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The fall of the theorem economy

davidbessis.substack.com

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Re: The fall of the theorem economy

#5

Post by jdw64 »

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?

Re: The fall of the theorem economy

#6

Post by pfortuny »

jdw64 wrote: post #5

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 enou…

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

Re: The fall of the theorem economy

#7

Post by jvanderbot »

pfortuny wrote: post #6
jdw64 wrote: post #5

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 enou…

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

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.

Re: The fall of the theorem economy

#8

Post by pfortuny »

jvanderbot wrote: post #7
pfortuny wrote: 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

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.

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

Re: The fall of the theorem economy

#9

Post by bsenftner »

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.

Re: The fall of the theorem economy

#10

Post by octopus143 »

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
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