Blue Flower



There are many unsolved mathematical problems which have counterparts in the difficulties and paradoxes in our understanding of nature, when the knowledge of nature are asserted as equations in the language of mathematics.  Our goal is to show that quantum mechanics is an incomplete model of reality, as was argued by Einstein, and that the incompleteness is related to the same difficulties of certain unsolved mathematical problems.

These problems all are related by the connection between the discrete points and the continuum of infinitely many points.

1. The Riemann Hypothesis (the real part of non-trivial zeros of the Zeta function (of infinite number of terms) are all 1/2).

2. The perimeter of an ellipse is finite (the sum of the infinite discrete segments of zero length) and difficult to compute as an integral.

3. A planner map of infinitely many regions can be colored in only 4 colors (proved by computer but difficult to prove by mathematical reasoning).

4. Fermat's Last Theorem (proved true for discrete powers of n>2 based on properties of continuous elliptic functions).

5. The Uncertainty Principal (the continuum of a  position in space is not real for a moving discrete particle).

6. Bell's Inequality (two discrete remote events of an experiment are mutually dependent at infinite speed).

7. Planck's constant (a discrete measurable number arises out of an infinite number of wavelengths in heat radiation).

8. .... more