Alexander Grothendieck is dead. RIP Sweet Prince!

[Anonymous No.6875534]

Alexander Grothendieck passed away today!

http://www.liberation.fr/sciences/2014/11/13/alexandre-grothendieck-ou-la-mort-d-un-genie-qui-voulait-se-faire-oublier_1142614

Greatest mathematician of 20th century is dead :(

[Anonymous No.6875539]

>>6875534
And we were just talking about him.
RIP in RIPIP

[Anonymous No.6875542]

>>6875539
>And we were just talking about him.
Who was? You mean on /sci/? He always comes up on here. Just yesterday I posted about him in thread about vonNeumann and I used the pic above.

And today he died. Fuck!

[Anonymous No.6875545]

>>6875534

[Anonymous No.6875563]

>>6875534
>in lab, computes grothedieck topology on site when coauthor ring
>'grothendieck is die'
>no

Seriously, though. My respects to the man that launched several new fields; and selfishly, I hope this means his later writings can finally be published.

I'll leave a wreath in the shape of a dessin d'enfant on his grave the next time I visit France.

RIP

[Anonymous No.6875671]

>>6875534
might have mattered thirty years ago

[Anonymous No.6875682]

>>6875671
Grothendieck will always matter ! (stars in the eye)

One of his student got the Abel prize not so long ago after all.

[Anonymous No.6875684]

>>6875682
The what?

[Anonymous No.6875742]

>>6875671
Actually, there's an extremely strong argument that people like Lurie and Mochizuki are gaining their fame from finishing what Grothendieck started, and elaborating on his results.

Grothendieck laid out foundations and roadmaps for several large programmes that still aren't close to being resolved.

[Anonymous No.6875842]

>>6875534
you changed the game niqqa RIP

[Anonymous No.6875855]

>>6875534
Sad :( I was sort of waiting for this to happen though. I mean the dude was old and never looked too healthy in photos.

I hope he was happy herding goats in isolation

[Anonymous No.6875866]

RIP in piece, sweet prince ;___;

[Anonymous No.6875959]

>>6875855
Supposedly, the most recent thing he was "working" on was how to define a meter, or something like that. It was seriously /x/ level pseudo-metaphysics.

The thing is though, until the late 1980s, he supposedly worked 16 hours a day on math. That's a good 40 years of his life, spent entirely on mathematics; it's no surprise that he burnt out; anyone would.

[Anonymous No.6875965]

>>6875959
(correction)

By which I mean that I saw a story on the Grothendieck Circle about how the last person that found his living quarters in the Pyrenees was faced with a barrage of questions along the lines of, "But how does one find a universal, non-arbitrary definition of an SI unit? What does a 'meter' **mean**?" or something along those lines.

[Anonymous No.6875967]

NOOOOOOOOOOOOO!!!!!!!!!!!!!!!!!!!!!!!!!

My dream to learn category theory, french and Indian philosophy, then becoming a mendicant traveler and making my way to the Pyrenees to have a conversation with Grothendieck is SHATTERED!

RIP Dude. You were one cool ass motherfucking dude.

Giving lectures on category theory in Hanoi while the US reigned down a bunch of cluster-bombs designed by soulless MIT engineers... sticking it to the man by refusing to touch any kind of military funding... writing weird mystical shit about the spiritual experience of doing mathematics.

Damn.

/sci/, he was really my favorite mathematician. He really, really was.

God bless everybody. War is evil and mathematics should never be used for it. Mathematics is for Pythagoreans, for spiritual, religious devotees of human beauty and Platonic truth- never for war, never for fame, never for prizes.

[Anonymous No.6875969]

>>6875959
>>6875965
I think a meter can't be defined neatly by a nice ratio of fundamental constants like some other ones can. That's probably what he was getting on.

[Anonymous No.6875976]

>>6875959
>it's no surprise he burnt out

True dat. I can only aspire to be smart enough to go that crazy

[Anonymous No.6875992]

>>6875959
>>6875976


Grothendieck didn't just snap like Nietzsche or something.

I don't think he was crazy. He had a rough life growing up, and was always politically conscious (how rare for a mathematician!). I think he just decided that humanity isn't ready for mathematics, and decided to become recluse.

In the west this is seen as a totally crazy gesture bordering on suicide, but it's common in India, and people who just drop everything and go off in search of something more ineffable are revered rather than accused of being crazy.

Maybe this would be the appropriate approach with Grothendieck.

[Anonymous No.6876005]

>>6875534
This is a much better article: http://inference-review.com/article/a-country-known-only-by-name

[Anonymous No.6876026]

>>6875992
You're right, and I was misremembering something that I read. A decent account can be found in the comments here:

https://golem.ph.utexas.edu/category/2006/08/letter_from_grothendieck.html

I don't think he was 'crazy' per se, but from my uninformed opinion (based entirely on internet reading), he was probably yearning for a "pure" life, whatever that means (I guess in his case it was to be free of guilt/'blood money', based on the fact that the French military was partially responsible for funding his work at IHES).

I don't know if it was that he was concerned that humanity "wasn't ready for mathematics" but more that he wanted to truly *understand*, from an objective level --- free of external influences.

It's appropriate that someone who was working at a higher level of mathematics would also escape from mathematics at a higher level.

>>6875969
From the context of the above link, I would assume that it was more of a koan, a zen-like question. Your guess is as good as mine though.

In some part we can probably all empathize with wanting to break free of the confines of our rigid social structures. Maybe that was it.

To quote Blur, "modern life is rubbish", I guess.

[Anonymous No.6876035]

>>6876026
(P.S. any frenchfags here that want to assist with a translation of Recoltes et Semailles?)

[Anonymous No.6876055]

>everyone discusses urban legends
>not a single person talk about his actual mathematical work
Never change /sci/.

[Anonymous No.6876058]

>>6876055

His work isn't exactly accessible, even insofar as mathematics is concerned.

[Anonymous No.6876061]

>>6876055
If you want to discuss higher category theory, K(K)-theory, stacks, the Weil conjectures and their resolutions, sites and topoi, or Grothendieck topologies on sites, then by all means go ahead and I will try as hard as I can to add meaningful responses (no promises, though -- I'm just beginning to learn these things myself).

However, it should be noted that the people who are competent enough to discuss these topics seriously form a very small group, and this thread would be buried while waiting for responses.

[Anonymous No.6876063]

>>6876026
>One story has it that Grothendieck is now convinced that the Devil is working to falsify the speed of light.

lol

[Anonymous No.6876074]

>>6876063
>implying he wasn't speaking figuratively

[Anonymous No.6876080]

>>6875534

RIP In Peace

Any idea what this means for his research?

[Anonymous No.6876092]

>>6876080
While I'm sure those that he sent personal letters to will try to keep his unpublished writings out of the hands of the public for the next year or two (out of respect for his wishes, which were to cease publication), it will mean that many of his works will probably be translated and elaborated and that a few other papers will become available soon. They were already available if you knew who to ask, though.

[Anonymous No.6876106]

>>6875967
i enjoyed reading your post and learned some new vocabulary

[noko No.6876201]

>>6876035
I'm reading the beginning at the moment, cool book. His views on the state of things in education and on people remind me a lot of mines. Also the way he doesn't accept anything for granted and want to find out things on his own. Good students are ranked by their ability to ingurgitate an regurgitate what they are taught, and if you fall outside that scope you're considered a failing student, when you try to come up with your own tools to solve problems in your own way, in a new way. Out of these failing students most get discouraged and get convinced that the field is not for them, and we never hear of them. A few do not give a fuck and keep doing things their own way, and eventually their genius is recognized when their ideas become appreciated by some high placed in the community. Grothendieck didn't get discouraged as a teen and kept doing things his own way because he realized he could come up with things other prestigious mathematicians had came up with in the past. He had confidence in what he was doing, and eventually he got recognized. So many geniuses must have never come to light because they didn't have enough confidence to persist in their way of doing things against the standards they were told to abide to. I bet there have been and there still are many Grothendiecks who are nipped in the bud because they haven't met the right people or haven't had the right epiphany to give them that persistance.

>inb4 i'm the next grothendieck

[Anonymous No.6876221]

>>6875534
RIP Alexander!

Thank you for everything you gave us!

[Anonymous No.6876224]

>>6875967
This guy speaking some truth for y'all!

[Anonymous No.6876263]

>>6876201
Sure, but I do also think the whole "working 16 hours a day" thing that I posted earlier was a major contributing factor too. 10% confidence, 90% sacrificing the majority of your life, IMO

[Anonymous No.6876329]

Who?

[Anonymous No.6876386]

>>6876201
don't be stupid, he had scolarship from the beginning and was supported by cartan schwarzt and dieudonné, all three were first importance mathematicians. How is that supposed to discourage him ?

[Anonymous No.6876399]

;_;

mods pls sticky

[Anonymous No.6876883]

>>6876201
But he knew TONS of math by that method before starting to construct things on his own, you on the other hand are just an edgelord

[Anonymous No.6876932]

I'm the next Grothendieck.

[Anonymous No.6876939]

>>6876932
What's your IQ?

[Anonymous No.6876943]

>>6876932
>I'm the next dickhead.
ftfy

[Anonymous No.6876971]

2 days ago I was telling my friends about Grothendieck and how he lives in isolation and how he even may be dead.

RIP ;_;

[Anonymous No.6877006]

>Perlman
>Grothendieck
>Ted Kaczynski

Why is their a strong tendency for genius mathematicians to go insane and retreat to a life of isolation (potentially innawoods)?

[Anonymous No.6877030]

>category theory

file that under who gives a shit.

[Anonymous No.6877038]

>>6875967

Great post mate! RIP Alexander "God of Mathematics" Grothendieck.

[Anonymous No.6877044]

>>6877006
Really smart people of this type tend to start taking ideas seriously. Most people don't do this.

[Anonymous No.6877048]

>>6877006
>Ted Kaczynski
>smart
pop-math redditor detected

[Anonymous No.6877050]

>>6877006

I am sorry but Perelman and Grothendieck didn't go "insane". They are just extremely principled people who are appalled by the lack of those principles and morals in other mathematicians.

[Anonymous No.6877056]

>>6877048
>Kaczynski
He is smart you doofus. His thesis was so advanced that his adviser had trouble understanding it. He would have won Fields medal had he stuck with math and not gone into fighting the AI.

And everything he said about the AI is true. We're truly fucked. The only messed up thing about Uncle Teddy is that he started killing off CS people.

[Anonymous No.6877071]

>>6877030
Category theory has become a universal language in virtually every area of high level mathematics. You can moan about it being useless if you want but it's far from irrelevant.

[Anonymous No.6877104]

>>6877006
Rumor has it that Perelman was worried for his safety, i.e. if he had accepted the million dollars, he would've been robbed or something.

Grothendieck's retreat into the rural lifestyle has already been discussed above.

Kaczynski was fucked up by the psychological experiments that the CIA inflicted on him as a test subject. That said, though, he did have a point (though I disagree with what he did about it); if you read his manifesto, he's pretty much hitting the nail on the head.

[Anonymous No.6877105]

>>6877056
autistic idiot savant with restricted interests =/= smart

[Anonymous No.6877107]

>>6877030
>combinatoricists
>analysts
>algebraists
>geometers
>topologists
>logicians

[Anonymous No.6877129]

>>6877105
He had an IQ of 170 you idiot. If that's not smart then what is?

[Anonymous No.6877135]

I heard he donated a whole cache of work to a university, I wonder if it will ever be seen.

[Anonymous No.6877178]

>>6877129
>IQ of 170
So he's the equivalent of any typical mathematician with a few unremarkable papers under their belt? Wow, you sure convinced me of his brilliancy.

[Anonymous No.6877194]

>>6877178
>So he's the equivalent of any typical mathematician
you're an awful troll.

[Anonymous No.6877226]

>>6877194
No, retard. Not everyone you subjectively disagree with is a "troll". I'm still waiting for an actual argument. Why don't you try telling me how any of his menial papers (all of them having below 5 citations each) are significant far-reaching intellectual contributions to mathematics or are salient enough beyond background noise to put him in line for a Fields medal. He's just a hyped-up media figure who appeals to mathematically illiterate teenagers and clueless far-left luddites alike.

[Anonymous No.6877295]

>>6877226
well, go on then. why is the topos so useless ?

[Anonymous No.6877301]

>>6877295
ehm, I think he was talking about the Unabomber, not Grothendieck. The ones who downplay his contributions to algebraic geometry *are* trolls (or first years who think they know everything), but the ones who dont think Kaczynski was a shoo-in for a fields medal do have a solid point.

[Anonymous No.6877362]

>>6877104
>The absolute de-industrialisation of mankind
>Hitting the nail on the head
?

[Anonymous No.6877366]

>>6877362
Yeah, talk about taking conclusions out of context. Read his manifesto properly.

[Anonymous No.6877390]

>>6877362
I stated, more or less, that I agree with his premises (that industrial society has created a lot of redundancies and is inefficient, that we are generating ad-hoc solutions to non-existent problems, that we have created pointless pursuits of what TK calls "the second variety") but I have also stated that I disagree with his conclusions (that "de-industrialization is the only answer").

[Anonymous No.6877410]

please stop talking about the unabomber and lets go back to topoi

[Anonymous No.6877431]

>>6877410
>elephant
reference to johnstone? clever.

[Anonymous No.6877522]

an amazing biography of the great mathematician here:
http://inference-review.com/article/a-country-known-only-by-name/

[Anonymous No.6877717]

>>6877431
Yes, I must be a genius.

Hey do you guys know in what sense idempotent monads can be considered modal operators?

It's claimed but \box^2 isn't even the identity, so what's up with that?

[Anonymous No.6877750]

http://www.gofundme.com/7ldiwo

crowdfunding for translation of the remaining parts of Scharlaus' biography.

[Anonymous No.6877800]

http://www.liberation.fr/sciences/2014/11/14/l-inedit-de-grothendieck-fait-d-amour-et-de-haine-des-maths_1143070

>Le mathématicien mort ce jeudi laisse un texte autobiographique de près de 1 000 pages, écrit dans les années 80 et jamais publié, «Récoltes et semailles».

> Il l’écrit dans les années 80 alors qu’il a décidé de rompre avec les maths et les mathématiciens. Il accuse, à tort, ses amis de le piller. Plus ils le citent pour lui rendre hommage et plus lui y voit l’envie de l’enterrer avec son œuvre. Le chaos a pris possession de son intelligence qui revient dans de merveilleux interstices

He basically got a burn out during the 80's and became somewhat paranoid. Blamed his friends for stealing his works, when they weren't.

This is the reason why he decided not to publish that book.

[noko No.6879210]

>>6876386
His teachers previous to meeting Schwarz & co would give him bad marks because he didn't solve problems the way they wanted him to.

>>6876883
No he started to construct things on his own as a teen, like coming up with something similar to Lebesgue integration without having heard of it before. He prefered to find his own problems and solutions rather than reading math books. Did you even read the book he wrote I was referring to?

[Anonymous No.6879259]

somebody know why syntetic differential geometry (SDG) negates the law of the excluded middle?
Well, can somebody tell me any semantic model where is doesn't hold - I can't quite see what that would mean.
Maybe it's just meant that the internal logic of a topos doesn't prove LEM, but in that case I don't see how SDG is said to -negate- it. What is the thingy where it fails? Is it something geometric, even?

[Anonymous No.6879270]

>>6875684
The Abel prize. There's no Nobel prize for maths because some mathematician fucked Nobel's wife. That's why they made the Abel prize.

[Anonymous No.6879302]

>>6879270
Actually, most people consider the Fields medal the mathematical equivalent to the Nobel prize. Also, the story of some mathematician banging Mrs Nobel is a myth. He never created a Nobel Prize because he considered mathematics to be nothing more than an ancillary discipline as compared to, say, phyics. Also Nobel never married.

[Anonymous No.6879334]

>>6879259
> why syntetic differential geometry (SDG) negates the law of the excluded middle
I can't give you a precise technical reason off the top of my head, but a first hint might be that SDG is formulated and modelled inside topos theory, which in general has intuitionistic behaviour. This said, Intuitionism isn't a direct contradiction to the law of the excluded middle, it just doesn't take it for granted (i.e. it's a more general viewpoint). The law of the excluded middle might work locally, but not universially in the entire structure or theory like it does in a classical context.

[Anonymous No.6879381]

>>6879334
I'm also not sure if the formulation
>SDG is formulated and modelled inside topos theory
>modelled inside
is good. Afaik the quantities such as tangent bundle are already the objects of a topos and so "SDG is modeled" seems like talking about a layer which isn't there.
I'm aware that the -internal logic- of a topos is intuitionistic, as I said, but that's topoi being used in a different way (for their logic, not as generalized spacess) and so I don't see how not(LEM) is the case for SDG

[Anonymous No.6879445]

>>6879381
>not(LEM) is the case for SDG
No. That (LEM) doesn't hold does not (generally) imply that not(LEM) does. (LEM) isn't negated, it's being dropped altogether.
From what I understand, one need intuitionistic logic to internally (i.e. in the internal language of the topos) interpret objects and functors as sets and functions.

I'm (obviously) not an expert in the field, but I dug up an article you might find helpful.

http://www.fuw.edu.pl/~kostecki/sdg.pdf

[Anonymous No.6879501]

>>6879445
I'm aware that e.g. intuitionistic frameworks are agnostic towards it and they they don't generally prove not(LEM). After all, any classical model is also one of the weaker theory.
However, I read that SDG rejects it.
If that's not merely to be interpreted in the sense that the topos (which contains e.g. your geometric objects) has an internal logic which negates it, then I'd like to know what statement about actual geometric objects there is, so that not(LEM) holds.
I'm going to peek at the link now.

[Anonymous No.6879566]

k I get it, it's actually discussed right at the beginning and the fact that topoi imply LEM just says you can use them, though it seems you could just as well use this part of the theory without Grothendieckian concepts.

What is done in SDF is that for discussing smooth geometric concepts, the role of the reals
<span class="math">\mathbb R[/spoiler]
is taken by another ring
<span class="math">R[/spoiler]
contianing a non-trivial subset <span class="math">D[/spoiler] of proper infinitesimal numbers <span class="math">d[/spoiler]. These are moreover are extra-small in that <span class="math">d^2=0[/spoiler].

Calculus of these objects is fragile in the sense that assuming

<span class="math">(D\neq\{0\})\ \to\ \exists (d\in D).\,D\neq 0[/spoiler]

already makes the system inconsistent.
So the framework is limited to constructive math, where you don't get existence of quantities from negations of non-existence.

I think the point just is that topoi are generally agnositc about it too, so you can model the geometry in them. From this, it should work for constructive set theory too, though.

[Anonymous No.6879573]

>>6879445
Okay, I get it, it's actually discussed right at the beginning.

What is done in SDF is that for discussing smooth geometric concepts, the role of the reals
<span class="math">\mathbb R[/spoiler]
is taken by another ring
<span class="math">R[/spoiler]
contianing a non-trivial subset <span class="math">D[/spoiler] of proper infinitesimal numbers <span class="math">d[/spoiler].
These are moreover extra-small in that <span class="math">d^2=0[/spoiler].

Calculus of these objects is fragile in the sense that assuming

<span class="math">D\neq\{0\}\ \ \to\ \ \exists (d\in D).\,d\neq 0[/spoiler]

already makes the system inconsistent.
So the framework is limited to constructive math, where you don't get existence of quantities from negations of non-existence.

I think the point just is that topoi are generally agnositc about it too, so you can model the geometry in them.
The fact that topoi don't imply LEM just says you can use them, though it seems you could just as well use this part of the theory without Grothendieckian concepts.
From this, it should work for constructive set theory too, though.

[Anonymous No.6879585]

>>6877226
>>6877226
No you retard, i'm waiting for an argument

Tell me. Why would anybody want to have a civilized conversation over differences of opinion with a person who is disrespectful towards them?

For the time being I sincerely believe you should be entitled to no argument with anybody with an attitude like that towards other people. That way those people are spared your disrespect and can go about their day happier and more fulfilled.

[Anonymous No.6879609]

>>6879573
Glad I could help, anon.

[None !!BJiYgff8zf2 No.6879619]

>>6875967
>Pythagoreans
>nonviolent

Is this a joke? I can't tell.

[Anonymous No.6880134]

Dumbledore died?!?!

[Anonymous No.6880220]

>>6880134
rip saruman

[Anonymous No.6880393]

>>6880220
rip gandalf

[Anonymous No.6880751]

what was his biggest weapon?