It would seem as though two of the millennium prize problems, namely P = NP? and the Riemann hypothesis, both seek to target the field of cryptography in favor of the bad guys. However, this is a rather naïve outlook on these proofs given we tend to remain oblivious of the enormous process going on behind the scenes and merely look at the "final product," per se; the magnitude of tools we'll develop with time as we work on these problems will prove to be far more useful than the actual proofs themselves. Do you think we'll ever be able to make any progress at proving these conjectures, and if
Do you think we'll ever be able to make any progress at proving these conjectures, and if so, where do you think that will lead the future of mathematics into?
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I think the solution of these two problems would be a fundamental and ground breaking asset to mathematics as a whole. It is through problems such as these that we further our mathematical rigour and understanding of the world. I believe that the real issue in qualifying this on an ethical and moral level is in the analysis of the phrase, "knowledge is powerful." Power is power; it does not possess a moral instinct nor guide. It is because of this that our increased knowledge simultaneously leads to horrible things and great things. It is all about the people who use the knowledge and their moral and ethical standards.
I certainly think these conjectures will be proven, by the way.
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