3 ms·

Might depend on the terms you have in mind, but current consensus seems to be more like 4-5 years as we speak on https://www.metaculus.com/questions/6728/ai-win

Might depend on the terms you have in mind, but current consensus seems to be more like 4-5 years as we speak on https://www.metaculus.com/questions/6728/ai-wins-imo-gold-medal/ https://www.metaculus.com/questions/6728/ai-wins-imo-gold-me...

auntienomen 3y ago
That's 4-5 years for solving Olympiad problems. Those are just very tricky high school math problems. They have solutions and can generally be solved by applying some combination of standard tricks. It's very much the sort of thing an LLM should be good at. Solving Millennium problems is a whole different ballgame. It's not known if these problems are solvable within ZFC axioms. (In one case, the Yang-Mills prize, stating the problem mathematically is part of the challenge.) All of the obvious applications of known tricks have been tried and failed. To solve such problems, one probably has to invent new and surprising mathematical definitions, building a framework in which the problem becomes solvable. This is something that LLMs will be crap at; the process of invention is not represented in any training data we have access to.
- EVa5I7bHFq9mnYK 3y ago
  We can look at it this way: there are ~1000 chess Grandmasters and one World Champion. It took very short time for AI to go from beating an average GM to beating World Champion. There are ~1000 MO winners and 1 (one) Millenial problem solver ...
  - auntienomen 3y ago
    We can. But doing so frames math research as the same sort of activity as math problem solving.. it's not. Many imo champions struggle to do any successful math research. And many successful math researchers (e.g., all of the most recent batch of Fields medallists) never did the Oympiad at all.
    - EVa5I7bHFq9mnYK 3y ago
      Yet the one and only Millenial problem solver was a MO winner too, so there is some overlap.
      - auntienomen 3y ago
        Sample size 1. Here's what Andrew Wiles, the only other person to have solved a Millennium-class problem has to say of math competition: "Let me stress that creating new mathematics is a quite different occupation from solving problems in a contest. Why is this? Because you don't know for sure what you are trying to prove or indeed whether it is true."
        EVa5I7bHFq9mnYK 3y ago
        Sample size > 1 for sure, Terence Tao comes to mind, as well as Dr. Maryam Mirzakhani. Nobody argues it's the same, after all MO problems are designed to be solved in ~an hour, but we are talking about mental capabilities.
        deleted 3y ago
        [deleted]

auntienomen 3y ago

That's 4-5 years for solving Olympiad problems. Those are just very tricky high school math problems. They have solutions and can generally be solved by applying some combination of standard tricks. It's very much the sort of thing an LLM should be good at. Solving Millennium problems is a whole different ballgame. It's not known if these problems are solvable within ZFC axioms. (In one case, the Yang-Mills prize, stating the problem mathematically is part of the challenge.) All of the obvious applications of known tricks have been tried and failed. To solve such problems, one probably has to invent new and surprising mathematical definitions, building a framework in which the problem becomes solvable. This is something that LLMs will be crap at; the process of invention is not represented in any training data we have access to.

EVa5I7bHFq9mnYK 3y ago
We can look at it this way: there are ~1000 chess Grandmasters and one World Champion. It took very short time for AI to go from beating an average GM to beating World Champion. There are ~1000 MO winners and 1 (one) Millenial problem solver ...
- auntienomen 3y ago
  We can. But doing so frames math research as the same sort of activity as math problem solving.. it's not. Many imo champions struggle to do any successful math research. And many successful math researchers (e.g., all of the most recent batch of Fields medallists) never did the Oympiad at all.
  - EVa5I7bHFq9mnYK 3y ago
    Yet the one and only Millenial problem solver was a MO winner too, so there is some overlap.
    - auntienomen 3y ago
      Sample size 1. Here's what Andrew Wiles, the only other person to have solved a Millennium-class problem has to say of math competition: "Let me stress that creating new mathematics is a quite different occupation from solving problems in a contest. Why is this? Because you don't know for sure what you are trying to prove or indeed whether it is true."
      - EVa5I7bHFq9mnYK 3y ago
        Sample size > 1 for sure, Terence Tao comes to mind, as well as Dr. Maryam Mirzakhani. Nobody argues it's the same, after all MO problems are designed to be solved in ~an hour, but we are talking about mental capabilities.
        deleted 3y ago
        [deleted]