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This passage caught my attention: He proceeds just as deliberately when doing mathematics. Wang was shocked when he first witnessed it. “I have this math compe

by ken47 4y ago

This passage caught my attention: He proceeds just as deliberately when doing mathematics. Wang was shocked when he first witnessed it. “I have this math competition experience, that as a mathematician you have to be clever, you have to be fast,” he said. “But June is the opposite. … If you talk to him for five minutes about some calculus problem, you’d think this guy wouldn’t pass a qualifying exam. He’s very slow.” So slow, in fact, that at first Wang thought they were wasting a lot of time on easy problems they already understood. But then he realized that Huh was learning even seemingly simple concepts in a much deeper way — and in precisely the way that would later prove useful. Having gone through the American education system, I felt like I was in a factory being evaluated as a potential end product. Steamroll through as much material as quickly as possible. Optimize behavioral patterns for the next performance metric. Rinse and repeat. Is this really the best system we can come up with? Can the pace of mathematical and scientific advancement be optimized by steamrollers? I wonder how much potential we've missed as a society because the education system has been trying to force everyone through the same hole, and destroying intellectual curiosity in the process. Personally, my experience with this educational system turned me off from "math." It was only much later in life when I learnt that the mindless algorithms that I had to personally execute for years on end to get into university could barely be considered math at all. Only then could I begin to appreciate how elegant real math could be. And I doubt I'm alone in my experience.

buchoo 4y ago
That passage reminded me of a remark by the 2002 French Fields Medalist Laurent Lafforgue: "My specificity today among French mathematicians is not to know more mathematics than others, I can even admit that I know less mathematics than most French and foreign mathematicians. It's not about being 'great' either, I'm not great at all, on the contrary I have a rather slow mind. When I listen to a seminar, I'm probably one of those who understand the least what is being said: an idea in an hour, for me, that's already a lot. No, the only explanation for the successes that I have been able to obtain in mathematics is my being imbued by the reading of the great classics." https://www.biennale-lf.org/b22/index.php?p=https://www.biennale-lf.org/b22/laurent-lafforgue.html https://www.biennale-lf.org/b22/index.php?p=https://www.bien... As for your experience, you are indeed very far from alone.
- ask_b123 4y ago
  I wonder which great classics would those be.
  - buchoo 4y ago
    Not very specific, but he says: "In my parents' house, there were a lot of books: all the great authors of the 17th, 18th and 19th centuries, translated foreign authors. I spent my youth, and still today I spend most of my time, reading literary works, and particularly those of French literature."
    - adamsmith143 4y ago
      He totally learned Abstract Algebra from Dumas.
      - Agingcoder 4y ago
        Thanks, this made made laugh :-)
        ttonelli 4y ago
        Thanks, this made me re-read parent more carefully, which then made me laugh :)
      - Viliam1234 4y ago
        The Three Musketeers -- Athos, Porthos, Aramis, and D'Artagnan If this doesn't make you think about math, nothing will.
rfrey 4y ago
My kid was enamored by math from the earliest age, and pretty good at it too. He read proofs for fun at about age 6, and was writing them for fun by 7. Calculation seemed to come pretty easy to him as well. But he is slow! He did a bunch of cognitive tests where he was testing 3rd std deviation on most tasks. Except processing speed, where he was in the 2nd percentile. You'd present him with his times tables, and he would take 15 seconds to get "8x7"... but he didn't slow down as as the psychiatrist progressed through the test. He'd get to some 6th grade problem, and it'd be the same 15 seconds and blank look before the solution came out. He was an O(1) machine with a huge constant. And school utterly killed his interest in math. From grade 2 onwards it was speed competitions and public humiliation in front of his class. After grade 3 he refused to do anything related to math outside of what's required because he was "way to stupid for that".
- Agingcoder 4y ago
  Laurent Schwartz (former fields medallist) states in his autobiography (which I do recommend) that he was particularly slow - however being slow doesn't mean you're bad. It just means that you're slow, but this has no implication as to how far you'll go!
  - agumonkey 4y ago
    make haste slowly
- colineartheta 4y ago
  I'm curious why you didn't get involved as the parent and possibly engage his interest outside of the classroom, or even put him in a different school or situation where he wouldn't be humiliated? I'm sorry for how this is going to sound, but your anecdote reads to me more that you killed his interest in math through your own (in)actions; the school simply serves as a useful copout.
  - kshahkshah 4y ago
    I don’t think the 6 year old was getting access to proofs to read on their own. It sounds like OP very much did encourage his interest.
nmfisher 4y ago
I felt the same way, but interesting that he grew up in South Korea. From what I gather, it's very similar to the Chinese system over there, particularly when it comes to maths. Endless rote learning and an overwhelming focus on standardized test results, to the exclusion of the type of slow, deep, "playful" learning referred to in the article.
- sanxiyn 4y ago
  As a former South Korean student, I'd say it's focused on standardized test but that doesn't imply rote learning. At some level of test difficulty, it starts to be more efficient to actually understand the material, because you can't memorize all possible questions.
blabberwocky 4y ago
Curiosity negative feedback loop aside, I wonder if the steamrolling incentive is also why so many people eventually “hit a wall” in their math studies. You can only get so far without a solid base for a cumulative knowledge area like math. The bar for SATs and similar college admissions tests is set remarkably low, though, such that one may never run into this problem without going into a mathy field. But it does seem like a slow-and-steady approach taken by a greater number of people could encourage more interest and deep thinking, and possibly a greater contribution to the field and society overall.
- Viliam1234 4y ago
  > I wonder if the steamrolling incentive is also why so many people eventually “hit a wall” in their math studies. You can only get so far without a solid base for a cumulative knowledge area like math. There is a known (but mostly ignored) educational method called https://en.wikipedia.org/wiki/Mastery_learning https://en.wikipedia.org/wiki/Mastery_learning -- you should teach kids until they actually get it, and only then move to the next lesson. This method may be slower at the start, but later gains speed because kids with solid background understand the new concepts faster, and do not need to relearn the old concepts all the time.
Azrael3000 4y ago
Well if you look at todays economy what do companies require? Fast and faster is the way. The schools are here to produce fast workers. There's hardly a day a year where you can sit down and work on a project without time pressure.
- Viliam1234 4y ago
  Ah, the pleasures of agile development! There is never time to implement something properly, but at least we are sure that all developers are kept busy every week. If you think about the problem, discuss it, and then implement the solution properly, it's only one ticket. But if you make a half-assed solution, change it twice, and fix seven related bugs, that is ten tickets, with a potential to make even more tickets in the future.
  - kadoban 4y ago
    Is that really what agile is in your experience? Who is preventing you from doing tickets that involve the real solution? Can you not write your own tickets? Are you pushed too much to size them too small or something?
    - Viliam1234 4y ago
      Agile is quite different in theory and in practice. In theory, it should be a replacement of management by autonomous developer teams making their own estimates and communicating directly with the customer. In practice, at least in my experience, it is just a buzzword and a set of empty rituals. In practice, if I write my own ticket, some manager will give it a priority 2. And the tickets with priority smaller than 1 never get done, because there are always enough tickets with priority 1, i.e. those written by the management. A few years later, when the project is decommissioned, the tickets with priority lower than 1 are still in the backlog. Of course, if having your ticket in the backlog makes you happy, just go ahead and make one. It is not how it should be done, in theory. Knowing that does not help much.
      - 4y ago
jebarker 4y ago
I am both a slow thinker and forgetful, but I've learned that those are not required skills for being good at maths. When I started my undergrad in maths (in the UK) they gave us a day 1 test to check we could recall certain pre-requisites from school. I did poorly because I had forgotten all the tricks for those particular exam questions and was put in an additional "catch up" class. It was a real gut punch and I questioned whether I was cut out for maths at all. Fast-forward six years and I ended up with a PhD in pure maths from the same university. Turned out that when given the time to read and think at my own pace and allowed reference to books and my own notes I was pretty good at abstract math. Fast-forward another ~15 years and I'm a machine learning researcher for a SV company. The same issue rears it's head now as an inability to contribute usefully in meetings. I can't think fast enough to keep up and don't have anything useful to say when put on the spot. I much prefer to read written communication and take the time to formulate my responses. This is not the company culture though, so I do suffer problems with effective collaboration.
- lordnacho 4y ago
  This thread struck a nerve with me. As a kid I loved math, did all the math contest stuff, even won one at one point, skipped a year in math. I went to visit my old retired math teacher a couple of weeks ago, he's in his 80s. In school I never had a problem with speed or understanding, nor at university. But what hit me was the realization that "actual math" is probably not a load of little riddles. I often wondered how I'd ever solve something that someone hadn't contrived to have an elegant solution, something completely new and insightful that nobody had proven before. There's quite a leap from your tricky olympiad problem that you can find a good video for, and proofs of things in higher math. The other thing that struck me was that our current system destroys all appreciation for beauty. There's so many beautiful things in math, but we're forced to calculate, quickly. Especially in the engineering side I went into, it ended up becoming very mechanical.
- filipmrc 4y ago
  Your post made me create an account because I'm in a very similar situation. I was not "good" at math until later years of undergrad, where more abstract topics made me fall in love with it. I never could follow courses by going to class and had a much easier time just reading and taking notes. I'm now finishing a robotics PhD where I had the opportunity to do pretty well as a slow thinker by taking the time to understand and apply concepts from computational algebraic geometry. Currently I'm doing an ML research internship at a SV company and this problem of "slowness" at meetings is really resonating with me. I have a hard time following quick verbal communication, I just need the time to think in order to contribute. I don't know it's like I just phase out or forget what we were talking about. Have you found any useful techniques to do better in this type of environment? Is there any advice you would give your younger self?
agumonkey 4y ago
Without school systems failures, there's a value in not rushing. I used to be quick, I'd iterate thousands of times in my head, until I could find an answer. But I didn't grasp the breadth of mathematical beauty, the coherence of abstractions, the various ways to interpret them, play with them. I was obsessed by finding "one answer".

by ken47 4y ago

buchoo 4y ago

That passage reminded me of a remark by the 2002 French Fields Medalist Laurent Lafforgue: "My specificity today among French mathematicians is not to know more mathematics than others, I can even admit that I know less mathematics than most French and foreign mathematicians. It's not about being 'great' either, I'm not great at all, on the contrary I have a rather slow mind. When I listen to a seminar, I'm probably one of those who understand the least what is being said: an idea in an hour, for me, that's already a lot. No, the only explanation for the successes that I have been able to obtain in mathematics is my being imbued by the reading of the great classics." https://www.biennale-lf.org/b22/index.php?p=https://www.biennale-lf.org/b22/laurent-lafforgue.html https://www.biennale-lf.org/b22/index.php?p=https://www.bien... As for your experience, you are indeed very far from alone.

ask_b123 4y ago
I wonder which great classics would those be.
- buchoo 4y ago
  Not very specific, but he says: "In my parents' house, there were a lot of books: all the great authors of the 17th, 18th and 19th centuries, translated foreign authors. I spent my youth, and still today I spend most of my time, reading literary works, and particularly those of French literature."
  - adamsmith143 4y ago
    He totally learned Abstract Algebra from Dumas.
    - Agingcoder 4y ago
      Thanks, this made made laugh :-)
      - ttonelli 4y ago
        Thanks, this made me re-read parent more carefully, which then made me laugh :)
    - Viliam1234 4y ago
      The Three Musketeers -- Athos, Porthos, Aramis, and D'Artagnan If this doesn't make you think about math, nothing will.

rfrey 4y ago

My kid was enamored by math from the earliest age, and pretty good at it too. He read proofs for fun at about age 6, and was writing them for fun by 7. Calculation seemed to come pretty easy to him as well. But he is slow! He did a bunch of cognitive tests where he was testing 3rd std deviation on most tasks. Except processing speed, where he was in the 2nd percentile. You'd present him with his times tables, and he would take 15 seconds to get "8x7"... but he didn't slow down as as the psychiatrist progressed through the test. He'd get to some 6th grade problem, and it'd be the same 15 seconds and blank look before the solution came out. He was an O(1) machine with a huge constant. And school utterly killed his interest in math. From grade 2 onwards it was speed competitions and public humiliation in front of his class. After grade 3 he refused to do anything related to math outside of what's required because he was "way to stupid for that".

Agingcoder 4y ago
Laurent Schwartz (former fields medallist) states in his autobiography (which I do recommend) that he was particularly slow - however being slow doesn't mean you're bad. It just means that you're slow, but this has no implication as to how far you'll go!
- agumonkey 4y ago
  make haste slowly
colineartheta 4y ago
I'm curious why you didn't get involved as the parent and possibly engage his interest outside of the classroom, or even put him in a different school or situation where he wouldn't be humiliated? I'm sorry for how this is going to sound, but your anecdote reads to me more that you killed his interest in math through your own (in)actions; the school simply serves as a useful copout.
- kshahkshah 4y ago
  I don’t think the 6 year old was getting access to proofs to read on their own. It sounds like OP very much did encourage his interest.

nmfisher 4y ago

I felt the same way, but interesting that he grew up in South Korea. From what I gather, it's very similar to the Chinese system over there, particularly when it comes to maths. Endless rote learning and an overwhelming focus on standardized test results, to the exclusion of the type of slow, deep, "playful" learning referred to in the article.

sanxiyn 4y ago
As a former South Korean student, I'd say it's focused on standardized test but that doesn't imply rote learning. At some level of test difficulty, it starts to be more efficient to actually understand the material, because you can't memorize all possible questions.

blabberwocky 4y ago

Curiosity negative feedback loop aside, I wonder if the steamrolling incentive is also why so many people eventually “hit a wall” in their math studies. You can only get so far without a solid base for a cumulative knowledge area like math. The bar for SATs and similar college admissions tests is set remarkably low, though, such that one may never run into this problem without going into a mathy field. But it does seem like a slow-and-steady approach taken by a greater number of people could encourage more interest and deep thinking, and possibly a greater contribution to the field and society overall.

Viliam1234 4y ago
> I wonder if the steamrolling incentive is also why so many people eventually “hit a wall” in their math studies. You can only get so far without a solid base for a cumulative knowledge area like math. There is a known (but mostly ignored) educational method called https://en.wikipedia.org/wiki/Mastery_learning https://en.wikipedia.org/wiki/Mastery_learning -- you should teach kids until they actually get it, and only then move to the next lesson. This method may be slower at the start, but later gains speed because kids with solid background understand the new concepts faster, and do not need to relearn the old concepts all the time.

Azrael3000 4y ago

Well if you look at todays economy what do companies require? Fast and faster is the way. The schools are here to produce fast workers. There's hardly a day a year where you can sit down and work on a project without time pressure.

Viliam1234 4y ago
Ah, the pleasures of agile development! There is never time to implement something properly, but at least we are sure that all developers are kept busy every week. If you think about the problem, discuss it, and then implement the solution properly, it's only one ticket. But if you make a half-assed solution, change it twice, and fix seven related bugs, that is ten tickets, with a potential to make even more tickets in the future.
- kadoban 4y ago
  Is that really what agile is in your experience? Who is preventing you from doing tickets that involve the real solution? Can you not write your own tickets? Are you pushed too much to size them too small or something?
  - Viliam1234 4y ago
    Agile is quite different in theory and in practice. In theory, it should be a replacement of management by autonomous developer teams making their own estimates and communicating directly with the customer. In practice, at least in my experience, it is just a buzzword and a set of empty rituals. In practice, if I write my own ticket, some manager will give it a priority 2. And the tickets with priority smaller than 1 never get done, because there are always enough tickets with priority 1, i.e. those written by the management. A few years later, when the project is decommissioned, the tickets with priority lower than 1 are still in the backlog. Of course, if having your ticket in the backlog makes you happy, just go ahead and make one. It is not how it should be done, in theory. Knowing that does not help much.
    - 4y ago

jebarker 4y ago

I am both a slow thinker and forgetful, but I've learned that those are not required skills for being good at maths. When I started my undergrad in maths (in the UK) they gave us a day 1 test to check we could recall certain pre-requisites from school. I did poorly because I had forgotten all the tricks for those particular exam questions and was put in an additional "catch up" class. It was a real gut punch and I questioned whether I was cut out for maths at all. Fast-forward six years and I ended up with a PhD in pure maths from the same university. Turned out that when given the time to read and think at my own pace and allowed reference to books and my own notes I was pretty good at abstract math. Fast-forward another ~15 years and I'm a machine learning researcher for a SV company. The same issue rears it's head now as an inability to contribute usefully in meetings. I can't think fast enough to keep up and don't have anything useful to say when put on the spot. I much prefer to read written communication and take the time to formulate my responses. This is not the company culture though, so I do suffer problems with effective collaboration.

lordnacho 4y ago
This thread struck a nerve with me. As a kid I loved math, did all the math contest stuff, even won one at one point, skipped a year in math. I went to visit my old retired math teacher a couple of weeks ago, he's in his 80s. In school I never had a problem with speed or understanding, nor at university. But what hit me was the realization that "actual math" is probably not a load of little riddles. I often wondered how I'd ever solve something that someone hadn't contrived to have an elegant solution, something completely new and insightful that nobody had proven before. There's quite a leap from your tricky olympiad problem that you can find a good video for, and proofs of things in higher math. The other thing that struck me was that our current system destroys all appreciation for beauty. There's so many beautiful things in math, but we're forced to calculate, quickly. Especially in the engineering side I went into, it ended up becoming very mechanical.
filipmrc 4y ago
Your post made me create an account because I'm in a very similar situation. I was not "good" at math until later years of undergrad, where more abstract topics made me fall in love with it. I never could follow courses by going to class and had a much easier time just reading and taking notes. I'm now finishing a robotics PhD where I had the opportunity to do pretty well as a slow thinker by taking the time to understand and apply concepts from computational algebraic geometry. Currently I'm doing an ML research internship at a SV company and this problem of "slowness" at meetings is really resonating with me. I have a hard time following quick verbal communication, I just need the time to think in order to contribute. I don't know it's like I just phase out or forget what we were talking about. Have you found any useful techniques to do better in this type of environment? Is there any advice you would give your younger self?

agumonkey 4y ago

Without school systems failures, there's a value in not rushing. I used to be quick, I'd iterate thousands of times in my head, until I could find an answer. But I didn't grasp the breadth of mathematical beauty, the coherence of abstractions, the various ways to interpret them, play with them. I was obsessed by finding "one answer".