
The Oracle of Arithmetic - retupmoc01
https://www.quantamagazine.org/20160628-peter-scholze-arithmetic-geometry-profile/
======
joaorico
Some additions to this profile:

Scholze won 3 gold medals at the International Mathematical Olympiad [1],
refused the Milner and Zuckerberg's Millenium Prize (without justification,
afaik) [2], answers once in a while on mathoverflow [3] and has played the
bass in a rock band, obviously. [4]

[1] [http://imo-official.org/participant_r.aspx?id=7867](http://imo-
official.org/participant_r.aspx?id=7867)

[2]
[https://mathematicswithoutapologies.wordpress.com/2015/11/09...](https://mathematicswithoutapologies.wordpress.com/2015/11/09/working-
the-red-carpet-part-2/)

[3] [https://mathoverflow.net/users/6074/peter-
scholze](https://mathoverflow.net/users/6074/peter-scholze)

[4] [http://www.express.de/bonn/professor-mit-24-so-tickt-
mathe-g...](http://www.express.de/bonn/professor-mit-24-so-tickt-mathe-genie-
peter-scholze-4572292)

------
bdavisx
>attending Heinrich Hertz Gymnasium, a Berlin high school specializing in
mathematics and science. At Heinrich Hertz, Scholze said, “you were not being
an outsider if you were interested in mathematics.”

I wonder how many people like him have never reach their potential because
they went to a high school where intelligence was looked down on or even could
get you hurt.

~~~
HillaryBriss
... or never reach their potential because there's a lot of random, mediocre
noise masquerading as education in their environment. there are probably
multiple people like Scholze aimlessly drifting in the US right now, working
as unpaid interns or playing video games all day, people who are literally
unaware of what they're missing.

~~~
superobserver
Right you are, and the unfortunate reality is no one particularly cares
either. Common Core (in the US) adds to this in its focus not on the problem,
not on the solution, not on the method(s) to approach the problem, but rather
on a seemingly sensible and internally coherent explanation for arriving at
some sort of (not necessarily correct) solution.

~~~
srtjstjsj
Please explain what you are talking about. If I were less charitable, I'd
worry you were taking an uninformed potshot at a curriculum you haven't read
up on.

What is "sensible and internally coherent explanation" if not a method to
approach the problem?

In the IMO, points are awarded for sensible and internally coherent
explanations (commonly called "proofs").

------
bumbledraven
> Scholze avoids getting tangled in the jungle vines by forcing himself to fly
> above them: As when he was in college, he prefers to work without writing
> anything down. That means that he must formulate his ideas in the cleanest
> way possible, he said. “You have only some kind of limited capacity in your
> head, so you can’t do too complicated things.”

Grigori Perelman also worked this way. According to "Perfect Rigor" (Google
Books link: [https://goo.gl/tFe6hP](https://goo.gl/tFe6hP)):

> Perelman did his thinking almost entirely inside his head, neither writing
> nor sketching on scratch paper.

~~~
moubry
Frank Lloyd Wright is known for working in a similar way [1]:

> Still another remarkable quality about Wright’s work habits was his practice
> of never doing a sketch until he had the entire project worked out in his
> head.

[1]:
[https://books.google.com/books?id=z40CNby1wnYC&lpg=PA113&dq=...](https://books.google.com/books?id=z40CNby1wnYC&lpg=PA113&dq=frank%20lloyd%20wright%20daily%20work%20habits&pg=PA113#v=onepage&q=frank%20lloyd%20wright%20daily%20work%20habits&f=false)

~~~
Zuider
The philosopher, Bertrand Russel was also known to work like this. He would
produce a perfectly structured, completed work on the first draft.

~~~
richardfeynman
The Feynman Algorithm: 1\. Write down the problem. 2\. Think real hard. 3\.
Write down the solution.

~~~
abecedarius
Actually, Feynman answered in an interview once that his notebooks were where
he did his work. The interviewer followed up with something like "You mean
where you wrote it down?" and he gave an emphatic no. Ah, here it is:

[https://www.aip.org/history-programs/niels-bohr-
library/oral...](https://www.aip.org/history-programs/niels-bohr-library/oral-
histories/5020-5)

> Weiner: Well, the work was done in your head but the record of it is still
> here.

> Feynman: No, it’s not a record, not really, it’s working. You have to work
> on paper and this is the paper. OK?

It was nice to see this because that algorithm, even if meant as a joke, never
sat right with me. The Feynman of the lectures would not encourage you to
believe in magic.

------
mrcactu5
I recommend this video (from Harvard Math Department) "Locally symmetric
spaces, and Galois representations"

[https://www.youtube.com/watch?v=cFdm0B9KLcQ](https://www.youtube.com/watch?v=cFdm0B9KLcQ)

He connects Galois Theory and Hyperbolic Geometry and off you go!

------
lordnacho
I'm always amazed by mathematician's stories like this.

Part of me wonders what would have happened if I'd gone that way, because my
uninformed 18 year old self thought that studying a mix of engineering and
management would be the best way to make sure I didn't end up running a
restaurant. I'd grown up in one, and I wasn't keen on my kids doing so. So
even though I quite liked math (I did contests) I chose something that seemed
a bit more practical.

Now I realise it's not exactly bad for your career prospects to have a math
degree. There's a family of sciences (and math) that tend to produce
employable graduates in tech related areas. People who can code, people who
can use math (without delving too deep), people who've visited the evidence in
a range of natural sciences.

Anyway, there's an atmosphere of awe about guys like this and Terence Tao,
like you have to be born a certain way to reach those heights. I wonder a bit
about the environment required as well. I suspect it's a lot less gift, and a
lot more hard work than it seems (well, hard work is easy if you like it).
Along with being fortunate enough to have the environment that takes you along
at the right pace. That math teacher who sees you've reached the edge, and
spends the time to show you what lies beyond. I had that, I still keep in
touch with him. Maybe what I needed was a peer who was interested, too.

Then again, there is something about the pure math people that's quite
special. With a physicist or chemist, the person needs to be shown a bunch of
stuff, and digest it. Naturally there's a limit to how much resource can be
directed at such a person, they need lab time, and they need simply sheer time
to digest the mass of existing evidence.

Maybe a mathematician can comment on this: With pure math, everything is
obvious, yet hiding in plain sight. Theorems that will be proven in the future
will rely on things that are already known, we just haven't come across a
connection yet. Everything is a forehead-slap, why didn't I think of that? For
the moment as a non-mathematician, I've only had that feeling with things that
are known. Things like the proof there's an infinite number of primes just
seem obvious once you know them. The moment when you understand it, you do the
forehead-slap. It seems the only thing preventing us from learning the next
thing is that nobody has come across it yet.

~~~
vladsotirov
It's not enough to like the work for it to be easy: it's also important that
your work be appreciated and encouraged. Scholze happens to be interested in a
popular/prestigious subfield of mathematics, but my experience suggests
there's a substantial number of talented mathematicians who leave academia and
mathematics itself for some kind of industry job because their interests are
in more obscure/less glamorous subfields of mathematics, meaning that they
receive little to no support (or even respect) from their colleagues.

For example, consider William Stein's recent exit from academia that was
discussed at
[https://news.ycombinator.com/item?id=11883987](https://news.ycombinator.com/item?id=11883987)
motivated by essentially the same lack of support; now imagine how many don't
even make it to tenure before they have to struggle with their interests and
values being misaligned from those of the academic mathematical community.

~~~
srtjstjsj
Stein left academia because he builds tools, and academia is only interested
in mathematical _results_ from academics. His work is seen (by the
mathematicians) on par with Intel, Dell, and the notebook paper manufacturers,
not a part of the pure math department.

------
mathgenius
I would recommend this book for more on the Langlands program: "Love and Math:
The Heart of Hidden Reality" by Edward Frenkel.

