The Oracle of Arithmetic | Hacker News Reader

The Oracle of Arithmetic

quantamagazine.org

112 pointsretupmoc0120 comments

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

[2] https://mathematicswithoutapologies.wordpress.com/2015/11/09...

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

[4] http://www.express.de/bonn/professor-mit-24-so-tickt-mathe-g...

>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.

Geez, at my high school, 33% (12) of kids in my gifted class didn't even graduate.

At 40, I finally have the time and money to actually get to play around with things I should have been learning at 16. And, I'm learning new things every day. P-adic numbers and perfectoid spaces? Wow, those things are the shit! And, I'd never even heard about them before.

Difference between wanting to and needing to.

... 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.

My early fear of mathematics has a lot to do with its being taught by permanently enraged adults who seemed to view the topic as an excuse to work themselves into paroxysms of ultra-violence. I am glad to see that percussive pedagogy has fallen out of fashion.

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.

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").

I went to a school in the same system, Werner-von-Siemens Gymnasium in Magdeburg. They are relicts from former East Germany.

It's a bit more complicated. But the teachers were generally much better than at other schools, and interested in competitions. More kids were interested in math and sciences, but not everyone.

We regularly have math and science competitions between these kinds of schools. (And of course, my school is better than theirs. ;)

> 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):

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

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=...

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

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

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...

> 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.

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

https://www.youtube.com/watch?v=cFdm0B9KLcQ

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

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.

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 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.

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.

To be #1 like Tao requires being a born genius -- recognized as a prodigy by the age of 5, extremely well supported by ambitious parents, and having a lifelong insatiable curiosity and work ethic.

It takes a bit less to be an average mathematician, though.

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

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