5 ms·

The Oracle of Arithmetic

112 points by retupmoc01 10y ago

joaorico 10y ago
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/working-the-red-carpet-part-2/ https://mathematicswithoutapologies.wordpress.com/2015/11/09... [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-genie-peter-scholze-4572292 http://www.express.de/bonn/professor-mit-24-so-tickt-mathe-g...
bumbledraven 10y ago
> 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 10y ago
  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=frank%20lloyd%20wright%20daily%20work%20habits&pg=PA113#v=onepage&q=frank%20lloyd%20wright%20daily%20work%20habits&f=false https://books.google.com/books?id=z40CNby1wnYC&lpg=PA113&dq=...
  - Zuider 10y ago
    The philosopher, Bertrand Russel was also known to work like this. He would produce a perfectly structured, completed work on the first draft.
    - richardfeynman 10y ago
      The Feynman Algorithm: 1. Write down the problem. 2. Think real hard. 3. Write down the solution.
      - abecedarius 10y ago
        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-histories/5020-5 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.
bdavisx 10y ago
>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.
- ap22213 10y ago
  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.
  - hackits 10y ago
    Difference between wanting to and needing to.
- HillaryBriss 10y ago
  ... 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.
  - Zuider 10y ago
    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.
  - superobserver 10y ago
    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.
mrcactu5 10y ago
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 10y ago
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 10y ago
  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.
mathgenius 10y ago
I would recommend this book for more on the Langlands program: "Love and Math: The Heart of Hidden Reality" by Edward Frenkel.

112 points by retupmoc01 10y ago

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/working-the-red-carpet-part-2/ https://mathematicswithoutapologies.wordpress.com/2015/11/09... [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-genie-peter-scholze-4572292 http://www.express.de/bonn/professor-mit-24-so-tickt-mathe-g...

bumbledraven 10y ago

> 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 10y ago
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=frank%20lloyd%20wright%20daily%20work%20habits&pg=PA113#v=onepage&q=frank%20lloyd%20wright%20daily%20work%20habits&f=false https://books.google.com/books?id=z40CNby1wnYC&lpg=PA113&dq=...
- Zuider 10y ago
  The philosopher, Bertrand Russel was also known to work like this. He would produce a perfectly structured, completed work on the first draft.
  - richardfeynman 10y ago
    The Feynman Algorithm: 1. Write down the problem. 2. Think real hard. 3. Write down the solution.
    - abecedarius 10y ago
      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-histories/5020-5 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.

bdavisx 10y ago

>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.

ap22213 10y ago
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.
- hackits 10y ago
  Difference between wanting to and needing to.
HillaryBriss 10y ago
... 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.
- Zuider 10y ago
  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.
- superobserver 10y ago
  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.

mrcactu5 10y ago

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 10y ago

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 10y ago
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.

mathgenius 10y ago

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