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My definition of "mathematical genius" is simply wider than yours. To me its people who can solve math problems that 99.9% of the population can't without assis

My definition of "mathematical genius" is simply wider than yours. To me its people who can solve math problems that 99.9% of the population can't without assistance. Which I think is a fair colloquial definition. ChatGPT went from struggling to provide the answer for 20x20 to easily being able to provide the right answer for any math problem wolfram alpha can.

dvt 4y ago
> To me its people who can solve math problems that 99.9% of the population can't without assistance. You're just kind of re-emphasizing my point: ChatGPT is using Wolfram as its assistance. So really, it's acting more like a "dumb" API call, not a "math genius" at all.
- Baeocystin 4y ago
  I mean, what is crystallized intelligence, but that which we can call upon without having to focus on it? I mean this honestly, no snark. When I was a kid, learning how to factor numbers was really hard. It took a lot of time and concentration to do even basic problems, and people who could do it quickly without much perceived effort were a mystery to me. By the time I reached high school, I had enough practice that I recognized the common patterns without difficulty, and often the answer bubbled up to my conscious mind without thinking about it at all. It sure feels like my brain is making an API call to a subsystem, you know?
- sebzim4500 4y ago
  He's not really saying that GPT-4 is a 'math genius', rather the combined system of GPT-4 and Wolfram is.
  - dvt 4y ago
    But that doesn't really mean much. It's like saying I'm a "geography genius" while I have Google Earth open.
    - atonse 4y ago
      And if you had Google earth hooked up to hidden headphones without us being able to tell, you would seem like a geography genius to us. that’s the point. it seems like you’re arguing whether the genius label only has to be innate. But if you are able to effectively get help from sources, the effect can be the same.
    - pixl97 4y ago
      It's a question of latency... It takes you, what, seconds to type digits into a calculator? But if you embedded a calculator into your brain and could put in and pull values out of it in microseconds how are you different from a math genius? Same with millisecond access to Google earth, at some point smarts+speed of access is a system within itself.
      - dvt 4y ago
        > But if you embedded a calculator into your brain and could put in and pull values out of it in microseconds how are you different from a math genius? Tao, Perelman, Wiles etc. aren't math geniuses because they can multiply numbers fast (which is a super weird definition of "math genius" tbh). They're math geniuses because they answer really hard questions in creative and unexpected ways; ways that often open up entire new areas of mathematics.
        aik 4y ago
        I think you’re sidestepping the point here. The point is that the combo of these systems becomes one unit. One integrated system. That’s the new system to measure. Similarly, your prefrontal cortex without a hippocampus sucks. The combo of them (and other distinct parts of the brain that handle specific functions and have specific purposes that interact with other parts in a specific way) - that is what causes our specific type of intelligence to emerge. The brain as a whole is much more interesting and practical to measure.
        dvt 4y ago
        Yeah this is a valid criticism of the Chinese Room (called the "Systems Counterargument")[1]. I think it's a weak-ish riposte in this context though, mainly because we have no real idea how our own brains work and how their parts causaly interact (other than handwavy "these neurons are firing in this area"). [1] https://iep.utm.edu/chinese-room-argument/#SH2a https://iep.utm.edu/chinese-room-argument/#SH2a
- Workaccount2 4y ago
  It goes back to my original point, that I suspect AGI will come from an AI that is essentially a master of all APIs. We can go back and forth splinting hairs about whether inserting a compute module into a neural net (organic or not) grants geniousness or assistance, but the overall point stands; there will be a single interface that can take any variety of inputs and properly parse and shape them, push them through the correct "APIs", and then take the results to form a clear and correct output. Whether or not it used it's neural net or transistor adders circuits to arrive at the answer would be immaterial.
jules 4y ago
Wolfram Alpha is computation. So it became a computational genius in precisely the things that Wolfram Alpha can do. A better test is whether it can prove new lemmas, like the average undergraduate in mathematics. From what I tried, it cannot do that yet. I'm convinced that doesn't require a breakthrough in the architecture or scale of LLMs, though. GPT-4 seems plenty smart enough to be able to learn that, if hooked up to a proof assistant like Lean or Coq with the right fine tuning iteration loop.

dvt 4y ago

> To me its people who can solve math problems that 99.9% of the population can't without assistance. You're just kind of re-emphasizing my point: ChatGPT is using Wolfram as its assistance. So really, it's acting more like a "dumb" API call, not a "math genius" at all.

Baeocystin 4y ago
I mean, what is crystallized intelligence, but that which we can call upon without having to focus on it? I mean this honestly, no snark. When I was a kid, learning how to factor numbers was really hard. It took a lot of time and concentration to do even basic problems, and people who could do it quickly without much perceived effort were a mystery to me. By the time I reached high school, I had enough practice that I recognized the common patterns without difficulty, and often the answer bubbled up to my conscious mind without thinking about it at all. It sure feels like my brain is making an API call to a subsystem, you know?
sebzim4500 4y ago
He's not really saying that GPT-4 is a 'math genius', rather the combined system of GPT-4 and Wolfram is.
- dvt 4y ago
  But that doesn't really mean much. It's like saying I'm a "geography genius" while I have Google Earth open.
  - atonse 4y ago
    And if you had Google earth hooked up to hidden headphones without us being able to tell, you would seem like a geography genius to us. that’s the point. it seems like you’re arguing whether the genius label only has to be innate. But if you are able to effectively get help from sources, the effect can be the same.
  - pixl97 4y ago
    It's a question of latency... It takes you, what, seconds to type digits into a calculator? But if you embedded a calculator into your brain and could put in and pull values out of it in microseconds how are you different from a math genius? Same with millisecond access to Google earth, at some point smarts+speed of access is a system within itself.
    - dvt 4y ago
      > But if you embedded a calculator into your brain and could put in and pull values out of it in microseconds how are you different from a math genius? Tao, Perelman, Wiles etc. aren't math geniuses because they can multiply numbers fast (which is a super weird definition of "math genius" tbh). They're math geniuses because they answer really hard questions in creative and unexpected ways; ways that often open up entire new areas of mathematics.
      - aik 4y ago
        I think you’re sidestepping the point here. The point is that the combo of these systems becomes one unit. One integrated system. That’s the new system to measure. Similarly, your prefrontal cortex without a hippocampus sucks. The combo of them (and other distinct parts of the brain that handle specific functions and have specific purposes that interact with other parts in a specific way) - that is what causes our specific type of intelligence to emerge. The brain as a whole is much more interesting and practical to measure.
        dvt 4y ago
        Yeah this is a valid criticism of the Chinese Room (called the "Systems Counterargument")[1]. I think it's a weak-ish riposte in this context though, mainly because we have no real idea how our own brains work and how their parts causaly interact (other than handwavy "these neurons are firing in this area"). [1] https://iep.utm.edu/chinese-room-argument/#SH2a https://iep.utm.edu/chinese-room-argument/#SH2a
Workaccount2 4y ago
It goes back to my original point, that I suspect AGI will come from an AI that is essentially a master of all APIs. We can go back and forth splinting hairs about whether inserting a compute module into a neural net (organic or not) grants geniousness or assistance, but the overall point stands; there will be a single interface that can take any variety of inputs and properly parse and shape them, push them through the correct "APIs", and then take the results to form a clear and correct output. Whether or not it used it's neural net or transistor adders circuits to arrive at the answer would be immaterial.

jules 4y ago

Wolfram Alpha is computation. So it became a computational genius in precisely the things that Wolfram Alpha can do. A better test is whether it can prove new lemmas, like the average undergraduate in mathematics. From what I tried, it cannot do that yet. I'm convinced that doesn't require a breakthrough in the architecture or scale of LLMs, though. GPT-4 seems plenty smart enough to be able to learn that, if hooked up to a proof assistant like Lean or Coq with the right fine tuning iteration loop.