Essentially it boils down to:
Map real numbers to complex numbers and vice versa using a Hilbert (or another) space filling curve and then encode non-trivial zeroes of the Reimann zeta function on the real number line
- Since any point on a line can be mapped one-to-one to a point in a plane using a Hilbert curve
- We can map every non-trivial zero of the Reimann zeta function, onto a space filling curve like the Hilbert curve
- Since Hilbert curve and some other space-filling curves have nice properties like continuity, I predict the non-trivial zeroes in the domain of the Reimann zeta function will lie in some predictable pattern on the real number line. This will, of course, vary depending on what space filling curve is chosen.
- Perhaps then we can prove that all the non-trivial zeroes encoded on the real number line lie on a nice pattern which we can prove to hold using proof-by-induction
Has anyone tried anything like this?