#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
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#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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Probability,
теорія ймовірностей, теория вероятностей
#Probability,
#теоріяймовірностей, #теориявероятностей
t.me/scilib_yura15cbx/193Number theory
Теория чисел, Теорія чисел
#Number theory
#Теориячисел, #Теоріячисел
t.me/scilib_yura15cbx/192References, Collected works
Література, Зібрання праць,
Ссылки, Собрание сочинений
t.me/scilib_yura15cbx/190Symmetry and groups
Симметрия и группы,
Симетрія і групи
#Symmetry
t.me/scilib_yura15cbx/189Philosophy of mathematics
Філософія математики, Философия математики
t.me/scilib_yura15cbx/188Mathematical physics
Математическая физика, Математична фізика
#Mathematical physics
#Математическаяфизика, #Математичнафізика
t.me/scilib_yura15cbx/187Optimization and control
Оптимізація та контроль, Оптимизация и контроль
t.me/scilib_yura15cbx/186Optimal control
Оптимальный контроль, Оптимальний контроль
#Optimal control
#Оптимальныйконтроль, #Оптимальнийконтроль
t.me/scilib_yura15cbx/185Numerical methods
Чисельні методи, Численные методы
#Numerical methods
#Чисельніметоди, #Численныеметоды
t.me/scilib_yura15cbx/184Lecture notes
Конспекты лекций, Конспект лекцiй
t.me/scilib_yura15cbx/183Encyclopaediae, School-level
Енциклопедії, Шкільний рівень
Энциклопедии, школьный уровень
t.me/scilib_yura15cbx/182Games, game theory
Ігри, теорія ігор
Игры, теория игр
#Games, #game theory
#Ігри, ₽теоріяігор
#Игры, #теорияигр
t.me/scilib_yura15cbx/181Geometry and topology
Геометрия и топология
Геометрія і топологія
#Geometry and #topology
#Геометрия и #топология
#Геометрія і #топологія
t.me/scilib_yura15cbx/180Biography, history
Биография, история
Біографія, історія
#Biography, #history
#Биография, #история
#Біографія, #історія
t.me/scilib_yura15cbx/178Mams_ Proceedings AMS
Праці AMS, Труды АМС
t.me/scilib_yura15cbx/177Algebra, Алгебра
#Algebra, #Алгебра
t.me/scilib_yura15cbx/176Optical devices
Оптика, оптические устройства, технологии, инжинерия
#Optical devices -
From a Mathematical Curiosity to the Foundation of Internet Security 🧮🧐🔐✨
In 1636, Pierre de Fermat made a remarkable observation: if you take an integer a, raise it to a prime power p, and then subtract a, the result is always divisible by p. In other words, for a prime p,
aᵖ ≡ a (mod p).
For example, when p = 5:
2⁵ − 2 = 30, which is divisible by 5, and
3⁵ − 3 = 240, which is also divisible by 5.Fermat found this property elegant and tried to spark interest in this curious corner of mathematics. Not everyone was impressed. John Wallis reportedly dismissed such results, remarking, “Big deal; I could find other relationships just as interesting without much effort, and none of them are important.”
About a century later, Leonhard Euler was encouraged by Christian Goldbach to study Fermat’s ideas. Though initially unenthusiastic, Euler soon uncovered deeper structure within them. His work laid much of the foundation for what we now call modern number theory.
#Mathematics #Math #NumberTheory #Fermat #Euler #EulerTheorem #FermatsLittleTheorem #ModularArithmetic #RSA #Cryptography #CyberSecurity #HistoryOfMathematics #MathHistory #PrimeNumbers #EulerTotient #AbstractMath #PureMathematics #STEM #ScienceCommunication #MathEducation #EducationalContent #DidYouKnow #MathematicalBeauty #InternetSecurity #Encryption #Curiosity #Innovation #History #Learning #Knowledge
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Number theory was the one area of mathematics on which Pierre de Fermat (1607–65) worked throughout his life, and he found it ‘very beautiful and very subtle’.
Among other results, he said that the Polygonal Number Theorem (which asserts that every natural number is the sum of at most $n$ $n$-gonal numbers) was ‘a most beautiful and wholly general proposition […] this marvellous proposition’.
(He offered no proof of this result, but claimed to have one in a marginal note to Diophantus' Arithmetica; this was the same book in which he noted what became known as Fermat's Last Theorem.)
Fermat also seems to have counted magic squares and analogous configurations as part of number theory, and wrote that: ‘I know hardly anything more beautiful in arithmetic than these numbers that some call planetary and others magic’. (The term ‘planetary’ is derived from certain treatises linking the magic squares to planets used in talismans.)
He said he had found a rule to find magic cubes (one of his examples is in the attached image) and also determined how many different ways each such cube can be arranged, which he called ‘one of the most beautiful things in arithmetic’.
1/2
[Each day of February, I am posting a short interesting story/image/fact/anecdote related to the aesthetics of mathematics.]
#Fermat #NumberTheory #HistMath #MathematicalBeauty #MagicSquare
