The Birch and Swinnerton-Dyer Conjecture

This conjecture relates to the study of algebraic solutions and to whether a certain variable can be counted accurately.

The idea was to visualise all solutions as graphically represented rational points on an elliptic curve and to study the mathematical properties of the curve.

This means that when the equations are projected, the resulting shape or pattern creates what is known as an elliptic curve.

The researchers wanted to know whether the size of the group of rational points in their example was finite or infinite.

This basically means whether their equations had a solution or not.

The ultimate size of the group of all rational points became so large and complex that Birch and Swinnerton-Dyer were unable to predict whether its size was ultimately finite (countable) or infinite (uncountable).

Birch and Swinnerton-Dyer suggested that when the rational points are of an abelian variety there may be a possible single solution to the total number of rational points in their example, subject to the behaviour of an associated zeta function ζ(s) near the point s=1

The Birch and Swinnerton-Dyer conjecture implies that if ζ(1) is equal to 0 there are an infinite number of rational points, and if ζ(1) is not equal to 0 there are only a finite number of points (solutions).

Is the size of the group of rational points infinite or finite?

The Millennium problem is to fully explain the Birch and Swinnerton-Dyer conjecture and to prove that it is either true or false.

For the exact problem description please refer to Claymath.org

The Answer

The Birch and Swinnerton-Dyer conjecture presents us with two options, finite or infinite, and asks us to choose one of them.

Everything has three potentials at any singular time, regardless of relative attributes such as name, form, amount or type.

This also means relative definitions such as “equation” or “conjecture.”

There will always be three theoretical answers to every equation or question and after three we create a loop.

There may theoretically be a finite number of rational points, an infinite number of such points, or no such points.

Simultaneously.

The applicable equations may be solved one day but even if they were, we still have to remember that opposite and neutral potentials within any proposed solution would still be theoretically possible.

The idea of a singularly accurate and final answer to this question, such as finite or infinite, is only possible if we choose to ignore the other two potential answers.

Is the conjecture true?

1. The Birch and Swinnerton-Dyer conjecture is true.

2. The Birch and Swinnerton-Dyer conjecture is false.

3. The Birch and Swinnerton-Dyer conjecture is neutral.

Simultaneously.

Am I wrong?

I simultaneously oppose, agree with, and neutralise all criticism ad infinitum.

There is no point creating a theory of everything that doesn’t work.