The proof involved checking the properties of 1,936 configurations by computer, and was not fully accepted at the time due to its complexity.

The proof involves a number of deep and original insights which have linked many apparently disparate fields to 3-manifolds.

Their proof involved replacing the Dirichlet box principle by techniques from the geometry of numbers.

The proof involves a reduction to the -graph colorability problem.

The original proof of the switching lemma involves an argument with conditional probabilities.

His proof involved statistics and experimental evidence from amino acid protein sequences.

On the other hand, Choi's original proof involves direct calculation of those operators.

The original proof of was long and involved.

Harsanyi's proof involves the strong assumption that the perturbations for each player are independent of the other players.

Sometimes, such proofs involve other areas of matematics or show connections between different areas.