[saagarjha]

> 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]

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-pr...

[saagarjha]

> I guess it depends on what you mean by university level mathematics.

Calculus.

[dan-robertson]

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]

In Germany we had plenty of calculus in the Abitur (like A-levels), too.

Uni adds a much more axiomatic and formal approach.

[OscarCunningham]

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.