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摘要(Abstract)：

基于人工智能（ＡＩ）的想象力，探索人工智能发展的终极场景，是一个超越人类思维或想象力且具有说服力的有效途径；通过这种途径而导出的人工智能发展的终极结论－－AI确实能帮我们人类突破一部分想象力，但ＡＩ终究会进化到一个连它自己都无法向我们解释清楚的境界--虽然看不懂，但却是一切奇迹的起点。
Leveraging the imagination of Artificial Intelligence (AI) to explore its ultimate developmental scenarios offers a compelling and effective pathway that transcends the boundaries of human thought. The ultimate conclusion derived through this approach is that while AI can indeed help humanity break through certain imaginative constraints, it will eventually evolve into a realm so profound that it cannot be explained even by itself. Though it may remain incomprehensible to us, it serves as the genesis of all future miracles.

关键词(Keywords)：

人工智能（ＡＩ），想象力，认知论，人类进化，文明发展，物理规律。
Artificial Intelligence (AI), Imagination, Epistemology, Human Evolution, Civilizational Development, Laws of Physics.

波利尼亚克猜想：数学表达式的一个推导 cnxiv  作者：胡坚 

Polignac's conjecture: Derivation of a Mathematical Formula cnXiv   cnXiv:2024080101 [PDF in Chinese / 中文]      by Jian Hu,

Abstract: With using the segmented Eratosthenes' sieve approach, a definite mathematical formula describing Polignac's conjecture, p_(k+1)=p_k+2h, is deduced from a newly uncovered unusual distribution of prime numbers in the p_k~l_k plot (l_k is the segment length and p_k the prime number), where the parameter h is a positive integer unique to prime numbers. Validity of the said formula is proved by mathematical induction.

Keywords: number theory, Polignac's conjecture, sieve of Eratosthenes, formula.

How and why ...Statistics  cnXiv: 2020100101  [PDF]   167 pages

by Charles Cheng Xia 

摘要(Abstract)： This book is written in Englis and focus on description of data and analysis of data with help you understand and learn exactly what you need to know about statistical ideas and techniques, fundamental formulas and calculations and statistical core topics in scope of applications. The book includes more than forty examples in explanation and/or illustration, step by step, to let you understand or have ideas to understand on how and why the statistic formula and calculation be applied.

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