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Comment by Workaccount2 | Hacker News Reader

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.

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> 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.

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?

He's not really saying that GPT-4 is a 'math genius', rather the combined system of GPT-4 and Wolfram is.

But that doesn't really mean much. It's like saying I'm a "geography genius" while I have Google Earth open.

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.

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.

> 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.

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.

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

I think the most likely case is that the properties of a system that leads to emergent behavior (part of complexity science) are very much present in the brain where the various components with a proper balance leads to the intelligence we have.

An interesting intelligence emerges from a colony of ants compared to one. An interesting intelligence emerges from the relations of the various parts of the brain. An interesting intelligence emerges from the combo of techniques that have led to GPT and other surprising AIs. Same with a human, to two humans collaborating, to tribes to companies to cities etc. And likely same by combining/integrating GPT-4 type of LLMs with other tools and with other specific purpose LLMs - a greater unit of significance will emerge. (The non-predictability of this with current science is what is kind of scary to me.)

>> Tao, Perelman, Wiles etc. aren't math geniuses because they can multiply numbers fast

You're getting stuck on semantics.

I expect Tao, Perelman, Wiles, etc. can process/handle/deal with numbers much more rapidly than I can.

Now imagine if these folks could do the same, except 10x or 100x or 1000x faster, without having to ever be bothered with things like sleep or food.

This may not be a good definition of a "Math Genius" but it is reasonable to think that all or most "Math Geniuses" possess this skill. Speed matters.

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.

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.

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