Talk:Langlands program

message: I'm not expert, but should the article say proof[en] [somewhere]?
Note: Langlands conjectures now redirect to Langlands program, while the former term is still uses (as sometime in math even when proven).
I'm reading "Love and math"-book (almost finished), and while I do not understand all of it (but do understand implications for string theory, and that the math might be sound just not as physics..(?) while not what the book says, on the contrary).
Googling now (as I do not have the book with me I find "Langlands correspondence implies" but also "proof", that I do not understand..:
"To summarize and complete, it is important to remember that in the case of number fields the correspondence between Galois representations and certain automorphic representations (the ones which are algebraic at infinity in the case of number fields) is only a part of the Langlands program, essentially because it concerns just certain automorphic representations, and Langlands functoriality is about all of them.
[..]
We can also do this for other groups (unitary, orthogonal, symplectic) but that gives no new Galois representations so I don't dwell on it (though in the proof, we need to do the case of these groups before going to GLn)." and , 
Hopefully, my recent edits (not in this page or it's talk) are correct, but if this is only a conjecture (or correspondence?) it might be premature. I would really like to know if something has been proven (I recall the book said that), and the implications (for at least physics – there might be none – only in math).
[Note: I also just recently finished Lee Smolin's Time Reborn (much more understandable, without being "proofs") that seems to be the way forward for physics and possibly "contradicting" (might be compatible with?) string theory - at least he's not a "proponent of it or multiverse interpretation of quantum mechanics. comp.arch (talk) 18:32, 18 August 2015 (UTC)
thread_title:  Proof vs. conjecture - "Love and math" book/physics 

message: Would it be possible to add an example to the very start of this entry? TrolleF (talk) 06:46, 27 March 2018 (UTC)
thread_title:  Example - for the non-nerd to understand?! 

message: Added a brief summary to some of the implications of proving the central langlands conjectures for specific cases. It appears to be essential to make clear the widespread potential and meaning this project has on mathematics and science, as it is a field seemingly unknown outside of professionals in its specialization. Especially so, since it is a somewhat unique framework of its kind, having connections to such seemingly distant subjects as number theory, and algebraic geometry (with further influences in many others; including algebraic topology and arithmetic dynamics). Providing a fairly unified construction for solutions of vast analytical power in automorphic forms. Please discuss and add citations as much as possible. The laglands program must be better understood; therefore known.12:38, 16 July 2021 (UTC)
replies: text: Added a simplified description of the program for specialists and possibly diligent lay readers. This is an imperfect reduction of the langlands conjectures to more well defined objects. If one can improve upon it or add citations please do, as such a lead description is indispensable for newcommers; both professional and not.12:18, 18 July 2021 (UTC)
thread_title:  Implications for nonspecialists and lay readers