[HN Gopher] The biggest project in modern mathematics [video]
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The biggest project in modern mathematics [video]
Author : peter_d_sherman
Score : 90 points
Date : 2022-06-12 04:06 UTC (1 days ago)
(HTM) web link (www.youtube.com)
(TXT) w3m dump (www.youtube.com)
| nestorD wrote:
| Interesting, to me the biggest project in contemporary[1]
| mathematics is the work done on theorem provers. The goal being
| not to be able to prove new things automatically, but to check
| all existing proofs automatically and make it possible for
| mathematicians to do their work using those tools.
|
| We are still far from those goals (it is a big project for a
| reason) but the work of professional mathematicians could look
| very different in a hundred years if those efforts succeed.
|
| [1]: And the distinction between contemporary and modern might be
| relavant.
| yamrzou wrote:
| That was a wonderful video. Thanks for posting.
| s-xyz wrote:
| Maybe I am the only one, but I do miss sometimes Bachelor's level
| (probably High school level in some countries) math. Have not
| applied it anywhere since, but there was something about those
| classes and exercises that were rewarding. This video brought
| back old memories and feelings.
| pmoriarty wrote:
| As a non-mathematician, the last truly big mathematical project
| that caught my imagination was Hilbert's attempt to found all of
| mathematics on a firm foundation of logic.
|
| That attempt famously and spectacularly failed with Godel's
| incompleteness theorems.
|
| Since then it seems that mathematicians have lost interest in
| foundations and are content to search for interesting results,
| structures, and systems, even if they don't have a solid
| foundation.
|
| More recently I've heard some proposals to revisit the
| foundational project but with higher-order logics proving the
| consistency and completness of lower-order ones, which sounds
| interesting, but I'm not sure how much progress has been made,
| and to a non-mathematician/non-logician even that attempt sounds
| a bit like a house of cards.
|
| Does anyone here know about this and if there are even any
| mathematicians around these days who are still interested in it?
| gnulinux wrote:
| > Since then it seems that mathematicians have lost interest in
| foundations
|
| This is very much not the case. What's closer to truth is that
| the discussion moved on from a framework laymen can seemingly
| understand conclusions, to one where conclusions (or their
| implications on mathematics proper) are a lot harder to explain
| to laymen. Foundational work is still a thing, but I don't
| think it affects the nature of mathematics in a way laymen can
| conceptualize.
|
| Take Godel's incompleteness. People say it's something laymen
| can understand, and people attempt explaining it to masses
| every day in youtube, reddit etc. But if you truly get into the
| formal conclusion (i.e. with Rosser's trick, the conclusion is:
| "a theory cannot be an extension of Q, complete and consistent
| all 3 at the same time") you'll see that it's already pretty
| far away from what laymen thought they understood. And modern
| foundational work exponentially drifted away from this too.
|
| I'm not a mathematician so everything in this comment should be
| taken with a grain of salt.
| superb-owl wrote:
| I've never had someone break down Wiles' proof of Fermat's last
| theorem so succinctly. I can't speak to its accuracy but I found
| it super helpful.
| Koshkin wrote:
| Agree, a wonderful explanation. The Langlands Program, on the
| other hand, was not explained in any detail at all (except
| mentioning the word "functoriality").
| throwaway81523 wrote:
| I hate blind youtube links, and this one even takes a while into
| the video to say what it is about. Spoiler: the Langlands
| Program. Video has some nice animations but not much about the
| math. The author has a writeup here:
|
| https://www.quantamagazine.org/what-is-the-langlands-program...
|
| See also: https://en.wikipedia.org/wiki/Langlands_program
| leoc wrote:
| It does say LANGLANDS on the thumbnail, as well as talk about
| it in the description.
| Simon_O_Rourke wrote:
| Thank you for the summary!
| javierga wrote:
| I guess it is fitting to mention the famous Wandsworth Constant
| (first 30% of the video can be skipped).
|
| In seriousness, having had some exposure to the Langlands
| program (through the wonderful Love and Math by Frenkel), I was
| counting the minutes to hear about it.
|
| I found the video to have a great layman explanation of what it
| is about.
| Koshkin wrote:
| One of the well-known category theorists has said [0],
|
| > _I've never succeeded in understanding the slightest thing
| about it._
|
| [0]
| https://golem.ph.utexas.edu/category/2010/08/what_is_the_lan...
| mjreacher wrote:
| I'm glad Tom was so open about his lack of knowledge here, so
| often it is easy to assume any professional mathematician
| should know all this things and it all comes easy to them.
| However this obviously isn't the case and I doubt things will
| be any easier in the future as mathematics becomes more
| specialized.
| xiphias2 wrote:
| For me it wasn't a spoiler, and also the video contained more
| math that I understand than the Wikipedia link (that just was a
| list of lots of mathematical structures that I don't know
| anything of, and not part of the computer science curriculum,
| so I don't expect other hackers to understand them either).
| [deleted]
| smelbe wrote:
| The graphic designer behind these incredible animations has my
| appreciation and respect. In the representation of such
| intangible concepts, the combination of creativity and deep
| technical expertise blends perfectly. Total command of the arts
| and crafts.
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