Technology @lemmy.world boem @lemmy.world 3 wk. ago

Why mathematics is set to be revolutionized by AI

www.nature.com Why mathematics is set to be revolutionized by AI

Cheap data and the absence of coincidences make maths an ideal testing ground for AI-assisted discovery — but only humans will be able to tell good conjectures from bad ones.

22 comments

AI is insanely bad at distinguishing fact from hallucination, which seems like a terrible match for math
- The article is about using computers to discover new conjectures (mathematical statements that are not yet known to be true or false). The conjecture can be then later be formally proven (or disproven) by humans.
  
  Sounds like a good match for me. Formulating conjectures is about finding an interesting pattern and argue that this pattern holds true. Computers are getting increasingly better at pattern matching, so why not use them?
  
  Title is a bit clickbaity by calling it AI.
  
  Title is a bit clickbaity by calling it AI.
  
  That's literally every article about "AI".
  
  ... the London Institute for Mathematical Sciences, of which I am director
  
  There's the reason. Self-promotion.
- AI isn't just LLMs.
  
  No one is talking about automated theorem provers (see 4 coloring theorem) or symbolic solvers (see Mathematica). These tools already revolutionized math decades ago.
  
  The only thing that came out in the past year or two are LLMs. Which is clearly overhyped bullshit.
- I haven't read this article, but the one place machine learning is really really good, is narrowing down a really big solution space where false negatives and false positives are cheap. Frankly, I'm not sure how you'd go about training an AI to solve math problems, but if you could figure that out, it sounds roughly like it would fit the bill. You just need human verification as the final step, with the understanding that humans will rule out like 90% of the tries, but if you only need one success that's fine. As a real world example machine learning is routinely used in astronomy to narrow down candidate stars or galaxies from potentially millions of options to like 200 that can then undergo human review.
This might be a worthy application.
Set to be revolutionized by AI because AI can't do math.

Says my brother, a Math Professor that works with people trying to develop AI
- AI is math, statistics specifically.
  
  While AI is math most AI cannot do any math.
  
  But in fairness, this is probably all about matching up formal logic tokens, which wouldn't require the ability to add 2 and 2.
  
  AI can't count the number of letters in a word
The article isn't about automatic proofs, but it'd be interesting to see a LLM that can write formal proofs in Coq/Lean/whatever and call external computer algebra systems like SageMath or Mathematica.
- I was thinking something similar: If you have the computer write in a formal language, designed in such a way that it is impossible to make an incorrect statement, I guess it could be possible to get somewhere with this
The absence of coincidence

Look up the strong law of small numbers.

Also, one of their examples of AI was an exhaustive search.
No
- Are you saying "No... let's not advance mathematics"? Or... "No, let's not advance mathematics using AI"?
  
  I was saying boourns
  
  Yes
  
  No
- Ok

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