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數理之境學社｜The Mathematical Foundations Society

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歡迎來到「數理之境學社」！

本社群是一個專為熱衷於以最嚴謹的態度，深入探索數學、邏輯學、幾何學、概率論等所有數學相關領域的學者、研究者與思辨者所設的高階學術平台。我們堅信，數學是宇宙的語言，是理解真理、構建精密知識... View more

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歡迎來到「數理之境學社」！

本社群是一個專為熱衷於以最嚴謹的態度，深入探索數學、邏輯學、幾何學、概率論等所有數學相關領域的學者、研究者與思辨者所設的高階學術平台。我們堅信，數學是宇宙的語言，是理解真理、構建精密知識體系的唯一基石。

在這裡，我們將超越傳統的學習，進行更深層次的探索與研究：

數學本質與公理體系：專注於數學各分支學科的基礎概念與公理體系，追溯其哲學根源與邏輯結構。

嚴謹的學術研討：共同分享並研討數學領域的最新研究成果、經典定理，以及那些尚未被解決的世紀難題，挑戰人類思維的極限。

跨學科的宏大視野：探索數學思想和工具在物理學、電腦科學、經濟學、甚至哲學中的應用與聯結，洞見世界的內在秩序。

多元的數學交流：無論是拓撲學的抽象之美、數論的精巧奧秘、還是概率論的隨機法則，我們鼓勵成員們分享各自的見解與研究心得，在理性的對話中互相啟發。

我們的目標是營造一個充滿智慧火花、互相尊重的學術氛圍，讓每一位成員都能在這裡，共同推動數學思維的邊界，提升自身的洞見與思辨能力。

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Welcome to The Mathematical Foundations Society!

This community is an advanced academic platform designed for scholars, researchers, and thinkers who are passionate about exploring all mathematics-related fields, including mathematics, logic, geometry, and probability theory, with the utmost rigor. We firmly believe that mathematics is the language of the universe and the foundational cornerstone for comprehending truth and constructing precise knowledge systems.

Here, we will go beyond conventional learning for deeper exploration and research:

The Nature of Mathematics & Axiomatic Systems: Focus on the foundational concepts and axiomatic systems of various mathematical branches, tracing their philosophical roots and logical structures.

Rigorous Academic Discourse: Collectively share and discuss the latest research findings, classic theorems, and unsolved problems that challenge the limits of human thought.

A Grand Interdisciplinary Vision: Explore the application and connection of mathematical ideas and tools in the cosmic mysteries of physics, the algorithmic essence of computer science, the model-building of economics, and even the rationalistic inquiry of philosophy, gaining insights into the inherent order of the world.

Diverse Mathematical Exchange: Whether it’s the abstract beauty of topology, the intricate secrets of number theory, or the probabilistic laws of chance, we encourage members to share their insights and research experiences, mutually inspiring each other through rational dialogue.

Our goal is to foster an academic environment filled with intellectual sparks and mutual respect, where every member can collectively push the boundaries of mathematical thought and enhance their insights and reasoning abilities.

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aloneontheway joined the group 數理之境學社｜The Mathematical Foundations Society 3 weeks ago

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soul Freedom joined the group 數理之境學社｜The Mathematical Foundations Society 2 months ago

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Sophia A joined the group 數理之境學社｜The Mathematical Foundations Society 2 months ago

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Antonio ZENG posted an update in the group 數理之境學社｜The Mathematical Foundations Society 2 months ago

2 months ago

光滑四维庞加莱猜想：研究脉络与文献综述

光滑四维庞加莱猜想（Smooth Four-Dimensional Poincaré Conjecture，简称SPC4）是微分拓扑学中一个核心且长期未解决的问题，它探究的是四维流形光滑结构的独特本质Deng & Zhu, 2017

Ermolits, 2013

. 该猜想的核心在于，任何与标准四维球面

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4

同伦等价的光滑闭合四维流形，是否也一定与

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4

S

4

微分同胚Deng & Zhu, 2017

Orson et al., 2021

.…

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1 Comment
- 穹許
  
  看不懂～😩
  
  2 months ago
Antonio ZENG posted an update in the group 數理之境學社｜The Mathematical Foundations Society 2 months ago

2 months ago

文献阅读:Lebesgue Measure of Feigenbaum Julia Sets

核心贡献

Artur Avila 和 Mikhail Lyubich 的论文《Lebesgue Measure of Feigenbaum Julia Sets》（2015 年发表于 arXiv:1504.02986v2，数学动态系统分类）证明了存在 Feigenbaum 二次多项式，其 Julia 集具有正 Lebesgue 测度（正面积）。具体而言，他们构建了这样的例子，包括重整化固定点及其稳定流形上的多项式，这是已知第一个 Hausdorff…

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friedrich and 穹許

1 Comment
- Antonio ZENG
  
  对比Dan的精彩解读，就可以看到AI的数学推理能力和人类相比还是差距明显的，我Po这些文献其实是想向大家展现AI在顶级水平数学理解与推理能力上离人类的真实差距。
  
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  2 months ago
穹許 started the discussion 【學術探討貼】拓扑柯西-施瓦茨不等式 in the forum 數理之境學社｜The Mathematical Foundations Society 2 months ago

2 months ago

【學術探討貼】拓扑柯西-施瓦茨不等式

拓扑柯西-施瓦茨不等式

发布于2009年6月28日

作者：Prof.Danny Calegari ,芝加哥大学数学系教授，当代动力系统论与低维拓扑理论大师

译者：Antonio Zeng, 数学、高能物理、数据科学…

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Antonio ZENG posted an update in the group 數理之境學社｜The Mathematical Foundations Society 2 months ago

2 months ago
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friedrich and Nuomt

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穹許 started the discussion 【學術探討貼】梯度、偏导数、旋度与关于它们的一切 in the forum 數理之境學社｜The Mathematical Foundations Society 2 months ago

2 months ago

【學術探討貼】梯度、偏导数、旋度与关于它们的一切

梯度、偏导数、旋度与关于它们的一切

发布于2014年5月26日

作者：Prof. Danny Calegari phd of math

译者：Dr. Antonio Zeng phd of mathhigh energy physicsdata science 作为数学博士论文之课题方向为动力系统论的专家，是芝加哥大学数学系教授、当代动力系统论与低维拓扑理论大师Dan（Danny Calegari) 的好朋友

本文标题致敬哈里·谢伊那部杰出而广为人知的《梯度、偏导数、旋度与所有这些》（或许也暗合英国慰藉史中一部较冷门续作的标题），…

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Nuomt
穹許 replied to the discussion 【規則貼】數理之境學社 — 群組與論壇守則 in the forum 數理之境學社｜The Mathematical Foundations Society 2 months ago

2 months ago

Reply to 【規則貼】數理之境學社 — 群組與論壇守則

曾老師這個應該單獨開帖子發，不適合再規則貼下面發，都亂了，不整齊了。😩
Antonio ZENG replied to the discussion 【規則貼】數理之境學社 — 群組與論壇守則 in the forum 數理之境學社｜The Mathematical Foundations Society 2 months ago

2 months ago

Reply to 【規則貼】數理之境學社 — 群組與論壇守則

拓扑柯西-施瓦茨不等式

发布于2009年6月28日

作者：Prof.Danny Calegari ,芝加哥大学数学系教授，当代动力系统论与低维拓扑理论大师

译者：Antonio Zeng, 数学、高能物理、数据科学…

Read more
Antonio ZENG replied to the discussion 【規則貼】數理之境學社 — 群組與論壇守則 in the forum 數理之境學社｜The Mathematical Foundations Society 2 months ago

2 months ago

Reply to 【規則貼】數理之境學社 — 群組與論壇守則

梯度、偏导数、旋度与关于它们的一切

发布于2014年5月26日

作者：Prof. Danny Calegari phd of math

译者：Dr. Antonio Zeng phd of mathhigh energy physicsdata science 作为数学博士论文之课题方向为动力系统论的专家，是芝加哥大学数学系教授、当代动力系统论与低维拓扑理论大师Dan（Danny Calegari) 的好朋友

本文标题致敬哈里·谢伊那部杰出而广为人知的《梯度、偏导数、旋度与所有这些》（或许也暗合英国慰藉史中一部较冷门续作的标题），…

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Antonio ZENG joined the group 數理之境學社｜The Mathematical Foundations Society 2 months ago

2 months ago

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穹許 started the discussion 【規則貼】數理之境學社 — 群組與論壇守則 in the forum 數理之境學社｜The Mathematical Foundations Society 2 months ago

2 months ago

【規則貼】數理之境學社 — 群組與論壇守則

# **數理之境學社 — 群組與論壇守則**

**The Mathematical Foundations Society — Group & Forum Code of Conduct**

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## 🌐 **社群願景 Community Vision**

**中文：**…

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穹許 created the group 數理之境學社｜The Mathematical Foundations Society 2 months ago

2 months ago

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