Open questions about how hard computational problems really are. P versus NP asks whether every problem whose solution can be checked quickly can also be solved quickly, the graph isomorphism problem asks whether deciding if two networks are the same shape is easy, and the unique games conjecture, proposed in 2002, concerns how well certain constraint problems can be approximated. None has a proof either way.
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Unresolved Problems in Complexity Theory
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Wikipedia: P versus NP Problem
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The P versus NP problem is a major unsolved problem in theoretical computer science.
Wikipedia: Graph isomorphism problem
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The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic.
Unique games conjecture, Wikipedia
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In computational complexity theory, the unique games conjecture (often referred to as UGC) is a conjecture made by Subhash Khot in 2002.
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