
The Anarchist Abstractionist – Who Was Alexander Grothendieck? - jorgenveisdal
https://medium.com/cantors-paradise/the-anarchist-abstractionist-who-was-alexander-grothendieck-cc396083d94e
======
colinhb
This biographical sketch is well-written, concise, and complete (or at least
it appears to be). It includes many quotes and photos that I hadn’t seen
before.

But I can imagine that some readers will be left wondering what was so
remarkable about this guy’s work. Unfortunately, it’s hard to explain without
some exposure to pure mathematics.

David Mumford, who pops up in this article, has a lengthy blog post[1] on this
exact problem, stemming from his experience writing Grothendieck’s obituary
for Nature. It’s an interesting read if you have some math background.

In any case, I think the New York Times obituary by Edward Frenkel[2] does a
nice job of giving a taste of his work to a lay audience (by tackling the
problem of defining Grothendieck’s schemes, just like Mumford did).

[1]
[http://www.dam.brown.edu/people/mumford/blog/2014/Grothendie...](http://www.dam.brown.edu/people/mumford/blog/2014/Grothendieck.html)

[2] [https://www.nytimes.com/2014/11/25/science/the-lives-of-
alex...](https://www.nytimes.com/2014/11/25/science/the-lives-of-alexander-
grothendieck-a-mathematical-visionary.html)

~~~
mikorym
And for the more nonlay audience, Grothendieck's real pull is the persistence
with which he applied category theoretic techniques successfully. Usually one
would qualify this to algebraic geometry, but I think his approach can be
followed in any of the many extensive fields in mathematics.

I would contrast this to what often happens in the physics community, albeit
not in a condescending manner, where techniques diverge rather than converge.
In fact, I would guess this is the role that Einstein played a hundred years
ago: to encourage sensible connections between researchers' work.

~~~
nabla9
Grothendieck's relative point of view
[https://en.wikipedia.org/wiki/Grothendieck%27s_relative_poin...](https://en.wikipedia.org/wiki/Grothendieck%27s_relative_point_of_view)

~~~
mikorym
Linked to via two degrees is this:
[https://en.wikipedia.org/wiki/Grothendieck%E2%80%93Riemann%E...](https://en.wikipedia.org/wiki/Grothendieck%E2%80%93Riemann%E2%80%93Roch_theorem#/media/File:Grothendieck-
Riemann-Roch.jpg).

I don't know German, but it would be really interesting to know what the text
says.

~~~
detaro
rough translation (it's kinda tricky to preserve the tone. Question marks are
words I'm not sure the translation works):

> _Riemann-Roch theorem: the last trend(?): the diagram(?) <formula> is
> commutative!

To give this statement over f:x->y an approximative sense I had try the
patience of the listeners for almost 2 hours. Black-on-white (in Springer's
Lecture Notes) its about 400, 500 pages. A fitting example how our drive to
knowledge and discovery more and more realizes itself in a far-from-life
logical delirium, while the life itself is ruined in a thousand ways - and is
threatened by total destruction. High time to change our path!_

~~~
mikorym
I wonder if he means what I think he means, which is that a concept that is
for some field all-encompassing in your mind takes 400 pages to write down in
a way that translates your ideas. University group theory is like that, when
the real objective may just be to show that you can't circle the square.

------
_hardwaregeek
A few months ago, I stumbled upon an antique store in Paris where the owner
had thousands of notes taken from Grothendieck's house after he died.
Apparently he was in charge of appraising them. Which is pretty stunning since
Grothendieck didn't publish anything for the last few decades of his life, so
it's quite possible there's new math there.

Anyways the guy described how Grothendieck's house didn't have a roof and was
pretty decrepit. Which made me pretty sad. One of the greatest mathematicians
of the 20th century dying alone in a house with no roof. Part of me wonders if
maybe, had he gotten proper mental health care, Grothendieck could have
enjoyed a longer, more healthy career. Or career aside, could he have just had
a better life? In the mathematical community it feels like there's a bit of an
acceptance of idiosyncrasies bordering on potential mental health issues. Well
I say acceptance but really it's bordering on willful ignorance. How many
advisors give their doctoral students advice on mental health? How many
advisors themselves received training on mental health? It's worth analyzing.

~~~
jorgenveisdal
Absolutely. Check out my essays on Wiener and Oppenheimer. Many of the same
tendencies, though with better outcomes

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einpoklum
Quick point: His parents were Anarchists - in the workers'-movement, anti-
Capitalist, revolutionary sense, Groethendieck wasn't. Or rather, his
activities did not involve Anarchist organizing/politics.

Also, in the summary, where it says "discovered a proof of the Lebesgue
measure" \- that's obviously nonsensical, he (re-)developed the Lebesgue
measure himself, without being aware of Lebesgue's work. Or so it says; I
don't know whether he actually focused on non-Riemann-measurable sets etc.

~~~
EthanHeilman
>His parents were Anarchists - in the workers'-movement, anti-Capitalist,
revolutionary sense, Groethendieck wasn't.

I'm not a Groethendieck scholar but I did read a short biography of him and it
definitely left me with the impression that he was an anarchist or left-
libertarian in the anti-Capitalist, liberty, revolutionary sense. What are
your sources to back up the claim that he wasn't?

>is activities did not involve Anarchist organizing/politics.

In Groethendieck's "The Responsibility of the Scientist Today [0] he writes:

"Thus the proliferation of military power and stocks of weapons throughout the
world poses an ever-increasing danger not only to our species, but also to
life in general. This predicament, unparalleled in the long history of
biological evolution, must be met with immediate radical action."

He directly calls for political organization and radical action.

 __Edit: __I don 't object to getting voted down, but I would encourage anyone
downvoting a comment on hackernews to provide their rational. This helps
improve the quality of the discussion.

[0] "The Responsibility of the Scientist Today" (translated from French)
[http://ccnr.org/grothendieck.pdf"](http://ccnr.org/grothendieck.pdf")

~~~
Melting_Harps
I'm not sure why you're being downvoted, thanks for the link, I've bookmarked
it for later reading. Was that short bio 'La Clef des Songes,' I heard it was
translated into Spanish, but never looked to deep for it.

People really should be forced to refute before they can downvote. Even if you
disagree with his points, he gives substance for what and why he said what he
did.

~~~
EthanHeilman
The short biography was "The Artist and the Mathematician: The Story of
Nicolas Bourbaki, the Genius Mathematician Who Never Existed" [0]. It
dedicates a good chunk of the book to the life of Grothendieck. Grothendieck
was a member of the group that used the Nicolas Bourbaki pseudonym. It's a fun
read you can finish in an afternoon. Not sure how accurate it is.

[0]:
[https://www.goodreads.com/book/show/208933.The_Artist_and_th...](https://www.goodreads.com/book/show/208933.The_Artist_and_the_Mathematician)

------
mathandpoop
You seem to have put quite an extensive amount of biographical research into
this. I have never seen these photos in this high quality on the internet
before.

As a maths person and a bit of a Grothendieck fan, thanks!

~~~
jorgenveisdal
Thanks a lot! Indeed, high res photos of Grothendieck are quite hard to come
by

------
papeda
I read a few articles about Grothendieck when he died, but I still learned a
lot from this one.

Those articles usually skipped over his early years as some version of
anarchy. This one better fills in those gaps. For example, I didn't realize
how haphazard Grothendieck's early professional progress was, or that it
depended on an interview with a French education official who recognized
unorthodox talent:

> “Instead of a meeting of twenty minutes, he went on for two hours explaining
> to me how he had reconstructed, ‘with the tools available’, theories that
> had taken decades to construct. He showed an extraordinary sagacity.”

It reminds me of Ramanujan, another exceptionally gifted and devoted
mathematician who acquired most of his education on his own, and was very
nearly lost to history but for the efforts of a few well-connected officials
who could see his potential. Conversely, what a bummer it is to think of
similar talents who didn't get so lucky.

It also gets at just how much the culture of math education matters to math
students, even ones like Grothendieck:

> [Grothendieck] felt free to ask questions, but also found himself
> “struggling to learn things that those around him seemed to grasp instantly
> […] like they had known them from the cradle”. The contrast lead
> Grothendieck to eventually leave Paris, in October of 1949 on the advice of
> Cartan and Weil who recommended he instead travel to Nancy to work with
> Schwartz and Dieudonné on functional analysis.

And this was a guy whose internal mathematical drive was strong enough to
independently discover measure theory as a teenager!

Then there are all the other "failures" absent from a short biographical
blurb: he finished his PhD "with few prospects for employment after his
graduation in 1953", then "planned to write a book on topological vector
spaces, but it never materialized", spent a year failing to solve the
"approximation problem", despaired that the field of his thesis was "dead",
pivoted away from analysis, rest is history, etc.

------
stareatgoats
An interesting, and sad story: that such a beautiful mind ended up with
paranoia. It seems to be a real danger that many geniuses run, maybe in part
(pardon the speculation) because they tend to work too hard: "Grothendieck was
working on the foundations of algebraic geometry seven days a week, twelve
hours a day, for ten years". That has to take a toll.

~~~
ur-whale
> that such a beautiful mind ended up with paranoia.

there's certainly a pattern here, that people that walk the edge of what a
human brain can do often drift to paranoia and/or extremism.

I'm thinking: Bobby Fischer, Grigory Perelman, Évariste Galois, and to a
certain extent, Isaac Newton. I suspect the list is a lot longer.

~~~
jorgenveisdal
Galois - shot in duel. Turing - committed suicide by cyanide-laced apple.
Boltzmann - committed suicide while on vacation. Gödel - died from starvation
and exhaustion. Cantor - died from starvation in an insane asylum. Ramanujan -
died from malnutrition. de Moivre - predicted the day of his death by
calculating his sleep cycle. Lie - became insane and attacked his friends.
Erdös - did amphetamines all his life. Nash - was legally insane for 30 years.
Perelman - refuses contact with anyone except his mother. Grothendieck -
refused contact with anyone. Kaczynski - serving a life sentence in maximum
security prison.

~~~
playing_colours
Erdős took amphetamine in the second half of his life, and apparently it
helped him a lot to stay productive. There is a story about it.

Erdős’s friends worried about his drug use, and in 1979 Graham bet Erdős $500
that he couldn’t stop taking amphetamines for a month. Erdős accepted, and
went cold turkey for a complete month. Erdős’s comment at the end of the month
was “You’ve showed me I’m not an addict. But I didn’t get any work done. I’d
get up in the morning and stare at a blank piece of paper. I’d have no ideas,
just like an ordinary person. You’ve set mathematics back a month.” He then
immediately started taking amphetamines again.

His biography “The Man Who Loved Only Numbers” is a very good interesting
book.

~~~
Koshkin
An idea of a title for a new book on group theory: Crystal Math.

------
mhartl
I recently enjoyed listening to this interview with someone who knew
Grothendieck. It takes a while to get going, but some of the stories are quite
gripping.

[https://youtu.be/L--9bJApz_A](https://youtu.be/L--9bJApz_A)

~~~
mhartl
The article mentions Jean-Pierre Serre, with whom Grothendieck corresponded
extensively, and Pierre Deligne, widely regarded as Grothendieck’s greatest
student. While investigating Grothendieck recently (inspired by the interview
linked in the parent comment), I came across this astonishing anecdote,
relating a comment by Serre about Deligne [1]:

 _“Look, I can take on anyone in Math.” — don’t forget, this guy [Serre] is
the youngest Fields medal winner ever, the first Abel prize laureate, etc. —
“I can understand the reasoning of the greats, handle them new ideas, you name
it.”_

 _“Except for Deligne.” (WHAT ?)_

 _“Deligne is totally out of my league. Above my head.”_

 _“The difference between Deligne and me, is the same difference between me
and an average good mathematician.”_

I found this anecdote especially astonishing considering that at the time I
had never even _heard_ of Deligne. (And most people, of course, haven’t even
heard of Grothendieck.)

[1]: [https://www.quora.com/What-is-the-height-of-
confidence/answe...](https://www.quora.com/What-is-the-height-of-
confidence/answer/Thomas-Cayne-1?share=1)

------
drummer
The name grothendieck sounds a lot like big dick. Like bigus dickus in monthy
pythons life of brian. Groot means big in dutch.

