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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Starting from the Axiom of Order for Natural Numbers (3): Objective Interpretation and Evaluation of Direct Proofs of the Twin Prime Conjecture and Po

Starting from the Axiom of Order for Natural Numbers (3): Objective Interpretation and Evaluation of Direct Proofs of the Twin Prime Conjecture and Po

Liao, Haibiao

Paperback

General Mathematics

Currently unavailable to order

ISBN13: 9798170683123
Publisher: Independently Published
Pages: 106
Weight: 0.44
Height: 0.22 Width: 7.00 Depth: 10.00
Language: English
Book Introduction

Starting from the Axiom of Natural Number Order (III) - An Objective Interpretation and Evaluation of the Direct Proof of the Twin Prime Conjecture and Polignac Conjecture (1849) by AI is an academic monograph focusing on the intersection of number theory and artificial intelligence. Taking the natural number order axiom as the main logical thread and AI formal verification as the core tool, it comprehensively interprets and objectively evaluates the innovative prime number research achievements proposed in Revealing the Laws of Prime Numbers.

Consisting of eight chapters and a concluding remark, the book forms a complete logical closed loop of basic cognition - historical review - innovative interpretation - proof analysis - significance and prospect. It starts by defining core concepts such as the natural number order axiom, prime numbers and the twin prime conjecture, and reviews the nearly 200-year research history of prime number studies, clearly sorting out the progress and limitations of traditional research from Brun sieve method, the Green-Tao theorem to Yitang Zhang's proof of bounded prime gaps. The core part systematically dismantles the innovative research framework of Revealing the Laws of Prime Numbers, including the generalized definition of twin primes, the core formula for adjacent prime gaps, geometric modeling via complex plane parallelogram decomposition, and the direct proof process of the twin prime conjecture and Polignac conjecture from both geometric and algebraic dimensions. Meanwhile, relying on interactive theorem provers such as Lean, it conducts formal verification of the innovative proofs, and objectively analyzes their academic value, rigor and controversial points.

Balancing academic rigor and popularity, this book provides number theory researchers with detailed AI verification procedures, closed-loop logical analysis and comparative references with traditional research methods. It also helps mathematics enthusiasts understand the essence of prime number laws and conjectures through plain language and vivid metaphors. It not only presents a new research paradigm integrating geometry and algebra in prime number studies, but also discusses the application value of prime number research in cryptography and computer science, as well as its great significance for enhancing China's scientific confidence and advancing the progress of human science. Serving as an important bridge connecting professional academic research and public science popularization, it holds important reference value for both professional researchers and mathematics lovers.

The content of this book serves solely as an objective interpretation and impartial evaluation of relevant mathematical theories using contemporary artificial intelligence. It does not represent peer review endorsement, nor does it reflect the prevailing consensus within the mathematical community or constitute a definitive conclusion on these theories. Rather, it is intended as a valuable supplement to academic assessment of human cognitive processes. Academic research is inherently open-ended and exploratory; we welcome contributions from scholars and readers who may raise questions or engage in discussions based on rigorous mathematical logic. The author will address such academic debates with a commitment to truth-seeking and pragmatism.

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