4 ms·

Let's put it this way, from another mathematician, and I'm sure I'll probably be shot for this one. Every LLM release moves half of the remaining way to the mi

Let's put it this way, from another mathematician, and I'm sure I'll probably be shot for this one. Every LLM release moves half of the remaining way to the minimum viable goal of replacing a third class undergrad. If your business or research initiative is fine with that level of competence then you will find utility. The problem is that I don't know anyone who would find that useful. Nor does it fit within any existing working methodology we have. And on top of that the verification of any output can take considerably longer than just doing it yourself in the first place, particularly where it goes off the rails, which it does all the time. I mean it was 3 months ago I was arguing with a model over it not understanding place-value systems properly, something we teach 7 year olds here? But the abstract problem is at a higher level. If it doesn't become a general utility for people outside of mathematics, which is very very evident at the moment by the poor overall adoption and very public criticism of the poor result quality, then the funding will dry up. Models cost lots of money to train and if you don't have customers it's not happening and no one is going to lend you the money any more. And then it's moot.

binarymax 2y ago
This is a great point that nobody will shoot you over :) But the main question is still: assuming you replace an undergrad with a model, who checks the work? If you have a good process around that already, and find utility as an augmented system, then get you’ll get value - but I still think it’s better for the undergrad to still have the job and be at the wheel, and does things faster and better when leveraging a powerful tool.
- hyhconito 2y ago
  Shot already for criticising the shiny thing (happened with crypto and blockchain already...) Well to be fair no one checks what the graduates do properly, even if we hired KPMG in. That is until we get sued. But at least we have someone to blame then. What we don't want is something for the graduate to blame. The buck stops at someone corporeal because that's what the customers want and the regulators require. That's the reality and it's not quite as shiny and happy as the tech industry loves to promote itself. My main point, probably cleared up with a simple point: no one gives a shit about this either way.
meroes 2y ago
Well said. As someone with only a math undergrad and as a math RLHF’er, this speaks to my experience the most. That craving for an understanding an elegant proof is nowhere to be found with verifying an LLM’s proof. Like sure, you could put together a car by first building an airplane, disassembling all of it minus the two front seats, and having zero elegance and still get a car at the end. But if you do all that and don’t provide novelty in results or useful techniques, there’s no business. Hell, I can’t even get a model to calculate compound interest for me (save for the technicality of prompt engineering a python function to do it). What do I expect?
qnleigh 2y ago
I think there's a pretty good case to be made that LLMs paired with automated theorem provers will become a useful tool to working mathematicians in the next few years. Another thread here links to a lecture from a professor of mathematics who makes this point about halfway in, based solely on Alpha Proofs current abilities (https://www.youtube.com/watch?v=vYCT7cw0ycw https://www.youtube.com/watch?v=vYCT7cw0ycw [54min]). Terence Tao, well-known mathematician at UCLA has been saying similar things for years. He's blogged about LLMs helping to learn new tools (like Lean) and occasionally helping with brainstorming. At this stage, the point they're making isn't 'OMG AGI!!!' but rather something like 'having an enthusiastic, often wrong undergrad assistant who's available 24/7 can be useful, if you use it carefully.'

binarymax 2y ago

This is a great point that nobody will shoot you over :) But the main question is still: assuming you replace an undergrad with a model, who checks the work? If you have a good process around that already, and find utility as an augmented system, then get you’ll get value - but I still think it’s better for the undergrad to still have the job and be at the wheel, and does things faster and better when leveraging a powerful tool.

hyhconito 2y ago
Shot already for criticising the shiny thing (happened with crypto and blockchain already...) Well to be fair no one checks what the graduates do properly, even if we hired KPMG in. That is until we get sued. But at least we have someone to blame then. What we don't want is something for the graduate to blame. The buck stops at someone corporeal because that's what the customers want and the regulators require. That's the reality and it's not quite as shiny and happy as the tech industry loves to promote itself. My main point, probably cleared up with a simple point: no one gives a shit about this either way.

meroes 2y ago

Well said. As someone with only a math undergrad and as a math RLHF’er, this speaks to my experience the most. That craving for an understanding an elegant proof is nowhere to be found with verifying an LLM’s proof. Like sure, you could put together a car by first building an airplane, disassembling all of it minus the two front seats, and having zero elegance and still get a car at the end. But if you do all that and don’t provide novelty in results or useful techniques, there’s no business. Hell, I can’t even get a model to calculate compound interest for me (save for the technicality of prompt engineering a python function to do it). What do I expect?

qnleigh 2y ago

I think there's a pretty good case to be made that LLMs paired with automated theorem provers will become a useful tool to working mathematicians in the next few years. Another thread here links to a lecture from a professor of mathematics who makes this point about halfway in, based solely on Alpha Proofs current abilities (https://www.youtube.com/watch?v=vYCT7cw0ycw https://www.youtube.com/watch?v=vYCT7cw0ycw [54min]). Terence Tao, well-known mathematician at UCLA has been saying similar things for years. He's blogged about LLMs helping to learn new tools (like Lean) and occasionally helping with brainstorming. At this stage, the point they're making isn't 'OMG AGI!!!' but rather something like 'having an enthusiastic, often wrong undergrad assistant who's available 24/7 can be useful, if you use it carefully.'