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#numbertheory — Public Fediverse posts

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

  1. 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

  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. 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

  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 - 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

  8. 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

  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 #number #sequence #AI #Claude #Fable #Anthropic

  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 #number #sequence #AI #Claude #Fable #Anthropic

  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. 🚨 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

  16. Alright, future engineers!
    **Modular Arithmetic:** Numbers wrap around after a certain value (the modulus).
    Ex: `(10 + 4) mod 12 = 14 mod 12 = 2`. Think of a clock!
    Pro-Tip: It's super useful in cryptography & computer science for cycles/remainders!
    #NumberTheory #DiscreteMath #STEM #StudyNotes

  17. Opus 5 - High-res PNG (slight origin offset for levels 1) 🧵

    1/4: The base case: the natural numbers - the sieve of Eratosthenes

    #decompwlj #math #Anthropic #Claude #Opus5 #sequence #numbers #NumberTheory

  18. Alright, future engineers!
    **Modulo Arithmetic:** Finding the remainder after division.
    Ex: `17 mod 5 = 2`.
    Pro-Tip: Crucial for cryptography, clock arithmetic, and hashing!
    #DiscreteMath #NumberTheory #STEM #StudyNotes

  19. Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ decompwlj.com/Opus5_decompwlj_

    The weight is unique:
    "The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

    Proof of Conjecture 9:
    "This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

    The atlas as an instrument:
    "About a thousand OEIS sequences have been decomposed and published at decompwlj.com. Today that is an archive. It could be an instrument."

    #decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

  20. Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ decompwlj.com/Opus5_decompwlj_

    The weight is unique:
    "The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

    Proof of Conjecture 9:
    "This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

    The atlas as an instrument:
    "About a thousand OEIS sequences have been decomposed and published at decompwlj.com. Today that is an archive. It could be an instrument."

    #decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

  21. Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ decompwlj.com/Opus5_decompwlj_

    The weight is unique:
    "The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."

    Proof of Conjecture 9:
    "This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."

    The atlas as an instrument:
    "About a thousand OEIS sequences have been decomposed and published at decompwlj.com. Today that is an archive. It could be an instrument."

    #decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition

  22. We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. Applied to prime numbers this decomposition leads to a new classification of primes.

    #decompwlj #math #mathematics #maths #sequence #OEIS #graph #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #SieveofEratosthenes #sieve #Eratosthenes #fundamental #theorem #arithmetic #research

  23. 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

  24. On the way to #Integers2025 , I told my colleague, trapped in the car with me, that I was going to be lost in the #NumberTheory talks. I mused that all I remembered from abstract algebra that might be relevant was Cayley groups.

    I didn't see that name (Cayley) until day three. I failed even at knowing what I wouldn't know.

  25. The second day of #Integers2025 was excellent! I heard some great talks, especially one from Carrie Finch-Smith. Me and the other three gamesters I know about here also took some time and I think we found a game to be #PSPACE complete, so we're definitely going to be writing that up!

    Tonight we got to see a tree that owns itself. Cool stuff!

    The organizers have been totally awesome. Great conference so far!

    #NumberTheory #CombinatorialGames

  26. 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.

    webusers.imj-prg.fr/~antoine.c

    #WeilConjectures #NumberTheory #Bourbaki