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The fall of the theorem economy

davidbessis.substack.com

21–30 of 127 posts

Re: The fall of the theorem economy

#21
post #16

The core thesis seems to be that the "real value" is not in producing/proving theorems, but in understanding them. AI might be good at producing and proving theorems, but it fails utterly at getting humans to understand them. Even worse, humans have no interest in working on theorems that have already been proven, so we end up with theorems that will never be understood by humans. I can understand why this is a major…

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Re: The fall of the theorem economy

#22

Tangential but this article got me thinking. Are we going to see less publicly shared science? With private actors or governments restricting access to AI resources to a few scientists and keeping new knowledge to themselves. Advancing science in the open was the best strategy when there was real advantage to share the load with every brain on the planet willing to give a try at science, but if a computer can match o…

The intelligence is only one part of the story. People need to actually go out there and do experiments. Science is not only theory, but also experimental. The best science happens when experiments show that a previously held assumption was not true. Eg the Michaelson Morley experiment where the assumption of ether was disproved. While AI is an incredibly powerful tool, it does not replace the act of observation. Thus Im sure we will still have scientists in the future and some degree of open science. There are experiments out there that by nature of their complexity need massive public coordination (CERN for instance) which in turn benefits from openness.

What is going to suck though is the ladder for juniors. We dont start out by working on big ticket problems, but usually early career researchers solve really tiny problems in a cheap way. The lowest bar for a cash strapped PhD student would be to contribute to some new theory in some way even if the student doesnt have access to equipment.

Re: The fall of the theorem economy

#23

Tangential but this article got me thinking. Are we going to see less publicly shared science? With private actors or governments restricting access to AI resources to a few scientists and keeping new knowledge to themselves. Advancing science in the open was the best strategy when there was real advantage to share the load with every brain on the planet willing to give a try at science, but if a computer can match o…

> to share the load with every brain on the planet willing to give a try at science

This is what a lot of scientists love to tell themself or talk about in celebratory speeches.

The truth is: a lot of science is kept behind journal paywalls, so that only "officially approved" (in the sense of: working at a university or an governmental research institute) scientists can easily access it.

Re: The fall of the theorem economy

#24
> to come up with a conceptual framework where it became easy to express

Feels a lot like building software from bottom - once you get the building blocks defined right, the action, or the program, are trivial to express. When doing it from the top-down, you write the program using the building blocks you haven't defined yet, and you might end up with overly specific building blocks, needing other blocks for expressing different behaviors.

When you do the bottom-up building blocks right, new behavior is easy to express with them. Essentially, you are building up the language to reach the problem. Or making a DSL, whatever definition you like best.

Re: The fall of the theorem economy

#26

Is being pompous and on the nose part of being in mathematics? "I was in Switzerland", "I was invited to a talk", "I started a machine learning company", look at me bro.

Being invited to conference talks around the world is a completely normal part of being an active researcher in almost any academic field, so it doesn't register as pompous to other academics.

Re: The fall of the theorem economy

#27
post #11
post #6

Earlier quoted context omitted.

Science is not about results, it is about the transmission of knowledge. So long as those AI-"sciences" are just inside AI, they are "engineering", not science. I am not dismissing engineering (it moves the world we live in), just trying to clarify what science is. Applied fluid dynamics works like that: noone has ever really "verified" that the finite-element method applied to some specific model does converge

Engineering is used fairly loosely these days but I insist engineering ends where you have to prove theorems.

That’s a strange delineation. Engineering is essentially about designing a thing, asking whether that thing really does satisfy the desired criteria, and then iterating when it does not. Mathematical models of the world are tremendously useful to this practice—engineers don’t need to guess about many aspect of the real world: they have physics. What they want, more than anything else, is strong evidence that a property holds. Internal validity (proof) and external validity (experiment) are the best evidence that you can get—why would you throw one of those approaches away?

Re: The fall of the theorem economy

#28

Tangential but this article got me thinking. Are we going to see less publicly shared science? With private actors or governments restricting access to AI resources to a few scientists and keeping new knowledge to themselves. Advancing science in the open was the best strategy when there was real advantage to share the load with every brain on the planet willing to give a try at science, but if a computer can match o…

It's not even just science. Anyone producing anything digital is now heavily incentivized to keep their wares away from the public internet, in a way we've not seen before. Drop any sample of your unique production online, and the AIs will obsolete you in days. That is a massive loss for people looking for inspiration and guidance.

Re: The fall of the theorem economy

#29

Tangential but this article got me thinking. Are we going to see less publicly shared science? With private actors or governments restricting access to AI resources to a few scientists and keeping new knowledge to themselves. Advancing science in the open was the best strategy when there was real advantage to share the load with every brain on the planet willing to give a try at science, but if a computer can match o…

> to share the load with every brain on the planet willing to give a try at science This is what a lot of scientists love to tell themself or talk about in celebratory speeches. The truth is: a lot of science is kept behind journal paywalls, so that only "officially approved" (in the sense of: working at a university or an governmental research institute) scientists can easily access it.

You know how I read new papers back in 1994? By going to the library, finding one in bi-annual publication list and requesting it through the University system. And it better be necessary because the uni had to pay both the catalogue and each reprint of an article. The access is most certainly easier today.

Re: The fall of the theorem economy

#30
post #29

Earlier quoted context omitted.

> to share the load with every brain on the planet willing to give a try at science This is what a lot of scientists love to tell themself or talk about in celebratory speeches. The truth is: a lot of science is kept behind journal paywalls, so that only "officially approved" (in the sense of: working at a university or an governmental research institute) scientists can easily access it.

You know how I read new papers back in 1994? By going to the library, finding one in bi-annual publication list and requesting it through the University system. And it better be necessary because the uni had to pay both the catalogue and each reprint of an article. The access is most certainly easier today.

This was a lot because of the technological restrictions of that time.

Also be aware that the world wide web was actually conceived by Tim Berners-Lee for the exchange of information between scientists.

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