#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
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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: 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
-
🚨 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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On May 20, 2026, OpenAI made an announcement that shook the mathematical world. An internal AI model, one not available to the public, had come up with a counterexample to the “unit distance” problem, a conjecture made in 1946 by Paul Erdős, the prolific, itinerant Hungarian mathematician. Erdős posed thousands of questions, but this one was special: It was both simple to explain and mathematically deep. It was the first historically significant proof to come from an AI model. Though the model’s result wasn’t definitive, human mathematicians would substantially improve on it within weeks, it was innovative, bringing in ideas from a distant branch of math that no one had successfully applied to this problem before. And it was influential: Within a few days, related techniques were used to solve other important problems. Then on August 1, OpenAI announced that an unreleased model named Astra made 10 additional mathematical advances, including finding solutions to three more problems posed by Erdős. Many mathematicians have hailed developments such as these as a phase transition in the mathematical capability of AI models. These models are “changing dramatically the way mathematical research is being done,” said Noga Alon of Princeton University, who has solved dozens of Erdős problems over his decades-long career.
https://www.quantamagazine.org/why-the-legendary-erdos-problems-are-falling-to-ai-20260803
#AI #Erdős #Erdos #ErdősProblems #PaulErdős #OpenAI #Revolution #ArtificialIntelligence #QuantaMagazine #Maths #Math #NumberTheory #MathRevolution
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Why weren't you taught the cubic formula?
https://www.youtube.com/watch?v=N-KXStupwsc
#Mathologer #BurkardPolster @Mathologer
#NumberTheory #algebra #geometry
#quadratic #cubic #polynomial
#maths #mathematics #education
#math -
One of the best things I saw this week: a paper uncovering alien signals in the Riemann Zeta function. April Fools always brings peak creativity. 😅
#Riemann #Zeta #ZetaFunction #RiemanZetaFunction #AprilFool #AprilFools #AprilFoolsDay #Creativity #Math #Maths #NumberTheory #PeakCreativity #Nerd #Nerds #Humor #Humour #Alien #AlienSignals
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7/
I must, therefore, cast my bread upon the waters and trust search engines to eventually find the few people who might be interested lurking in the long tail of the internet.
Keywords: #philosophy #plato #parmenides #numberTheory #subitization
https://ibiblio.org/bosak/pub/numbers-parmenides-20240331.pdf
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Accessible proofs of the transcendence of e and pi:
https://www.youtube.com/watch?v=WyoH_vgiqXM
#maths #e #pi #transcendental #polynomial #number #numbertheory #Mathologer #math
