Math table October 23, 2018: Goldbach Comets
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Oliver Knill: "Goldbach Comets" ``The Goldbach comet is the graph of the function which tells in how many ways an integer 2n can be written as a sum of two primes. While it is preposterous trying to prove that the function is positive (this is the Goldbach conjecture), one can investigate the comet statistically and experiment with variations or in other number systems. I'm personally convinced that every mathematician has secretly worked on the problem, but of course few admit it as there is a serious danger to reach a high score on the ``Prime numbers crackpot index" of Chris Caldwell Having not much to lose in matters of reputation, I can tell about my own foolish attempts which started 35 years ago both trying to find a root of the comet as well as trying to prove that none exists. There will be also a bit of history. While serious mathematicians use heavy analytic number theory, I will explain a simple real analysis attempt which only uses single variable calculus and relates to the Riemann zeta function. There is no reason for excitement: the approach does not prove it but there are interesting patterns and opportunities to experiment with computer algebra systems.`` |