
Robert Langlands: The Greatest Mathematician You’ve Never Heard Of? - ColinWright
https://thewalrus.ca/the-greatest-mathematician-youve-never-heard-of/
======
nilkn
If you haven't heard of Langlands but have heard of Andrew Wiles and his proof
of Fermat's Last Theorem, you may be interested to learn that the two are
somewhat closely related. Wiles actually proved a part of the modularity
theorem, which had been shown by Frey, Serre, and Ribet to imply FLT in the
80s.

The modularity theorem is very much a Langlands-style theorem and could be
seen as a more concrete version of many of the ideas and conjectures that form
the Langlands program. The conjecture now known as the modularity theorem was
formulated as early as the 50s and 60s by Taniyama and Shimura, thus predating
the Langlands program, and it was taken seriously once Weil gave conceptual
evidence for it (but did not come close to a proof).

In fact, the modularity theorem is just a very oddly phrased reciprocity law.
General reciprocity laws often look astonishingly nothing like the simple law
of quadratic reciprocity, or they require some clever squinting to see the
relationship. Modularity gives you for any rational elliptic curve E a modular
form which is a simultaneous eigenvector for the Hecke operators (one for each
prime number p) and whose eigenvalues give the solution counts of the elliptic
curve equation modulo p for various primes p. These eigenvalues are also the
coefficients in the Fourier expansion of the modular form.

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martinbalsam
Oh, Robert Langlands!

I worked on a short film about him, for the Abel Prize ceremony, last March.

[http://www.abelprize.no/artikkel/vis.html?tid=73176](http://www.abelprize.no/artikkel/vis.html?tid=73176)

~~~
wenc
Nice short film. Langlands was a theory builder as opposed to someone like
Erdos who was more interested in solving problems. Theory builders are often
admired, but because the endeavor is so broad, very few of them emerge and
even fewer are actually successful.

I like the part where he said he began to write before he understood
everything, and in order to write he had to discover many things, and even had
to discover them after he started to write.

It underscores the crucial role of writing in discovery. Most writers will
tell you they are exploring the space during the writing process. Writing
isn't a process of committing what you already know to paper; it's a process
of learning what you don't know and or haven't considered. It often leads you
down paths you would never expect. (this happens to me with my HN comments too
-- I often myself writing a very different comment from the one I set out to
write)

This is why I think a Ph.D. dissertation should be a continuously evolving
collection of notes, and not something you "write-up" in the end after all the
work is ostensibly done.

~~~
Koshkin
> _as opposed_

From _The Rising Sea: Grothendieck on simplicity and generality_ by C.
McLarty:

Grothendieck describes two styles in mathematics. If you think of a theorem to
be proved as a nut to be opened, so as to reach “the nourishing flesh
protected by the shell”, then the hammer and chisel principle is: “put the
cutting edge of the chisel against the shell and strike hard. If needed, begin
again at many different points until the shell cracks—and you are satisfied”.
He goes on to say: "I can illustrate the second approach with the same image
of a nut to be opened. The first analogy that came to my mind is of immersing
the nut in some softening liquid, and why not simply water? From time to time
you rub so the liquid penetrates better, and otherwise you let time pass. The
shell becomes more flexible through weeks and months—when the time is ripe,
hand pressure is enough, the shell opens like a perfectly ripened avocado!"

~~~
JadeNB
Incidentally, I have heard Serre's work described as the exemplar of the
hammer-and-chisel approach. (McLarty goes on to say that Bourbaki's work fits
in the rising-sea approach, which is surprising to me.)

------
maliker
More like greatest mathematician whose work I’ve never understood. Sadly. At
least I can reduce Grothendieck to algebraic topology or Wiles to number
theory plus that one old problem. Terry Tao to analysis. But Langlands?
Interconnectivity of all sub-fields? I’ve got nothing.

~~~
nicklaf
I highly recommend reading Edward Frenkel's memoir, _Love and Math_ , which is
more or less an up close and personal popular account of the author's
involvement with the Langlands Program:

 _Perhaps the most remarkable part of the book though is the way it makes a
serious attempt to tackle the problem of explaining one of the deepest sets of
ideas in mathematics, those which go under the name of the “Langlands
program”. These ideas have fascinated me for years, and much of what I have
learned about them has come from reading some of Frenkel’s great expository
articles on the subject. To anyone who wants to learn more about this subject,
the best advice for how to proceed is to read the overview in “Love and Math”
(which you likely won’t fully understand, but which will give you a general
picture and glimpses of what is really going on), and then try reading some of
his more technical surveys [...]_

[http://www.math.columbia.edu/~woit/wordpress/?p=6266](http://www.math.columbia.edu/~woit/wordpress/?p=6266)

~~~
maliker
Thanks! I'll take a look.

------
BucketSort
He has a lecture series I've posted about a few times -
[https://video.ias.edu/The-Practice-of-Mathematics](https://video.ias.edu/The-
Practice-of-Mathematics)

------
impendia
Working mathematician here --

1\. Langlands is indeed a great mathematician, whose work has been enormously
influential.

2\. Most of us aren't all that eccentric. He wrote his paper in _Russian_ , a
language which he (presumably) does not natively speak, apparently just for
the heck of it? That's just weird.

Most of the mathematicians I know, including the most influential ones, are
relatively normal people. And they want as many people to read their work as
possible, and don't throw up artificial roadblocks. (Most working
mathematicians cannot read or write Russian.)

3\. There is not that big of a conflict between pure and applied
mathematicians. (Except when they're competing for money, or trying to decide
whom to hire in their departments.)

The most common attitude among pure mathematicians is: we work on mathematical
questions for their own sake, and don't think too much about applications to
the "real world" \-- but we are happy if it is brought to our attention that
such applications exist.

~~~
huhtenberg
Presumably that's the paper in Russian -
[https://publications.ias.edu/sites/default/files/iztvestiya_...](https://publications.ias.edu/sites/default/files/iztvestiya_3.pdf)

It's understandable, but with lots of grammatical, spelling and stylistic
mistakes. Basically it reads like something Google Translate would produce.

~~~
schoen
He has a discussion at the very end (on the last two pages) about his decision
to write in Russian, in which he acknowledges that he may not have done very
well. Google Translate's version of the final paragraph:

> This article is a consequence of two pushes, first of all, an attempt to
> understand the nature of the geometric theory, to form a clear idea about
> the difference between it and the arithmetic theory and their similarity.
> Here I think I was successful, although I do not argue a little. Secondly, I
> wanted to significantly improve my knowledge of Russian. Here I had only
> limited success. For me, Russian is on a completely different level than the
> two foreign languages ​​with which I am familiar, French and German. As I
> noted above, Russian is much more difficult than I appreciated, even more
> than Turkish, another language in which I have a limited but hard-to-work
> ability. Therefore, my efforts and the efforts of friends and acquaintances
> who encouraged me as I wrote this article had limited success. I am still
> pleased that, despite my age, I do not regret either the time or the effort
> that I have given her.

------
vanderZwan
> _Most mathematicians also agree that the Langlands Program could help find a
> proof for the Riemann Hypothesis, probably the most famous unsolved
> mathematical problem (about the distribution of prime numbers). These
> problems are just as abstract as Langlands’s own work, however, which means
> his research program as it was originally conceived has little relevance to
> everyday life._

I dunno, figuring out the Riemann Hypothesis could have some far reaching
consequences for our understanding of prime numbers, and therefore
cryptography, no?

~~~
zornthewise
No, for any practical applications, we might as well work assume it is true,
the same way we assume quantum physics or relativity are true when building
stuff.

~~~
c3534l
And if we actually prove it's not true?

------
Koshkin
E. Frenkel who was also mentioned in the article (as being in a kind of
opposition to Langlands), is an interesting figure in his own right. His own
account on his career in mathematics is fascinating.

~~~
gnulinux
I took linear algebra from Professor Frenkel. He was indeed one of the most
eccentric professors I had. He made a film called Rites of Math and Love whose
trailer was very popular (as a laughing material) in our class.

------
dang
HN has heard of him:
[https://hn.algolia.com/?query=Langlands%20points%3E3&sort=by...](https://hn.algolia.com/?query=Langlands%20points%3E3&sort=byDate&dateRange=all&type=story&storyText=false&prefix=false&page=0)

------
diegoperini
I've heard of him and I'm just a regular everyday normal guy who codes for a
living.

~~~
coldtea
You'd be surprised how "regular everyday guys" haven't heard of him.

In fact I'd be surprised if most US citizens can even name the vice president
of the US, even with all the hoopla around Trump's presidency...

~~~
h91wka
Conversation topic transition diagram in the past few years:

Politics -> Trump

History -> Trump

Computing -> Trump

...

Mathematics -> Trump

Trump -> Trump

* -> Trump

That gets old pretty soon.

~~~
madez
Is this how Godwin's law ends?

------
oluckyman
“Langlands’s”! Now that’s eccentric.

------
garblegarble
It's Robert Langlands[1], for anybody who doesn't want to give in to the
clickbait title

1:
[https://en.wikipedia.org/wiki/Robert_Langlands](https://en.wikipedia.org/wiki/Robert_Langlands)

~~~
coldtea
We should stop abusing the term clickbait for everything and anything.

Journalists (and editors) used juicy titles since centuries, as part of the
art of writing a piece, even when the piece was buried well inside a newspaper
or magazine that you would have already bought to see it anyway...

"This is an article about Robert_Langlands the mathematician" doesn't strike
as nice as a title.

This is a typical journalistic title, and not at all the same as the modern
notion of clickbait (not to mention the article is a legit article, and not
some clickbait listicle or similar BS).

~~~
garblegarble
>This is a typical journalistic title, and not at all the same as the modern
notion of clickbait

I can see where you're coming from (since the article does contain interesting
details and isn't just restating the headline), but I think this title sits
closer to modern clickbait, in the spectrum that runs from dry description to
full-on clickbait.

I will admit, that this style of title has always infuriated me in particular:
it feels like the editor is infantilising their audience by imagining the
public only know the things that journalists decide to write.

Also I'd personally expect a journalistic title to at least mention the
subject. Even something as simple as "Robert Langlands: the mathematician
you've never heard of" would be a big improvement

------
avip
There should be a submission guideline that disallows such useless titling.

~~~
Rainymood
You can downvote and flag the post, but the title of the submission is the
same as the title of the article, so I see no problem. Unless of course the
article is pure clickbait.

~~~
avip
I don't think it worth flagging, maybe some HN readers are interested in
Langland's work? Just retitle it, prefix [note for clickbait-aversed: it's
Langland]

~~~
OJFord
I wouldn't do that, I'd just prefix `Langland: `, so the title remains as in
the article, but a bit like a subtitle.

(I Would Also Remove Clickbait Case But Maybe That's Just Me!)

~~~
avip
Well, The work of Saints is done through others. It's been fixed by forces
higher than us.

------
imron
But did he win the Putman?

~~~
ColinWright
It seems to me that doing well in competitions is a separate question from
going on to do amazing research. There are plenty of people who did
phenomenally well in competitions and then went on to be successful being
mathematicians in other fields, working at _Big Co,_ or starting up their own
company, but most of the really, really top mathematicians that I know didn't
go in for competitions.

There are exceptions, but it's almost like being a top research mathematician
is independent (in the technical sense) of doing well in competitions.

~~~
gjm11
I'm pretty sure the comment you're replying to wasn't so much a serious
question as a reference to this little incident on HN:
[https://news.ycombinator.com/item?id=35079](https://news.ycombinator.com/item?id=35079)

~~~
ColinWright
Indeed, but I like to play with a straight bat, and I think the point was
worth making regardless.

