• Question: If you could choose to know the answer to one mathematical problem, as yet and solve, what would it be?

    Asked by James on 1 Jan 2020. This question was also asked by Greta Thunberg.
    • Photo: Andrew Harrison

      Andrew Harrison answered on 1 Jan 2020:

      Whether P = NP, which is one of the Clay Maths Institute’s Millennium problems: https://www.claymath.org/millennium-problems/p-vs-np-problem.

      The assumption that this isn’t true is the basis of cryptography and implies that many everyday problems are hard to solve.

    • Photo: Gary Munnelly

      Gary Munnelly answered on 1 Jan 2020:

      I have to agree with Andrew’s answer here. The implications of finding a solution for P=NP are immense! It would be fantastic to have an answer.

      It also helps that it is a Millenium Prize Problem, which means the Clay Mathematical Institute will give you $1,000,000 if you can find a solution. I wouldn’t say no that.

    • Photo: Giuseppe Cotugno

      Giuseppe Cotugno answered on 2 Jan 2020:

      I would be tempted to know whether P = NP

      This is an old unsolved problem of computer science, which can be read as “can difficult problems (NP = non-polynomial problem) be solvable within acceptable time (P = polynomial time).

      That said, I think we as world population, are not as interested as we used to be on knowing if this problem has a solution.

      If somebody will ever prove that P = NP then the whole of cryptography will collapse. Cryptography is based on the assumption that you can’t find a password or a decoding key (the NP problem) in an acceptable time and at least a few centuries are needed to find the solution. If we prove the opposite it will not be possible to encode communications anymore, sign digital documents, prove the authenticity of software downloads and even Bitcoins won’t work anymore!