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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. Probability,
    теорія ймовірностей, теория вероятностей
    #Probability,
    #теоріяймовірностей, #теориявероятностей
    t.me/scilib_yura15cbx/193

    Number theory
    Теория чисел, Теорія чисел
    #Number theory
    #Теориячисел, #Теоріячисел
    t.me/scilib_yura15cbx/192

    References, Collected works
    Література, Зібрання праць,
    Ссылки, Собрание сочинений
    t.me/scilib_yura15cbx/190

    Symmetry and groups
    Симметрия и группы,
    Симетрія і групи
    #Symmetry
    t.me/scilib_yura15cbx/189

    Philosophy of mathematics
    Філософія математики, Философия математики
    t.me/scilib_yura15cbx/188

    Mathematical physics
    Математическая физика, Математична фізика
    #Mathematical physics
    #Математическаяфизика, #Математичнафізика
    t.me/scilib_yura15cbx/187

    Optimization and control
    Оптимізація та контроль, Оптимизация и контроль
    t.me/scilib_yura15cbx/186

    Optimal control
    Оптимальный контроль, Оптимальний контроль
    #Optimal control
    #Оптимальныйконтроль, #Оптимальнийконтроль
    t.me/scilib_yura15cbx/185

    Numerical methods
    Чисельні методи, Численные методы
    #Numerical methods
    #Чисельніметоди, #Численныеметоды
    t.me/scilib_yura15cbx/184

    Lecture notes
    Конспекты лекций, Конспект лекцiй
    t.me/scilib_yura15cbx/183

    Encyclopaediae, School-level
    Енциклопедії, Шкільний рівень
    Энциклопедии, школьный уровень
    t.me/scilib_yura15cbx/182

    Games, game theory
    Ігри, теорія ігор
    Игры, теория игр
    #Games, #game theory
    #Ігри, ₽теоріяігор
    #Игры, #теория
    игр
    t.me/scilib_yura15cbx/181

    Geometry and topology
    Геометрия и топология
    Геометрія і топологія
    #Geometry and #topology
    #Геометрия и #топология
    #Геометрія і #топологія
    t.me/scilib_yura15cbx/180

    Biography, history
    Биография, история
    Біографія, історія
    #Biography, #history
    #Биография, #история
    #Біографія, #історія
    t.me/scilib_yura15cbx/178

    Mams_ Proceedings AMS
    Праці AMS, Труды АМС
    t.me/scilib_yura15cbx/177

    Algebra, Алгебра
    #Algebra, #Алгебра
    t.me/scilib_yura15cbx/176

    Optical devices
    Оптика, оптические устройства, технологии, инжинерия
    #Optical devices

    t.me/scilib_yura15cbx/173

  23. 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

  24. 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