic Forms'(from Harmonic Analysis) where does the Arithmetic actually enter?

@ludvigm

3 жыл бұрын

One way it enters from the algebraic geometry side is the following: The example Arthur brings up of the motive of an elliptic curve tells you about the number of solutions to an equation like y^2+y=x^3-x^2 modulo primes, using the Grothendieck-Lefschetz trace formula. This bounds the number of honest integer solutions (i.e. the left hand side is equal to the right hand side and not only to the right hand side plus some multiple of a prime), as any integer solution gives you a solution modulo every prime.

@johnhughes1556

3 жыл бұрын

@@ludvigm n mm

Logic is here part of arithmetic? Russell?

I find it odd that the description of the Langlands work is so simplistic and over-arching yet, for may years, mathematics has abandoned notions that are such. A for-instance would be the concept of 'remarkable points'. before the introduction of Algebraic Geometry to describe what is 'interesting' about curves, remarkable points would be anything that was not the most straightforward notion of curvature. hence, points of inflection would be 'remarkable'. but, for Algebraic Geometry, they are differentiable and give no information, and are hence not 'remarkable'. even the idea of spirality, the point wherein a curve must either have a remarkable point (if, when following a curve, the trajectory as a straight line intersects the part of the curve already described) is not interesting because infinite spirals cannot be Algebraic. but the proof of this highlights, to me, anyway, one of the fundamental results of early work on curves, Cramer's Theorem. Certainly for combinatorical questions and possibilities this gives rise to an interesting set of questions which can be asked in either domain analogously. these pertain mainly to convexity which is a question of the straightforward notion of curvature which has been lost to time.

Think he is referring to graphite

The noise at 41:15 gives me a heart attack

@jackozeehakkjuz

10 ай бұрын

ikr it's horrible

Like most mathematicians, James Artur apologizes to mathematicians for having to put the subject's ideas in laymans' terms and then proceeds to cover much of the topic in terms only mathematicians will understand. It's a common disability (or inside joke) among that group.

@leon_noel1687

8 ай бұрын

😂😂😂

@magnuswahlstrom766

8 ай бұрын

I don't think you understand just how technical this talk would have been if he'd allowed himself to use notions he'd expect every mathematician, but not every layperson, to know.

14 15

math is more like 'music/art'. I get it

' motives ' & " motifs " convey his general perceptual ' abstract inuendos ' but definition wise they mean discretely different things....if I were going to describe the visuals of an afterdeath experience and stated there exist no.proper language to adequately describe....the motive/motif dichotomy would best represent the divide WITH the qualification that one understand from maths perspective THAT of the implied " motive "

Was he breathing helium?

What a load of rubbish..two mathematians construct two different ivory towers and try to get from one to to the other without going all the way down and climbing up the other..even a cursory analysis shows that There is an infinite number of possible towers and no one is more relevatory than the other. This was shown by Godel over a century ago

@zeonive1173

2 жыл бұрын

Can you tell me what Gödel's work has to do with this? Sure, some theorems might be undecidable but why would it not be worth it to investigate whether some interesting conjectures are true?

@hygvbug

2 жыл бұрын

Academic hater

@dankurth4232

2 жыл бұрын

@Gringohuevon You mistake Gödel for having shown ( or having intended to show) that mathematics is futile, but he has shown that mathematics essentially is incomplete and not omniscient. That leaves an infinite space of research and challenges for mathematicians to tackle. Langlands program is fascinating as it unveils intrinsic correspondences or dualities of otherwise - or at least traditionally seen as - unrelated mathematical structures

@leon_noel1687

8 ай бұрын

This might be the most disrespectful comment about fundamental science ever written.