> we ask them to stop testing advanced mathematical problems on proprietary models.
Maybe I'm alone on this, but for some reason these sorts of requests strike me as akin to gatekeeping how someone should breathe air. It's math... the numbers and symbols are just out there in the platonic realm available for anyone to do as they like with them. It's patently absurd to request other people to stop.
Ensuring credit where credit is due? That's fine. If your model incorporates the efforts of many others, then it's reasonable to request acknowledgement of everyone who contributed (even indirectly). But that's not what the request states — presumably their ask subsumes any advanced ML model, including those that weren't trained on a giant corpus of text.
The problem with proprietary models is that you don't get to poke inside and see what it is doing and how it arrives at its answer, which is precisely what mathematicians do. Mathematical understanding derives less from any particular result than the insights and methods that pave the road to results. Whenever a theorem is proved, researchers seek to unpack the proof and get inside the author's mind to learn their ways of thinking.
LLM generated results might benefit mathematical understanding if people can inspect their intermediate reasoning traces to discover erroneous human biases or patterns that they might have previously overlooked. Otherwise, the results might as well be produced by oracles.
>Otherwise, the results might as well be produced by oracles.
no. The math result is a result only when it includes proof. The proof is the value here. The way somebody came to it isn't really important - we don't know how Newton came to his results, whether it was apple or pear, and it isn't really important. Or how Einstein was walking the city streets looking at the tower watches - it is just historic curiosity having no real value for science.
That has been one of the greatest thing about math departments - smooth talkers were always clearly visible as smooth talkers. You're either producing proofs, or you're anything but a mathematician.
I feel for mathematicians. They have similar situation like we have in programming. Well, we all just have to evolve and adjust (in particular reign in our pride as just in a few years - i think once LLMs start hitting 100T+ - we may loose our "top of God's creation" position). Any attempts at gatekeeping, ludditing, organizing in quasi observational/advisory boards really intended to protect their tenures, etc. ... - well, you just can't stop the wave.
It all reminds how Catholic Church insisted on responsible release of the Bible in German. The Church even unleashed the devastating 30 Years War trying to protect its monopoly on religion including the right to sell indulgences, etc.
>AI labs should provide significant support, including funding
And now all those "responsible math" and advisory boards would like to preserve their monopoly on math and would like to sell the indulgences to the AI labs. As usually it is all about money and power, not about science. As a Math PhD dropout myself i feel a bit of a shame and disappointment for that undignified scramble by the mathematics establishment. Being smart they should have led the way and show an example to the rest of humanity ...
> The math result is a result only when it includes proof. The proof is the value here. The way somebody came to it isn't really important - we don't know how Newton came to his results, whether it was apple or pear, and it isn't really important. Or how Einstein was walking the city streets looking at the tower watches - it is just historic curiosity having no real value for science.
This mischaracterizes the role of rigourous proofs in mathematical understanding. While undergrads and early grad students focus primarily on proofs, formalism recedes into the secondary role of honing intuition as mathematicians transition to their "post-rigourous" stage of development[1].
The importance of intuition in mathematics cannot be overstated. That's why people go to math talks even when the actual results are codified in papers. In a less formal setting, they get to pick the author's brain to learn their mental pictures and heuristics that don't make their way into papers. Those would be analogous to chain-of-thought traces and agent-to-agent messages for a computer generated result.
throwaway713 · · focus · HN ↗
Maybe I'm alone on this, but for some reason these sorts of requests strike me as akin to gatekeeping how someone should breathe air. It's math... the numbers and symbols are just out there in the platonic realm available for anyone to do as they like with them. It's patently absurd to request other people to stop.
Ensuring credit where credit is due? That's fine. If your model incorporates the efforts of many others, then it's reasonable to request acknowledgement of everyone who contributed (even indirectly). But that's not what the request states — presumably their ask subsumes any advanced ML model, including those that weren't trained on a giant corpus of text.
curt15 · · focus · HN ↗
LLM generated results might benefit mathematical understanding if people can inspect their intermediate reasoning traces to discover erroneous human biases or patterns that they might have previously overlooked. Otherwise, the results might as well be produced by oracles.
trhway · · focus · HN ↗
no. The math result is a result only when it includes proof. The proof is the value here. The way somebody came to it isn't really important - we don't know how Newton came to his results, whether it was apple or pear, and it isn't really important. Or how Einstein was walking the city streets looking at the tower watches - it is just historic curiosity having no real value for science.
That has been one of the greatest thing about math departments - smooth talkers were always clearly visible as smooth talkers. You're either producing proofs, or you're anything but a mathematician.
I feel for mathematicians. They have similar situation like we have in programming. Well, we all just have to evolve and adjust (in particular reign in our pride as just in a few years - i think once LLMs start hitting 100T+ - we may loose our "top of God's creation" position). Any attempts at gatekeeping, ludditing, organizing in quasi observational/advisory boards really intended to protect their tenures, etc. ... - well, you just can't stop the wave.
It all reminds how Catholic Church insisted on responsible release of the Bible in German. The Church even unleashed the devastating 30 Years War trying to protect its monopoly on religion including the right to sell indulgences, etc.
>AI labs should provide significant support, including funding
And now all those "responsible math" and advisory boards would like to preserve their monopoly on math and would like to sell the indulgences to the AI labs. As usually it is all about money and power, not about science. As a Math PhD dropout myself i feel a bit of a shame and disappointment for that undignified scramble by the mathematics establishment. Being smart they should have led the way and show an example to the rest of humanity ...
curt15 · · focus · HN ↗
This mischaracterizes the role of rigourous proofs in mathematical understanding. While undergrads and early grad students focus primarily on proofs, formalism recedes into the secondary role of honing intuition as mathematicians transition to their "post-rigourous" stage of development[1].
The importance of intuition in mathematics cannot be overstated. That's why people go to math talks even when the actual results are codified in papers. In a less formal setting, they get to pick the author's brain to learn their mental pictures and heuristics that don't make their way into papers. Those would be analogous to chain-of-thought traces and agent-to-agent messages for a computer generated result.
[1]: <a href="https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/" rel="nofollow">https://terrytao.wordpress.com/career-advice/theres-more-to-...