Where will that hypothetical superintelligent mathematics machine be built?
--- all AI labs will have it.
Who will operate it?
--- for easy mathematics (defined in terms of the computational resources, not difficulty for a human), everyone will have access to it. Just like everyone has access to calculators. All mathematics that can be done by humans without the help of AI is by definition easy. For difficult mathematics, only those with resources will have access to it. The problem will need to justify the resources (eg grants in the case of research).
How will it be powered?
--- the economic benefit of energy is getting higher and higher, so this incentives to produce more energy is there. It will be powered by whatever means we can find.
Who will build it?
--- again, all AI labs.
And why?
--- they will build it because it is with much more than thousands of trillions of dollars
So you believe that pure mathematics is "worth much more than thousands of trillions of dollars?" Or perhaps you misunderstood the point of the question?
No, this touches on what I said below. You seem to be under the impression that a machine that is better than any mathematician will need to be a specialized machine. It won't. Any conjecture that a human can solve is by definition computationally easy to solve, and hence it will be cheap.
That has absolutely nothing to do with the purpose of my post. Your science fiction about mathematics has the same setup and build as the scenario reported here, but it is still missing the payoff. So the question is: where's the payoff?
I am not sure I understand your argument, the same money the finances mathematicians now can finance mathematics done with AI. There's nothing special with mathematicians. There's something special with mathematics, in the sense that it's easier to automatize than other human activities. The value of many mathematicians will go down (eg, "theorem provers"). The value of other mathematicians will go up (theory builders). Most scientists will be able to do custom mathematics on their own, the AI will do that for them. For example, Einstein would not be handicapped as he was. Etc.
So university students (and their parents) will in the future be financing AI mathematicians? And since the AI will not be specialized, so will be able to do anything, the actual access to the machines will not cost more than a university education, and university purchases will contribute part of the industry's return on investment. That is definitely one way to fill in a few, though hardly all, of the missing pages. Why, for example, would students' parents want to pay machines to prove theorems?
Mathematicians are special in at least one way that most students' parents are not: mathematicians care about mathematics.
The claim that mathematics is easier to automate than other human activities actually requires some argument in order to be credible, but that's not relevant to the present post.
If the Hodges Conjecture can be solved by a human brain, it means it's easy to solve and will be solved by computer cheaply in the not so distant future.
"It is delusional to think that any corporation will invest 200 trillion dollars to cover the earth’s surface with data centers in order to prove the Hodge Conjecture."
So the error in your reasoning is to think that this argument matters for anything. If this is something a human can do, then by definition you don't need 200 trillion dollars to do it.
Problems that not within the reach of AI are also not within the reach of humanity without AI.
What are you talking about man? There is a giant error in your argument. There are a ton of things humans cannot do without capital expensive machines. But usually, when they spend trillions of dollars on something ... they expect a return on it. Like humans could not do mathematics without 1) writing, 2) pencils or 3) paper ... but those are cheap. The point isn't that AGI won't be able to "solve x" ... but we have a name for people that "operate mathematical machinery to solve mathematical questions": "Mathematicians". They decide what questions to ask, based on what they all find interesting. Sometimes questions and ideas are difficult to formulate, and even harder to formalize. If there are zero people left to ask certain types of mathematical questions ... then there is no point to build a machine to answer them (irrespective of it being general purpose or specialized). And if you think that the only people who ask mathematical questions are scientists and that they ask the entire gamut of mathematical questions ... then I am not sure how you found your way to the substack of a number theorist. **Someone has to understand the symbols that come out of the god machine!!**
Huh, this feels like a point that is painfully obvious after you've heard someone make it, but I'm not sure I've thought about it so explicitly before. Thank you for that! I wonder if the same goes even for seemingly incremental uses of AI, for example, just today Scott Aaronson is blogging about using AI for part of a proof but it took some back-and-forth for the machine to get it right, and you sorta have to ask the question about just how many resources are needed to eliminate that back-and-forth, especially for some bigger step in a proof.
I'm sincerely hoping for one of the people who predict that machines will "solve" mathematics to explain how they think this will work in practice. So far several days have gone by and no one has offered an explanation.
"No: the error I’m highlighting here is purely logical. More precisely, it is logical as soon as you grant that any process of any kind that can be described in words or represented on a screen can only be realized as a material process in the physical world.' Tech philosopher Nicholas Gessler (who's Kate Hayles husband) has been making this vital point for 40 years. You may like to see my interview with him in Cabinet - he has a magnificent collection of physical computation devices through the ages to support this argument. https://www.cabinetmagazine.org/issues/21/wertheim_gessler.php
1) NL is behind US in their drugs policies - possession of weed is still a misdemeanor. There was never a full legalize. What happened was that police stopped prosecuting these misdemeanors. It's called gedooggebied - "zone of tolerance". (As a naturalized Dutch citizen, I just must comment on this :-))
2) Where is a juicy quote from Erdos promoting amphetamines as a brain opener? :-)
Where will that hypothetical superintelligent mathematics machine be built?
--- all AI labs will have it.
Who will operate it?
--- for easy mathematics (defined in terms of the computational resources, not difficulty for a human), everyone will have access to it. Just like everyone has access to calculators. All mathematics that can be done by humans without the help of AI is by definition easy. For difficult mathematics, only those with resources will have access to it. The problem will need to justify the resources (eg grants in the case of research).
How will it be powered?
--- the economic benefit of energy is getting higher and higher, so this incentives to produce more energy is there. It will be powered by whatever means we can find.
Who will build it?
--- again, all AI labs.
And why?
--- they will build it because it is with much more than thousands of trillions of dollars
So you believe that pure mathematics is "worth much more than thousands of trillions of dollars?" Or perhaps you misunderstood the point of the question?
No, this touches on what I said below. You seem to be under the impression that a machine that is better than any mathematician will need to be a specialized machine. It won't. Any conjecture that a human can solve is by definition computationally easy to solve, and hence it will be cheap.
That has absolutely nothing to do with the purpose of my post. Your science fiction about mathematics has the same setup and build as the scenario reported here, but it is still missing the payoff. So the question is: where's the payoff?
I am not sure I understand your argument, the same money the finances mathematicians now can finance mathematics done with AI. There's nothing special with mathematicians. There's something special with mathematics, in the sense that it's easier to automatize than other human activities. The value of many mathematicians will go down (eg, "theorem provers"). The value of other mathematicians will go up (theory builders). Most scientists will be able to do custom mathematics on their own, the AI will do that for them. For example, Einstein would not be handicapped as he was. Etc.
So university students (and their parents) will in the future be financing AI mathematicians? And since the AI will not be specialized, so will be able to do anything, the actual access to the machines will not cost more than a university education, and university purchases will contribute part of the industry's return on investment. That is definitely one way to fill in a few, though hardly all, of the missing pages. Why, for example, would students' parents want to pay machines to prove theorems?
Mathematicians are special in at least one way that most students' parents are not: mathematicians care about mathematics.
The claim that mathematics is easier to automate than other human activities actually requires some argument in order to be credible, but that's not relevant to the present post.
If the Hodges Conjecture can be solved by a human brain, it means it's easy to solve and will be solved by computer cheaply in the not so distant future.
"It is delusional to think that any corporation will invest 200 trillion dollars to cover the earth’s surface with data centers in order to prove the Hodge Conjecture."
So the error in your reasoning is to think that this argument matters for anything. If this is something a human can do, then by definition you don't need 200 trillion dollars to do it.
Problems that not within the reach of AI are also not within the reach of humanity without AI.
What are you talking about man? There is a giant error in your argument. There are a ton of things humans cannot do without capital expensive machines. But usually, when they spend trillions of dollars on something ... they expect a return on it. Like humans could not do mathematics without 1) writing, 2) pencils or 3) paper ... but those are cheap. The point isn't that AGI won't be able to "solve x" ... but we have a name for people that "operate mathematical machinery to solve mathematical questions": "Mathematicians". They decide what questions to ask, based on what they all find interesting. Sometimes questions and ideas are difficult to formulate, and even harder to formalize. If there are zero people left to ask certain types of mathematical questions ... then there is no point to build a machine to answer them (irrespective of it being general purpose or specialized). And if you think that the only people who ask mathematical questions are scientists and that they ask the entire gamut of mathematical questions ... then I am not sure how you found your way to the substack of a number theorist. **Someone has to understand the symbols that come out of the god machine!!**
Several typos (iPhone + autocorrect), but you understand the message.
Also you seem to be under the impression that you will need a special model for mathematics. You won't.
Huh, this feels like a point that is painfully obvious after you've heard someone make it, but I'm not sure I've thought about it so explicitly before. Thank you for that! I wonder if the same goes even for seemingly incremental uses of AI, for example, just today Scott Aaronson is blogging about using AI for part of a proof but it took some back-and-forth for the machine to get it right, and you sorta have to ask the question about just how many resources are needed to eliminate that back-and-forth, especially for some bigger step in a proof.
I'm sincerely hoping for one of the people who predict that machines will "solve" mathematics to explain how they think this will work in practice. So far several days have gone by and no one has offered an explanation.
"No: the error I’m highlighting here is purely logical. More precisely, it is logical as soon as you grant that any process of any kind that can be described in words or represented on a screen can only be realized as a material process in the physical world.' Tech philosopher Nicholas Gessler (who's Kate Hayles husband) has been making this vital point for 40 years. You may like to see my interview with him in Cabinet - he has a magnificent collection of physical computation devices through the ages to support this argument. https://www.cabinetmagazine.org/issues/21/wertheim_gessler.php
1) NL is behind US in their drugs policies - possession of weed is still a misdemeanor. There was never a full legalize. What happened was that police stopped prosecuting these misdemeanors. It's called gedooggebied - "zone of tolerance". (As a naturalized Dutch citizen, I just must comment on this :-))
2) Where is a juicy quote from Erdos promoting amphetamines as a brain opener? :-)