The Fall of the Theorem Economy

62 pointsposted 3 hours ago
by varjag

14 Comments

stackbutterflow

a minute ago

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 or surpass the collective output of the entire human scientific community the equation will change.

It's a sad outlook.

bsenftner

15 minutes ago

This kills me, it is correct, but misses the forest for the trees. Yes, mathematics is a discipline of understanding, but an insular one. The entire field is about trying to understand, but the discipline does not try to be understood. No, that is "your job, not theirs" and that is why this discipline is struggling, struggling in a culture that can barely communicate without emotional morons destroying any constructive communications.

mojosmojo

2 hours ago

Incredibly thoughtful. This essay gives that very rare sense of being well reasoned, gods at forest and trees, and sitting atop a shit ton of domain expertise.

jdw64

an hour ago

Someday, there might be mathematics designed for AI. Mathematics that only a tiny fraction of humans can understand, but a different kind of mathematics might emerge. I wonder if we would still call it mathematics.

What would happen if a non-human layer of mathematics emerged on top of human mathematics? In this article, the distinction between Mathlib and Mathslop might be a precursor to that.

If models advance enough in the future, and new definitions, compressions, and representational forms that are convenient for AI-to-AI communication emerge, what would happen then? Would mathematics split into Human-facing and Machine-facing branches?

pfortuny

44 minutes ago

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

jvanderbot

40 minutes ago

Agree, but more specifically Math is clearly about a human understanding structure of things. Math is basically for humans. It's one of the main reasons understandable proof is so important.

pfortuny

36 minutes ago

Well, by "understanding" I mean "understanding by humans", indeed.

jdw64

4 minutes ago

So what I’m most curious about is this: if there are axioms and proofs so enormous that a human could never prove them in a lifetime, but a machine can, does that make it engineering? That’s the point I’m really wondering about.

I mean, what if a human could follow every single step of the process in principle, but the sheer volume is so vast that a human can never see the whole thing—would that be engineering?

But I don’t think of that as engineering. In the future, maybe it will be called an Oracle

varjag

11 minutes ago

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

j7ake

an hour ago

Does the the ⁡(,1) conjecture paper in annnals of Math say 7 years between submission and acceptance? Insane

bananaflag

9 minutes ago

These stories are common in math, e.g. these recently happened to me, a lowly mathematician:

1) Two and a half years with no reply from a journal (not even to emails I sent that I'd like to retract the paper so I could send it somewhere else). Then suddenly they tell me the paper is accepted.

2) One year with no reply. Then, my "anxious" collaborator sends them countless emails and gets redirected from person to person and finally an editor tells us that they decided almost immediately to reject our paper but they didn't tell us because "they hate giving bad news".

These were not top journals like Annals, but decent, prestigious ones, from whom you'd expect some professionalism.

cubefox

4 minutes ago

This might be the most interesting essay on the nature of mathematics I have ever read.

khalic

2 hours ago

I see the AI panic has reached mathematics…

octopus143

11 minutes ago

Some previous submissions

HN history

  +-- 2mo before by sdfrew
  |   4 points / 1 comments
  |   The Fall of the Theorem Economy
  |   https://news.ycombinator.com/item?id=47862472
  |
  +-- 2mo before by fuglede_
  |   3 points / 1 comments
  |   The Fall of the Theorem Economy
  |   https://news.ycombinator.com/item?id=47891494
  |
  +-- 2mo before by mathgenius
  |   2 points / 0 comments
  |   The Fall of the Theorem Economy
  |   https://news.ycombinator.com/item?id=47909751
  |
  +-- 2mo before by delis-thumbs-7e
  |   15 points / 4 comments
  |   David Bessis on AI destroying mathematics
  |   https://news.ycombinator.com/item?id=47985962
  |
  +-- 1mo before by magoghm
  |   4 points / 0 comments
  |   The Fall of the Theorem Economy
  |   https://news.ycombinator.com/item?id=48084737
  |
  +-- 1mo before by cubefox
  |   2 points / 0 comments
  |   The Fall of the Theorem Economy
  |   https://news.ycombinator.com/item?id=48089716
  |
  +-- 1mo before by cubefox
  |   5 points / 0 comments
  |   The Fall of the Theorem Economy
  |   https://news.ycombinator.com/item?id=48152469
  |
  +-- 1mo before by tmp10423288442
  |   4 points / 1 comments
  |   The Fall of the Theorem Economy
  |   https://news.ycombinator.com/item?id=48214866
  |
  `-- this submission by varjag
      58 points / 7 comments
      The Fall of the Theorem Economy
      https://news.ycombinator.com/item?id=48758048