#numbertheory — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #numbertheory, aggregated by home.social.
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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"
https://doi.org/10.13140/RG.2.2.27464.07682
#numbertheory #ZeroDensity -
Fable 5.1 - max: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html
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
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Fable 5.1 - max: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html
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
-
Fable 5.1 - max: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html
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
-
Fable 5.1 - max: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html
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
-
Fable 5.1 - max: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html
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
-
Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html
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
-
Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html
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
-
Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html
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
-
Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html
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
-
Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html
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
-
Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html
How to read this report
Primes VS Model A, the classic Cramér sequence
Twelve fingerprints
The complete status ledger
-
Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html
How to read this report
Primes VS Model A, the classic Cramér sequence
Twelve fingerprints
The complete status ledger
-
Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html
How to read this report
Primes VS Model A, the classic Cramér sequence
Twelve fingerprints
The complete status ledger
-
Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html
How to read this report
Primes VS Model A, the classic Cramér sequence
Twelve fingerprints
The complete status ledger
-
Fable 5.1: pedagogical report for Graduate / researcher new to the #decompwlj ➡️ https://decompwlj.com/WeightLevelJump_Primer.html
How to read this report
Primes VS Model A, the classic Cramér sequence
Twelve fingerprints
The complete status ledger
-
#decompwlj #math #mathematics #NumberTheory #numbers #sequence #OEIS #JavaScript #threejs #3D #graph #decomposition #classification #sieve
A081605 ➡️ https://oeis.org/A081605
3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A081605.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A081605.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A081605.html -
#decompwlj #math #mathematics #NumberTheory #numbers #sequence #OEIS #JavaScript #threejs #3D #graph #decomposition #classification #sieve
A081605 ➡️ https://oeis.org/A081605
3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A081605.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A081605.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A081605.html -
#decompwlj #math #mathematics #NumberTheory #numbers #sequence #OEIS #JavaScript #threejs #3D #graph #decomposition #classification #sieve
A081605 ➡️ https://oeis.org/A081605
3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A081605.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A081605.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A081605.html -
#decompwlj #math #mathematics #NumberTheory #numbers #sequence #OEIS #JavaScript #threejs #3D #graph #decomposition #classification #sieve
A081605 ➡️ https://oeis.org/A081605
3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A081605.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A081605.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A081605.html -
#decompwlj #math #mathematics #NumberTheory #numbers #sequence #OEIS #JavaScript #threejs #3D #graph #decomposition #classification #sieve
A081605 ➡️ https://oeis.org/A081605
3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A081605.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A081605.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A081605.html -
🚨 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: https://arxiv.org/pdf/2609.04176
#GPT #NumberTheory #AI4Maths #CatalanConstant #ChatGPT #AIinMaths
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🚨 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: https://arxiv.org/pdf/2609.04176
#GPT #NumberTheory #AI4Maths #CatalanConstant #ChatGPT #AIinMaths
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🚨 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: https://arxiv.org/pdf/2609.04176
#GPT #NumberTheory #AI4Maths #CatalanConstant #ChatGPT #AIinMaths
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🚨 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: https://arxiv.org/pdf/2609.04176
#GPT #NumberTheory #AI4Maths #CatalanConstant #ChatGPT #AIinMaths
-
🚨 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: https://arxiv.org/pdf/2609.04176
#GPT #NumberTheory #AI4Maths #CatalanConstant #ChatGPT #AIinMaths
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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 https://arxiv.org/pdf/2609.02882
#RiemannZeta #RiemannHypothesis #NumberTheory #Mathematics #AnalyticNumberTheory #PrimeNumbers #ZetaFunction #ComplexAnalysis #MathematicalResearch #Mathstodon
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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 https://arxiv.org/pdf/2609.02882
#RiemannZeta #RiemannHypothesis #NumberTheory #Mathematics #AnalyticNumberTheory #PrimeNumbers #ZetaFunction #ComplexAnalysis #MathematicalResearch #Mathstodon
-
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 https://arxiv.org/pdf/2609.02882
#RiemannZeta #RiemannHypothesis #NumberTheory #Mathematics #AnalyticNumberTheory #PrimeNumbers #ZetaFunction #ComplexAnalysis #MathematicalResearch #Mathstodon
-
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 https://arxiv.org/pdf/2609.02882
#RiemannZeta #RiemannHypothesis #NumberTheory #Mathematics #AnalyticNumberTheory #PrimeNumbers #ZetaFunction #ComplexAnalysis #MathematicalResearch #Mathstodon
-
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 https://arxiv.org/pdf/2609.02882
#RiemannZeta #RiemannHypothesis #NumberTheory #Mathematics #AnalyticNumberTheory #PrimeNumbers #ZetaFunction #ComplexAnalysis #MathematicalResearch #Mathstodon
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🤔🔍 Ah, the riveting pursuit of finding meaning by dividing numbers until they masquerade as integers! In this thrilling mathematical escapade, our hero discovers... almost 8! And just when you thought things couldn't get more exciting, we dive into base six calculations because, clearly, everyone was clamoring for that sequel. 🍿📉
https://www.johndcook.com/blog/2025/10/26/987654321/ #mathematics #integers #base6 #numericaladventure #mathhumor #numbertheory #HackerNews #ngated -
Decomposing a Factorial into Large Factors
https://terrytao.wordpress.com/2025/03/26/decomposing-a-factorial-into-large-factors/
#HackerNews #Decomposing #a #Factorial #into #Large #Factors #mathematics #factorials #algorithms #numbertheory #TerryTao
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Just experimenting a little —
will add more explanation later —#RiffsAndRotes
• https://oeis.org/wiki/Riffs_and_Rotes#Riffs from 1 to 60
• https://oeis.org/w/images/1/17/Animation_Riff_60_x_0.16.gif#Rotes from 1 to 60
• https://oeis.org/w/images/e/ee/Animation_Rote_60_x_0.16.gif#Arithmetization #GödelNumbering
#DoublyRecursiveFactorization #DRF
#Arithmetic #GraphTheory #NumberTheory
#Primes #PrimeNumbers #PrimesFactorization -
I just uploaded some notes (in French) for my last Friday “Séminaire Bourbaki du vendredi” talk on the Weil conjectures (history, approaches, generalizations): I recounted the history of the conjectures by Weil on the number of solutions of polynomial equations in finite fields, and some of the approaches that have been proposed to solve them.
https://webusers.imj-prg.fr/~antoine.chambert-loir/publications/exposes/weil-20221118.pdf