Can computers be mathematicians?
quantamagazine.org
Can computers be mathematicians?
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Re: Can computers be mathematicians?
#2Search for 24:07, about 3/4 down where Strogatz poses the question: "do you imagine ... there will be a time when the descendants of Lean will be able to teach themselves math, rather than having human teachers creating libraries?"
Re: Can computers be mathematicians?
#3Search for 24:07, about 3/4 down where Strogatz poses the question: "do you imagine ... there will be a time when the descendants of Lean will be able to teach themselves math, rather than having human teachers creating libraries?"
It's interesting because Kevin Buzzard in this interview basically says that other people are interested in the application of AI to proof generation, but he's not so interested in that.
But in an earlier Quanta article, he sort of said he was:
https://www.quantamagazine.org/at-the-international-mathemat...
I guess the IMO work is more about having computers automatically apply known theorems and techniques to novel (but not, fundamentally, "unsolved"!) problems, while this interview alludes to the more difficult task of getting computers to solve unsolved mathematics problems, and discover proofs of interesting theorems from scratch?
Re: Can computers be mathematicians?
#4Related:
Advancing mathematics by guiding human intuition with AI
Re: Can computers be mathematicians?
#5This is related to my pet favorite question of who is doing the art if an artist uses AI (e.g. [input image] -> Photoshop painting/masking -> AI Upscaler -> Crop and Print to Physical Medium?
I think I feel like an artist, but part of the production of this art feels like curation, and not precisely the practice of art. The eye for composition feels similarly artistic, but the inability of envisioning the final product at the early stages (pre-AI steps) of the work is very weird, and might be the bright red line. I don’t know how I feel yet.
I have a project titled “Is This Art?” currently showing at a local coffee shop - avoiding the issue.
Re: Can computers be mathematicians?
#6This is related to my pet favorite question of who is doing the art if an artist uses AI (e.g. [input image] -> Photoshop painting/masking -> AI Upscaler -> Crop and Print to Physical Medium? I think I feel like an artist, but part of the production of this art feels like curation , and not precisely the practice of art. The eye for composition feels similarly artistic, but the inability of envisioning the final prod…
Was Duchamp the artist or the factory worker who produced the urinal? Sometimes the curation is the art.
Re: Can computers be mathematicians?
#7Search for 24:07, about 3/4 down where Strogatz poses the question: "do you imagine ... there will be a time when the descendants of Lean will be able to teach themselves math, rather than having human teachers creating libraries?"
It's interesting because Kevin Buzzard in this interview basically says that other people are interested in the application of AI to proof generation, but he's not so interested in that. But in an earlier Quanta article, he sort of said he was: https://www.quantamagazine.org/at-the-international-mathemat... I guess the IMO work is more about having computers automatically apply known theorems and techniques to novel…
Buzzard as far as I'm aware is interested in finding mistakes in mathematical work by "real" (i.e. in his own words people doing topology rather than category theory) mathematicians, so that position makes sense.
Re: Can computers be mathematicians?
#8This is from the Joy of Why podcast.
Re: Can computers be mathematicians?
#9This is related to my pet favorite question of who is doing the art if an artist uses AI (e.g. [input image] -> Photoshop painting/masking -> AI Upscaler -> Crop and Print to Physical Medium? I think I feel like an artist, but part of the production of this art feels like curation , and not precisely the practice of art. The eye for composition feels similarly artistic, but the inability of envisioning the final prod…
I'm no artist but I've had an idea for a minor art project and please feel free to steal this. It's called "I pay rent therefore I am."
Basically, a neural network is set up in a public space. The artificial neurons are literally shown as Christmas lights. This neural network has a few little gadgets it can control to entertain you. Let's say, a puppet, an electronic keyboard, a pen plotter. But, the installation is not here for your entertainment. You have to pay the neural network if you want to be entertained. There's a small interface where you can make an offer, and it can either accept or counter offer, and then you can either accept or counter offer, until either one of you says "I'm walking away from this" or until there's an agreement and you insert cash. Behind the scenes, the neural network is learning how to optimize the objective function "make money", quietly figuring out which entertaining things it is good at and which are most profitable. In other words, just like us, the neural network is motivated by its need to pay rent.
Cut the artist out of the equation completely and have the artwork work for itself. If the machine has full creative control, and can even say no to you, does it have free will?
Re: Can computers be mathematicians?
#10Disappointing that there's no mention of infinities.
How do you teach a computer to think in symbolic terms about Cantor's concepts of infinity? There's no computational representation for irrational numbers, and barely for rational numbers. Even floating-point representations are a long-standing problems - and integers? Overflows are a problem, even just signed integers are a problem.
The pencil-and-paper mathematicians and their symbolic representations of infinities, will computers and AI ever come to grasps with that?
i.e. https://www.bbvaopenmind.com/en/science/mathematics/georg-ca...