I am happy to invite the ResearchGate community to share feedback, thoughts, and critiques on what I believe marks a once-in-history achievement: the definitive and comprehensive disproof of two of mathematics’ most legendary unsolved problems — the Riemann Hypothesis and the Goldbach Conjecture.
These works, now available as preprints, present:
1. Seven independent disproofs for Riemann Hypothesis 2. Ten independent disproofs for Goldbach Conjecture
— each combining analytic, computational, probabilistic, structural, and topological approaches, rewriting the foundations of number theory.
This isn’t just mathematical progress — it is a paradigm-shifting, Nobel Prize–level breakthrough that opens the door to a new era of discovery, not only in mathematics but across every human endeavour, even fields yet unimagined. My research pushes beyond limits, exploring truths that transform our understanding of both the known and the unknown.
👉 Read the papers and share your thoughts, critiques, and insights:
- Riemann Hypothesis: DOI: 10.13140/RG.2.2.12073.71528
- Goldbach Conjecture: DOI: 10.13140/RG.2.2.35561.81764
- Supersolid Light Research: DOI: 10.13140/RG.2.2.14590.29763
👉 Visit my ResearchGate profile for more groundbreaking works: https://www.researchgate.net/profile/Sandeep-Jaiswal-9?ev=hdr_xprf
Let’s engage in an open, constructive, and pioneering discussion. How do you see these results reshaping number theory, analytic mathematics, or even the future of scientific thought itself? I welcome your perspectives, debates, and reflections!
Peter Kepp
Good catch. Thanks for pointing this out. The new file on RH is now available.
Regards and happy reading,
Sandeep
Your comments are correct, because we use complex functions. It is different with real functions. In my proof, I find a contradiction to the symmetry of the function eta then zeta function. This contradiction gives that RH is valide. We wait to see.
Sandeep Jaiswal
I wonder if the mathematical community accepts your article as proof. I was hoping my article would be among your references.
Preprint Goldbach's Conjecture: partial proof
Abdelmajid Ben Hadj Salem
Dear Prof. Abdelmajid,
Thank you for your thoughtful reply.
Indeed, complex functions introduce rich behaviours not mirrored in the realm of reals. Your observation on the η-function symmetry is noted — but it is precisely this assumed symmetry, when extended analytically, that leads to contradictions I rigorously explore across multiple frameworks.
The seven (RH) and ten (Goldbach) disproofs I present are not mere numerical counterexamples or asymptotic speculations. They are built from deep contradictions — ranging from analytical divergences, spectral mismatches, prime irregularities, to formal logic breakdowns — each independently and jointly showing that these conjectures cannot universally hold.
My goal is not to challenge beliefs, but to illuminate a final, unified perspective that brings closure to humanity’s greatest mathematical enigmas. I welcome mathematical critique and validation — because the truth, when complete, defends itself.
Let’s elevate this discourse as a global community. The preprints are available here for full review.
Looking forward to your insights and those of the entire mathematical fraternity.
Warm regards, Sandeep Jaiswal
Jan Slowak
Dear Jan,
Thank you for your thoughtful message and for sharing your contribution to this enduring mathematical enigma. I deeply appreciate your work and your hope to be part of this larger discussion.
My recent article doesn't aim to present a partial or extended proof but rather to decisively demonstrate the impossibility of the conjecture itself through ten independently formulated disproofs — each attacking a different foundational assumption. These disproofs are not just mathematical arguments but structural exposures of contradiction, aimed at settling this question conclusively and irrevocably.
As for community acceptance — I believe that truth earns its place over time, regardless of initial resistance. I welcome scrutiny and peer feedback, including yours, as part of this evolving dialogue.
Your article (DOI: 10.13140/RG.2.2.36787.23848) will be reviewed with interest, and I would be glad to reference it in future updates if it aligns with or complements any of the contradictions identified in my framework.
Looking forward to a constructive exchange — and thank you again for your engagement and collegial spirit.
With rgs, Sandeep Jaiswal
Abdelmajid Ben Hadj Salem
Dear Abdelmajid, if you had meant me in `Your comments are correct, because we use complex functions.´, you may see this:
Every function bases on a defined combination of the values of the arguments. So a complex argument has to be combined for any – one dimensional – solution of f(z). [z := a, bi]
But real and imaginary are incommensurable by definition!
What do you think about?
Think by complete units:
Argument `x´ => ABC, which means:
A := number (of amount, by naturals)
B := measure (free choice of a part of the unit)
C := unit (in geometry: length, width, hight)
• `Complex´ got explained by different units (real and imaginary, which are incommensurable, at the complex plane)
• y = f(x) => x is by unit X, y is by unit Y [both one-dimensional]
• z = f(x, y) => all by different unit [argument two-dimensional]
If z is by a single unit, x and y must be combined. To combine real and imaginary part is excluded by definition!
If z is two-dimensional we talk about scaling, not about a function!
See my article `A Proof in respect to the Riemann-Hypothesis´.
it is wonderful mathematical progress.in number theory these two Riemann Hypothesis is very important. in this article every even integer greater than 2 can be expressed as the sum of two prime numbers. Both problems remain open.