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#numbertheory — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #numbertheory, aggregated by home.social.

  1. The Method Matters More Than the Number: A Proposed Improvement to the Guth–Maynard Bound 30/13

    The interest in lowering the coefficient to 24000/10451 ≈ 2.29643 lies mainly in the technique. The method aims to preserve relationships between oscillating terms, including how they can cancel, as sums are transformed. Bounding terms by their sizes alone can erase that information and weaken the estimates. Preserving it might help with other problems in number theory and harmonic analysis that share similar structures. That potential remains to be explored; the paper’s result is still pending verification.

    The entire process was interactive and iterative: hundreds of exchanges with a frontier model, without a single autonomous agent, without using the API, and with zero client-side automation. My local computing resources were ordinary home equipment. I proposed, questioned and redirected each step. I believe this continuous involvement was essential to bring human creativity into the process and guide the model’s reasoning. Many conversations bordered on the absurd, the unfamiliar or the unorthodox. For me, that is where the human–machine “magic” emerged.

    The manuscript is currently almost indigestible for a human reader: it contains failed attempts, detours and corrections. I estimate that the proof’s chain of arguments could fit into a dozen pages, out of the current 172. That distillation, and of course, formal proof, have yet to be done. Finally, math community help will ease human learning.

    Apologies for the AI-generated image: it may contain errors.

    "A Zero-Density Estimate with Coefficient 24000/10451 < 30/13 for the Riemann Zeta-Function"
    doi.org/10.13140/RG.2.2.27464.
    #numbertheory #ZeroDensity

  2. Fable 5.1 - max: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ decompwlj.com/WeightLevelJump_

    How to read this report

    Primes VS Model A, the classic Cramér sequence

    Twelve fingerprints

    The complete status ledger

    #math #NumberTheory #number #sequence #AI #Claude #Fable #Anthropic

  3. Fable 5.1 - max: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ decompwlj.com/WeightLevelJump_

    How to read this report

    Primes VS Model A, the classic Cramér sequence

    Twelve fingerprints

    The complete status ledger

    #math #NumberTheory #number #sequence #AI #Claude #Fable #Anthropic

  4. Fable 5.1 - max: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ decompwlj.com/WeightLevelJump_

    How to read this report

    Primes VS Model A, the classic Cramér sequence

    Twelve fingerprints

    The complete status ledger

    #math #NumberTheory #number #sequence #AI #Claude #Fable #Anthropic

  5. Fable 5.1 - max: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ decompwlj.com/WeightLevelJump_

    How to read this report

    Primes VS Model A, the classic Cramér sequence

    Twelve fingerprints

    The complete status ledger

    #math #NumberTheory #number #sequence #AI #Claude #Fable #Anthropic

  6. Fable 5.1 - max: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ decompwlj.com/WeightLevelJump_

    How to read this report

    Primes VS Model A, the classic Cramér sequence

    Twelve fingerprints

    The complete status ledger

    #math #NumberTheory #number #sequence #AI #Claude #Fable #Anthropic

  7. Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ decompwlj.com/WeightLevelJump_

    How to read this report

    Primes VS Model A, the classic Cramér sequence

    Twelve fingerprints

    The complete status ledger

    #math #NumberTheory #number #sequence #AI #Claude #Fable #Anthropic

  8. Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ decompwlj.com/WeightLevelJump_

    How to read this report

    Primes VS Model A, the classic Cramér sequence

    Twelve fingerprints

    The complete status ledger

    #math #NumberTheory #number #sequence #AI #Claude #Fable #Anthropic

  9. Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ decompwlj.com/WeightLevelJump_

    How to read this report

    Primes VS Model A, the classic Cramér sequence

    Twelve fingerprints

    The complete status ledger

    #math #NumberTheory #number #sequence #AI #Claude #Fable #Anthropic

  10. Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ decompwlj.com/WeightLevelJump_

    How to read this report

    Primes VS Model A, the classic Cramér sequence

    Twelve fingerprints

    The complete status ledger

    #math #NumberTheory #number #sequence #AI #Claude #Fable #Anthropic

  11. Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ decompwlj.com/WeightLevelJump_

    How to read this report

    Primes VS Model A, the classic Cramér sequence

    Twelve fingerprints

    The complete status ledger

    #math #NumberTheory #number #sequence #AI #Claude #Fable #Anthropic

  12. Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ decompwlj.com/WeightLevelJump_

    How to read this report

    Primes VS Model A, the classic Cramér sequence

    Twelve fingerprints

    The complete status ledger

    #math #NumberTheory #AI #Claude #Fable #graph #sequence

  13. Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ decompwlj.com/WeightLevelJump_

    How to read this report

    Primes VS Model A, the classic Cramér sequence

    Twelve fingerprints

    The complete status ledger

    #math #NumberTheory #AI #Claude #Fable #graph #sequence

  14. Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ decompwlj.com/WeightLevelJump_

    How to read this report

    Primes VS Model A, the classic Cramér sequence

    Twelve fingerprints

    The complete status ledger

    #math #NumberTheory #AI #Claude #Fable #graph #sequence

  15. Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ decompwlj.com/WeightLevelJump_

    How to read this report

    Primes VS Model A, the classic Cramér sequence

    Twelve fingerprints

    The complete status ledger

    #math #NumberTheory #AI #Claude #Fable #graph #sequence

  16. Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ decompwlj.com/WeightLevelJump_

    How to read this report

    Primes VS Model A, the classic Cramér sequence

    Twelve fingerprints

    The complete status ledger

    #math #NumberTheory #AI #Claude #Fable #graph #sequence

  17. 🚨 BREAKING NEWS 🚨

    Number theorist Zhi-Wei Sun, with AI assistance, has published a paper on arXiv claiming to prove that Catalan’s constant is irrational.

    If the result holds up to scrutiny, this would be a major breakthrough in number theory. The irrationality/transcendence of Catalan’s constant has long been an important open problem.

    Preprint link: arxiv.org/pdf/2609.04176

    #GPT #NumberTheory #AI4Maths #CatalanConstant #ChatGPT #AIinMaths

  18. 🚨 BREAKING NEWS 🚨

    Number theorist Zhi-Wei Sun, with AI assistance, has published a paper on arXiv claiming to prove that Catalan’s constant is irrational.

    If the result holds up to scrutiny, this would be a major breakthrough in number theory. The irrationality/transcendence of Catalan’s constant has long been an important open problem.

    Preprint link: arxiv.org/pdf/2609.04176

    #GPT #NumberTheory #AI4Maths #CatalanConstant #ChatGPT #AIinMaths

  19. 🚨 BREAKING NEWS 🚨

    Number theorist Zhi-Wei Sun, with AI assistance, has published a paper on arXiv claiming to prove that Catalan’s constant is irrational.

    If the result holds up to scrutiny, this would be a major breakthrough in number theory. The irrationality/transcendence of Catalan’s constant has long been an important open problem.

    Preprint link: arxiv.org/pdf/2609.04176

    #GPT #NumberTheory #AI4Maths #CatalanConstant #ChatGPT #AIinMaths

  20. 🚨 BREAKING NEWS 🚨

    Number theorist Zhi-Wei Sun, with AI assistance, has published a paper on arXiv claiming to prove that Catalan’s constant is irrational.

    If the result holds up to scrutiny, this would be a major breakthrough in number theory. The irrationality/transcendence of Catalan’s constant has long been an important open problem.

    Preprint link: arxiv.org/pdf/2609.04176

    #GPT #NumberTheory #AI4Maths #CatalanConstant #ChatGPT #AIinMaths

  21. 🚨 BREAKING NEWS 🚨

    Number theorist Zhi-Wei Sun, with AI assistance, has published a paper on arXiv claiming to prove that Catalan’s constant is irrational.

    If the result holds up to scrutiny, this would be a major breakthrough in number theory. The irrationality/transcendence of Catalan’s constant has long been an important open problem.

    Preprint link: arxiv.org/pdf/2609.04176

    #GPT #NumberTheory #AI4Maths #CatalanConstant #ChatGPT #AIinMaths

  22. The world was recently stunned by a major breakthrough on the Riemann Hypothesis: >67% of zeta zeros are on the critical line and simple. The AI proof was sprawling. Today, a HUMAN stepped in to show how it's done with pure elegance.

    Youness Lamzouri (U. of Lorraine) reproved this result in a super slick way, replacing heavy machinery with a clean Hilbert space inequality.

    This is Terry Tao's "digestion" at its finest: pure human ingenuity and mathematical taste.

    Youness kindly gave Axiom Math a sneak peek, and we formalized his proof in Lean, formal verification on day one!

    A monumental milestone for mathematics.

    Read it here on arxiv.org/pdf/2609.02882

    #RiemannZeta #RiemannHypothesis #NumberTheory #Mathematics #AnalyticNumberTheory #PrimeNumbers #ZetaFunction #ComplexAnalysis #MathematicalResearch #Mathstodon

  23. The world was recently stunned by a major breakthrough on the Riemann Hypothesis: >67% of zeta zeros are on the critical line and simple. The AI proof was sprawling. Today, a HUMAN stepped in to show how it's done with pure elegance.

    Youness Lamzouri (U. of Lorraine) reproved this result in a super slick way, replacing heavy machinery with a clean Hilbert space inequality.

    This is Terry Tao's "digestion" at its finest: pure human ingenuity and mathematical taste.

    Youness kindly gave Axiom Math a sneak peek, and we formalized his proof in Lean, formal verification on day one!

    A monumental milestone for mathematics.

    Read it here on arxiv.org/pdf/2609.02882

    #RiemannZeta #RiemannHypothesis #NumberTheory #Mathematics #AnalyticNumberTheory #PrimeNumbers #ZetaFunction #ComplexAnalysis #MathematicalResearch #Mathstodon

  24. The world was recently stunned by a major breakthrough on the Riemann Hypothesis: >67% of zeta zeros are on the critical line and simple. The AI proof was sprawling. Today, a HUMAN stepped in to show how it's done with pure elegance.

    Youness Lamzouri (U. of Lorraine) reproved this result in a super slick way, replacing heavy machinery with a clean Hilbert space inequality.

    This is Terry Tao's "digestion" at its finest: pure human ingenuity and mathematical taste.

    Youness kindly gave Axiom Math a sneak peek, and we formalized his proof in Lean, formal verification on day one!

    A monumental milestone for mathematics.

    Read it here on arxiv.org/pdf/2609.02882

    #RiemannZeta #RiemannHypothesis #NumberTheory #Mathematics #AnalyticNumberTheory #PrimeNumbers #ZetaFunction #ComplexAnalysis #MathematicalResearch #Mathstodon

  25. The world was recently stunned by a major breakthrough on the Riemann Hypothesis: >67% of zeta zeros are on the critical line and simple. The AI proof was sprawling. Today, a HUMAN stepped in to show how it's done with pure elegance.

    Youness Lamzouri (U. of Lorraine) reproved this result in a super slick way, replacing heavy machinery with a clean Hilbert space inequality.

    This is Terry Tao's "digestion" at its finest: pure human ingenuity and mathematical taste.

    Youness kindly gave Axiom Math a sneak peek, and we formalized his proof in Lean, formal verification on day one!

    A monumental milestone for mathematics.

    Read it here on arxiv.org/pdf/2609.02882

    #RiemannZeta #RiemannHypothesis #NumberTheory #Mathematics #AnalyticNumberTheory #PrimeNumbers #ZetaFunction #ComplexAnalysis #MathematicalResearch #Mathstodon

  26. The world was recently stunned by a major breakthrough on the Riemann Hypothesis: >67% of zeta zeros are on the critical line and simple. The AI proof was sprawling. Today, a HUMAN stepped in to show how it's done with pure elegance.

    Youness Lamzouri (U. of Lorraine) reproved this result in a super slick way, replacing heavy machinery with a clean Hilbert space inequality.

    This is Terry Tao's "digestion" at its finest: pure human ingenuity and mathematical taste.

    Youness kindly gave Axiom Math a sneak peek, and we formalized his proof in Lean, formal verification on day one!

    A monumental milestone for mathematics.

    Read it here on arxiv.org/pdf/2609.02882

    #RiemannZeta #RiemannHypothesis #NumberTheory #Mathematics #AnalyticNumberTheory #PrimeNumbers #ZetaFunction #ComplexAnalysis #MathematicalResearch #Mathstodon