The Landau--Kolmogorov problem is to bound the norm of the intermediate derivative $f^(k)$
for $1 /leq k /leq n-1$ when the bounds for the norms of the function $f$ and of its higher derivative $f^(n)$, are given.

This problem is closely related to finding optimal numerical approximations to the $k$-th derivative of an $n$ times differentiable function $f$ using $N$ bits of information about $f$. 

We will overview existing results, and give an outline of our recent proof of Karlin's conjecture which deals with the case of functions given on a finite interval.

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