12 ms·

> Since then I've had the chance, in the world of mathematics that bid me welcome, to meet quite a number of people, both among my "elders" and among young peop

by catgary 15d ago

> Since then I've had the chance, in the world of mathematics that bid me welcome, to meet quite a number of people, both among my "elders" and among young people in my general age group, who were much more brilliant, much more "gifted" than I was. I admired the facility with which they picked up, as if at play, new ideas, juggling them as if familiar with them from the cradle - while for myself I felt clumsy. even oafish, wandering painfully up a arduous track, like a dumb ox faced with an amorphous mountain of things that I had to learn ( so I was assured), things I felt incapable of understanding the essentials or following through to the end. (Alexander Grothendieck, Recoltes et Semailles) Amazing that he managed to keep going after hitting his abstract ceiling in graduate school.

D-Machine 15d ago
You clearly don't understand the meaning of the term. Grothendieck was almost certainly wrong about his gifts here, and even if not, your mathematical ability and output isn't fully explained by your ability ceiling. Honestly, the pushback on this post is utterly baffling. Clearly the human mind has limits on what it can comprehend and the rate at which it can learn difficult things. Clearly these limits differ among individuals and are related to intelligence broadly. Huge proportions of the population struggle to ever even grasp simple fractions, and not for a lack of effort from them or society. Fourth-year undergraduate mathematics is another beast entirely. Pretending the world is otherwise is pure fantasy and also plainly harmful, to the world and people that are unfairly pushed beyond their capabilities.
- magicalist 15d ago
  > Grothendieck was almost certainly wrong about his gifts here, and even if not, your mathematical ability and output isn't fully explained by your ability ceiling lol, see, it's unfalsifiable. No true abstraction ceiling.
  - D-Machine 15d ago
    Find me the magical teaching method that can make anyone learn any kind of mathematics at nearly the same rate, and you have falsified the idea that anyone has mathematical limits. Given we as a society can't even figure out how to do this for educating stuff involving simple fractions, my theory is far superior than whatever exactly it is you think.
- catgary 15d ago
  That's far different than telling a math PhD whom you've never met that they hit their "abstraction ceiling" based on a 2/3 paragraph comment on hacker news. I'm sure you'd have said a similar thing to a young Grothendieck if he were describing his early struggles in graduate school. You're getting pushback because you were being rude and presumptuous.
  - D-Machine 15d ago
    Work on your reading comprehension, I made it clear that increased effort is what an abstraction ceiling feels like, but also made it clear that GP could have been talking about the effort of academic busywork. Let's also not pretend that "you could have learned epsilon delta proofs, you just didn't try hard enough or your teachers weren't competent" or "you just didn't have enough time" and etc. is also not rude and presumptuous. Denying the existence of such limits is equally offensive.
    - catgary 15d ago
      Well you're just a generally rude person, aren't you.
    - 2snakes 14d ago
      You’re in a kind of compulsive ideology here. This same vein of thought and why it is harmful is described by David Bessis in the book Mathematica: A Secret World of Intuition and Curiosity. “To stop thinking in terms of “gifts” and “talents,” one has to find an alternate explanation. My way of looking at things, which has served me well throughout my career, was to imagine that creative mathematicians were hackers who had found ways to unlock “hidden modes” of our cognition. Most of the time, they’d done so unwittingly, and were entirely incapable of explaining how.” It is a phenomenon like child-like mental yoga of attention.
      - D-Machine 14d ago
        Uh huh. A bunch of quasi-mystical bullshit to justify utterly inept garden variety intelligence denialism (it also just shifts terminology: if we accept your metaphysics, it would still be strange to propose that everyone has exactly equal "hacking" ability). The hubris and willful ignorance required to imagine that everyone is just equally and infinitely unbounded in their cognitive ability is simply mind-boggling in 2026.

by catgary 15d ago

D-Machine 15d ago

You clearly don't understand the meaning of the term. Grothendieck was almost certainly wrong about his gifts here, and even if not, your mathematical ability and output isn't fully explained by your ability ceiling. Honestly, the pushback on this post is utterly baffling. Clearly the human mind has limits on what it can comprehend and the rate at which it can learn difficult things. Clearly these limits differ among individuals and are related to intelligence broadly. Huge proportions of the population struggle to ever even grasp simple fractions, and not for a lack of effort from them or society. Fourth-year undergraduate mathematics is another beast entirely. Pretending the world is otherwise is pure fantasy and also plainly harmful, to the world and people that are unfairly pushed beyond their capabilities.

magicalist 15d ago
> Grothendieck was almost certainly wrong about his gifts here, and even if not, your mathematical ability and output isn't fully explained by your ability ceiling lol, see, it's unfalsifiable. No true abstraction ceiling.
- D-Machine 15d ago
  Find me the magical teaching method that can make anyone learn any kind of mathematics at nearly the same rate, and you have falsified the idea that anyone has mathematical limits. Given we as a society can't even figure out how to do this for educating stuff involving simple fractions, my theory is far superior than whatever exactly it is you think.
catgary 15d ago
That's far different than telling a math PhD whom you've never met that they hit their "abstraction ceiling" based on a 2/3 paragraph comment on hacker news. I'm sure you'd have said a similar thing to a young Grothendieck if he were describing his early struggles in graduate school. You're getting pushback because you were being rude and presumptuous.
- D-Machine 15d ago
  Work on your reading comprehension, I made it clear that increased effort is what an abstraction ceiling feels like, but also made it clear that GP could have been talking about the effort of academic busywork. Let's also not pretend that "you could have learned epsilon delta proofs, you just didn't try hard enough or your teachers weren't competent" or "you just didn't have enough time" and etc. is also not rude and presumptuous. Denying the existence of such limits is equally offensive.
  - catgary 15d ago
    Well you're just a generally rude person, aren't you.
  - 2snakes 14d ago
    You’re in a kind of compulsive ideology here. This same vein of thought and why it is harmful is described by David Bessis in the book Mathematica: A Secret World of Intuition and Curiosity. “To stop thinking in terms of “gifts” and “talents,” one has to find an alternate explanation. My way of looking at things, which has served me well throughout my career, was to imagine that creative mathematicians were hackers who had found ways to unlock “hidden modes” of our cognition. Most of the time, they’d done so unwittingly, and were entirely incapable of explaining how.” It is a phenomenon like child-like mental yoga of attention.
    - D-Machine 14d ago
      Uh huh. A bunch of quasi-mystical bullshit to justify utterly inept garden variety intelligence denialism (it also just shifts terminology: if we accept your metaphysics, it would still be strange to propose that everyone has exactly equal "hacking" ability). The hubris and willful ignorance required to imagine that everyone is just equally and infinitely unbounded in their cognitive ability is simply mind-boggling in 2026.