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There was a good link about why AI algorithms tend to approach human level performance rapidly for some tasks: https://www.coursera.org/lecture/machine-learning

There was a good link about why AI algorithms tend to approach human level performance rapidly for some tasks: https://www.coursera.org/lecture/machine-learning-projects/why-human-level-performance-FWkpo https://www.coursera.org/lecture/machine-learning-projects/w... The answer turns out to be pretty boring: As long as humans are still better than machine, humans can provide algorithmic insights and be a source of cheap labels. So I am pretty pessimistic about this particular task. There are only a small handful of humans in the world who are qualified to help! (according to IMO scores: https://www.imo-official.org/hall.aspx https://www.imo-official.org/hall.aspx)

OscarCunningham 7y ago
The pool of people who can solve IMO problems is much larger than the pool of people who can solve IMO problems at the rate of one every 90 minutes. Also consider that fact that human IMO contestants have little training in university-level mathematics. The problem setters try to choose problems where knowledge of advanced mathematics doesn't help, in order to produce a level playing field which only measures raw problem-solving ability. But I suspect that postgraduate-level mathematics will nevertheless be useful in programming the AI.
- saagarjha 7y ago
  > Also consider that fact that human IMO contestants have little training in university-level mathematics. I don't think this is true, as in my experience many of the contestants have already cultured a background in calculus but refrain from using it as the problems are usually designed to actively discourage its use.
  - eru 7y ago
    I guess it depends on what you mean by university level mathematics. Terrence Tao definitely says that doing university math changed his approach to these problems. See https://terrytao.wordpress.com/books/solving-mathematical-problems/ https://terrytao.wordpress.com/books/solving-mathematical-pr...
    - saagarjha 7y ago
      > I guess it depends on what you mean by university level mathematics. Calculus.
      - dan-robertson 7y ago
        This definitely depends on the country. There’s a reasonable amount of calculus in high school (strictly sixth form) mathematics in the U.K. The things one tends to see in university begin with (abstract) algebra and analysis with some “calculus” topics being things like vector calculus, more generic R^n->R^m calculus and contour integration.
        eru 7y ago
        In Germany we had plenty of calculus in the Abitur (like A-levels), too. Uni adds a much more axiomatic and formal approach.
  - OscarCunningham 7y ago
    I was thinking of mathematics more advanced than calculus, but it provides a good example. The IMO problems are designed to be done without it, but if I was programming a computer to solve IMO style inequality problems I would certainly want it to have the "Lagrange multiplier" method in its toolbox.
ngcc_hk 7y ago
Yes some are but not all. There are self learning one and there are one which human to id only.

OscarCunningham 7y ago

The pool of people who can solve IMO problems is much larger than the pool of people who can solve IMO problems at the rate of one every 90 minutes. Also consider that fact that human IMO contestants have little training in university-level mathematics. The problem setters try to choose problems where knowledge of advanced mathematics doesn't help, in order to produce a level playing field which only measures raw problem-solving ability. But I suspect that postgraduate-level mathematics will nevertheless be useful in programming the AI.

saagarjha 7y ago
> Also consider that fact that human IMO contestants have little training in university-level mathematics. I don't think this is true, as in my experience many of the contestants have already cultured a background in calculus but refrain from using it as the problems are usually designed to actively discourage its use.
- eru 7y ago
  I guess it depends on what you mean by university level mathematics. Terrence Tao definitely says that doing university math changed his approach to these problems. See https://terrytao.wordpress.com/books/solving-mathematical-problems/ https://terrytao.wordpress.com/books/solving-mathematical-pr...
  - saagarjha 7y ago
    > I guess it depends on what you mean by university level mathematics. Calculus.
    - dan-robertson 7y ago
      This definitely depends on the country. There’s a reasonable amount of calculus in high school (strictly sixth form) mathematics in the U.K. The things one tends to see in university begin with (abstract) algebra and analysis with some “calculus” topics being things like vector calculus, more generic R^n->R^m calculus and contour integration.
      - eru 7y ago
        In Germany we had plenty of calculus in the Abitur (like A-levels), too. Uni adds a much more axiomatic and formal approach.
- OscarCunningham 7y ago
  I was thinking of mathematics more advanced than calculus, but it provides a good example. The IMO problems are designed to be done without it, but if I was programming a computer to solve IMO style inequality problems I would certainly want it to have the "Lagrange multiplier" method in its toolbox.

ngcc_hk 7y ago

Yes some are but not all. There are self learning one and there are one which human to id only.