Is the Birch and Swinnerton-Dyer conjecture true?

[Guest]

FYI: "Birch and Swinnerton-Dyer conjecture",

https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture.

"Simple seeks simplest (best) solution."

[Guest]

"Hmm. Any problem is a state of mind, and likewise, its solution is also a state of mind."

“No problem can be solved from the same level of consciousness that created it." -- Albert Einstein.

[Guest]

"Hmm. Any problem is a state of mind, and likewise, its solution is also a state of mind."

“No problem can be solved from the same level of consciousness that created it." -- Albert Einstein.

C: [tex]P^{m} (problem) \rightarrow P^{n} (solution)[/tex] where n > m...

[Guest]

"Hmm. Any problem is a state of mind, and likewise, its solution is also a state of mind."

“No problem can be solved from the same level of consciousness that created it." -- Albert Einstein.

C: [tex]P^{m} (problem) \rightarrow P^{n} (solution)[/tex] where n > m...

(C)onsciousness computes complexity...

[Guest]

"Hmm. Any problem is a state of mind, and likewise, its solution is also a state of mind."

“No problem can be solved from the same level of consciousness that created it." -- Albert Einstein.


C: [tex]P^{m} (problem) \rightarrow P^{n} (solution)[/tex] where n > m...

(C)onsciousness computes complexity...

[tex]P^{m}[/tex] represents a multidimensional problem space. And it has both qualitative and quantitative aspects. And the more we know about our problem, the more [tex]P^{m}[/tex] expands from [tex]P^{m}[/tex] to [tex]P^{n}[/tex] (problem solution).


Example: Is the Birch and Swinnerton-Dyer conjecture true?

We do not know! But we seek an affirmative solution if it exists. And there has been considerable work done to answer our question. And therefore, we expect a definitive answer (yes or no) within 48 (DH) months in honor of the great mathematician, David Hilbert.

"We must know. We will know!" -- David Hilbert.

FYI: "An Introduction to the Theory of Elliptic Curves" by Prof. J. H. Silverman,

https://www.math.brown.edu/johsilve/Presentations/WyomingEllipticCurve.pdf.

[Guest]

FFYI (Food For Your Intellect): "Problem Theory", by Prof. R. Casares,

https://arxiv.org/pdf/1412.1044.pdf.

Hmm. Enjoy!

[Guest]

FYI: "Birch and Swinnerton-Dyer conjecture",
...

"Simple seeks simplest (best) solution."

FYI: "Ranks (r) of Elliptic Curves" by Prof. K. Conrad,

https://math.berkeley.edu/~molsson/KConrad-ranks.pdf.


Reference Link: https://en.wikipedia.org/wiki/Rank_of_an_elliptic_curve.

Remark: Yes! We can prove or disprove the Birch and Swinnerton-Dyer conjecture.

Good Luck!

[Guest]

Some Food for Thought: "Vision and Routine: Why you need both to strike a balance" by By Ven. Bhikkhu Bodhi,

https://tricycle.org/magazine/vision-and-routine/.

We hope our visions and routines help us generally to live a peaceful, productive, and satisfying life. Good Luck!

[Guest]

Remark Update: We assume the Birch and Swinnerton-Dyer conjecture is true. But we are open to the possibility the conjecture could be proved false...

Moreover, a deeper analysis/understanding of the rank (r) of elliptic curves is essential... More discovery awaits us. And a decisive breakthrough is forthcoming.

Good Luck!

[Guest]

Remark Update: We assume the Birch and Swinnerton-Dyer conjecture is true. But we are open to the possibility the conjecture could be proved false...

Moreover, a deeper analysis/understanding of the rank (r) of elliptic curves is essential... More discovery awaits us. And a decisive breakthrough is forthcoming.

Good Luck!

Hmm. There's probably a key idea that supports the truth of the Birch and Swinnerton-Dyer conjecture that we have overlooked. It may be hiding in plain sight.

What is that key idea? Hmm... It must exist since the conjecture must be true!

[Guest]

Remark Update: We assume the Birch and Swinnerton-Dyer conjecture is true. But we are open to the possibility the conjecture could be proved false...

Moreover, a deeper analysis/understanding of the rank (r) of elliptic curves is essential... More discovery awaits us. And a decisive breakthrough is forthcoming.

Good Luck!

Hmm. There's probably a key idea that supports the truth of the Birch and Swinnerton-Dyer conjecture that we have overlooked. It may be hiding in plain sight.

What is that key idea? Hmm... It must exist since the conjecture must be true!

[Guest]

[tex]x^{y}[/tex]

Remark Update: We assume the Birch and Swinnerton-Dyer conjecture is true. But we are open to the possibility the conjecture could be proved false...

Moreover, a deeper analysis/understanding of the rank (r) of elliptic curves is essential... More discovery awaits us. And a decisive breakthrough is forthcoming.

Good Luck!

Hmm. There's probably a key idea that supports the truth of the Birch and Swinnerton-Dyer conjecture that we have overlooked. It may be hiding in plain sight.

What is that key idea? Hmm... It must exist since the conjecture must be true!

Hmm. Of course, we must consider the Prime Number Theorem ( ), and we can simplify matters too... Please give it a try. Good Luck!

[Guest]

Are we convinced the conjecture is true? Or do we need to do more work to prove the conjecture?

And what about our analysis of the important parameter, r (the rank)?

[Guest]

Are we convinced the conjecture is true? Or do we need to do more work to prove the conjecture?

And what about our analysis of the important parameter, r (the rank)?

Keywords: Fundamental Theorem of Arithmetic (FTA), Prime Number Theorem (PNT), and Birch and Swinnerton-Dyer conjecture (BSD), ...

C'mon... Must we present proof here? How are FTA, PNT, and BSD related? ... Good Luck!

[Guest]

What is the proof of the Birch and Swinnerton-Dyer conjecture?

Hmm... We are computing. And yes! It can be done! When? Soon!

[Guest]

How soon? We are waiting on Lord GOD to provide the best proof for BSD...

Keep the greatest faith in Lord GOD! Amen!

[Guest]

We think/believe the experts have confirmed the BSD (Birch and Swinnerton-Dyer) conjecture... Well done!! Congratulations!!

Go Blue!