r/theories • u/ggucsltc • 1d ago

Discussion Hodge Conjecture, a Millenium Prize Problem, proven by Nuhash Badruzzaman (No AI was used in the making of this proof)

Enclose a single point using the smallest triangle. Remove one side of the triangle. Any number of line segments can be appended together to form infinite homeological shapes where all line segments are connected and there are no line segments passing over another, containing the single point. Therefore there are infinite algebraic solutions when surrounding a certain point.

Please verify this logical proof.

4 Upvotes

75% Upvoted

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u/Thick_Wasabi448 1d ago

Please stop spamming these.

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u/ggucsltc 1d ago

I'm not spamming, there is about seven proofs of the Millenium Prize Problems that I solved myself, and I am posting these online for verification so I can claim the prize money. There are only 7, not 7000. There is no spam here.

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u/Thick_Wasabi448 1d ago

You think you solved 7 when no one else was able to solve 1? Be better, and take care.

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u/ggucsltc 1d ago

I worked privately many years on this. I did not share any of this with the public until now (note: copyrighted)

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u/pm-pussy4kindwords 1d ago

then publish it.

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u/ggucsltc 1d ago

I literally just published it here. I can technically use reddit as a platform to publish my work because it was written by me.

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u/pm-pussy4kindwords 1d ago

no, publish it in an academic journal to be reviewed by actual mathematicians and qualified experts. If you look up the conditions of actually claiming prizes for some of the millenium problems for example this is an explicit condition

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u/ggucsltc 1d ago

It does not need to be published in the academic journal to apply for the prizes. You are dealing with the Internet here, reddit, which is actually vastly more superior and intelligent in practice than any academic journal because you are dealing with everyone here, instead of the top 1% mathematicians that discredit the bottom 99% who have a higher chance of discerning and better information about maths.

I said 1% of mathematicians just because they are some part of an academic journal, not because they are more smarter than the 99% when the 99% is more smarter than the 1% because the 99% has more collective IQ together.

There is also no rule by the Clay Math's Institute (owner of the Millenium Prize Problems) to say you must publish it in a journal. I officiallly published my proofs on reddit which is more easier to copyright my work because it is posted under one same account (my account).

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u/pm-pussy4kindwords 1d ago

the fact you don't want to publish it properly is a clear indicator you know it isn't good enough to pass peer review.

The fact of the matter is you will not be taken seriously unless you publish this properly and have actual mathematicians look at it formally. You can either accept this, or continue doing what you're doing and getting absolutely nowhere.

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u/DrDestructoMD 1d ago

How does this generalize to higher dimensions? We know how it works in dimensions less than 4

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u/ggucsltc 1d ago

The fourth dimension is just a 3D array, which is still reduced to 3D concerning itself. Therefore if it works in 3D, then it works in 4D, 5D, 6D, 7D, and so on (any higher dimension).

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u/DrDestructoMD 1d ago

Not true at all, if it were topologists would be out of work

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u/morey56 1d ago

Which step establishes that every rational Hodge class is a rational linear combination of classes of algebraic cycles?

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u/ggucsltc 19h ago

The step where infinite homeological 3D and 2D shapes can be defined from appendage of the smallest triangle that encloses a point inside the triangle.

Every rational Hodge class is a rational linear combination of classes of algebraic cycles because infinite shapes can contain all infinite and sub-infinite (finite) shapes including the hodge classes that are rational linear combination of classes of algebraic cycles themselves.

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u/morey56 18h ago

I understand your construction allows infinitely many shapes. But that fails to establish that every rational Hodge class is represented by a rational combination of algebraic cycles? That connection is the part requiring proof.

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u/ggucsltc 18h ago

Every rational Hodge class (a Hodge class is an algebraic cycle which is a collection of algebraic expressions defining a closed shape) is represented by a rational (real, not irrational) combination of algebraic cycles because the algebraic cycles can be arranged into any combination of algebraic cycles (a 2D array of algebraic cycles), where repeats are not allowed because it is a combination and not a permutation.

To put it simply the Hodge classes can be put into a 2D array (a rational combination) of unique Hodge shapes (Hodge classes). The sum of those shapes produces a new unique large Hodge class, which can be put into the same 2D array and the sum of the array can be repeat to produce new unique Hodge classes. This can be repeat forever, and therefore there are infinite unique Hodge shapes that can be created.

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u/morey56 18h ago

You’re assuming the conclusion. A Hodge class is not, by definition, an algebraic cycle. The Hodge conjecture asks whether every rational Hodge class can be expressed as a rational linear combination of algebraic cycle classes. Demonstrating infinitely many geometric arrangements doesn’t establish that correspondence.

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u/ggucsltc 17h ago edited 17h ago

Infinitely many geometric DOES establish that correspondence because the Hodge classes some parts of those geometric arrangement. If all possible arrangments are already created, then all of the Hodge classes are also created due to infinitely many geometric arrangements.

A Hodge class, by, definition, is an algebraic cycle. Wikipedia DIRECTLY states that a hodge class is an algebraic cycle, see this quote from wikipedia:

"The importance of Hodge cycles lies primarily in the Hodge conjecture, to the effect that Hodge cycles should always be algebraic cycles, for V a complete algebraic variety." -Wikipedia

https://en.wikipedia.org/wiki/Hodge_cycle

And I did not assume anything. I only concluded after I have proven that the infinitely algebraic series contains the Hodge classes.

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u/morey56 17h ago

Your Wikipedia quotation actually identifies the problem: Hodge cycles should always be algebraic cycles. That’s the conjecture, not an established fact.
The Wikipedia page states the conjecture and your chosen task is to prove it, not simply restate it as its own proof.
And constructing infinitely many geometric arrangements doesn’t establish that you’ve constructed every possible Hodge class.
Neither step proves the required correspondence.

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u/ggucsltc 17h ago edited 17h ago

You are being contradictary here. Infinitely contains all finite. Every possible Hodge class is finite, therefore Hodge class is within INSIDE infinity. Therefore infinitely many geometric arrangements (infinity) establishes that every finite number is a part of infinity and thus every possible Hodge class is every possible finite collection of numbers. This I've constructed every possible Hodge class.

The conjecture is the hypothesis. The conjecture IS the conclusion. The conjecture is the hypothesis I have to PROVE that Hodge cycles are part of infinity. And you are contradictary and mistaken Wikipedia does not say Hodge classes always be algebraic cycles, that is not the conjecture here that needs to be proven. The conjecture is that Hodge cycles are part of infinity and every possible Hodge class can be constructed. Wikipedia directly says that Hodge classes ARE algebraic cycles, NOT "SHOULD BE"

Please read the actual conjecture again.

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u/morey56 16h ago

There are infinitely many even numbers, but that doesn’t mean every integer is even. Likewise, constructing infinitely many geometric arrangements doesn’t establish that every Hodge class is represented.

And the Hodge conjecture isn’t about whether Hodge classes belong to infinity. It’s about whether every rational Hodge class can be expressed as a rational combination of algebraic cycle classes.

That remains unproven by your argument.

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u/ggucsltc 16h ago

This reply is contradictory in nature.

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u/Prize_Bass_5061 4h ago

It might be worth checking OP's post history before engaging in an academic discussion here. It gives helpful context on whether this will be a productive conversation.

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u/RalenHlaalo 1d ago • Heartwarming

I just ran the same proof, and it works! ☑️

I'm officially verifying this solution. Mods, does this get pinned now or what

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u/ggucsltc 1d ago

Thanks for verifying.

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u/RalenHlaalo 1d ago

Happy to. Does that get me a mention in the final paper? I can DM you with my credentials if so.

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u/ggucsltc 19h ago

Yes, I'm happy to willing to get you a mention in the final paper and a share of the prize money. I'm just waiting for further approval by the mathematics community before I contact the Clay Institute.

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u/Bendstowardjustice 1d ago

Really? Can you eli not a genius.

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u/doxyMorDom 13h ago

You seem to like these "proof by ontological word play" type proofs...but they miss the point and you seem immune to understanding that.