Fragments

Thoughts, correspondence, and miscellaneous notes. A collection of unfinished ideas and fleeting moments.

These are not formal research reports; to save time, they are mostly quick summaries and compilations of relevant materials using LLMs, but some of them can be quite interesting.

2025-12-17

From Divergent Series to Stable Homotopy — On the Equation $0=1-1=-1+1=0$

2025-12-10

A First Glimpse of AI and Topos Theory: Aha Moment Brought by a Lecture at PKU

2025-12-08

Discussion on Explaining VAE to New Students and Reflections on Its Core Principles

2025-11-27

Follow-up on Hugo Duminil-Copin's Lecture: Probing SAW Universality and 4D Triviality

2025-11-26

A Successful Star-Chase: Cutting Class for Hugo Duminil-Copin's Lecture on Self-Avoiding Walks

2025-11-15

The "Holy War" Moves to the Server Room — Notes on Mochizuki’s Oct 2025 Report

2025-10-12

Discussion and Reflection on MLP Teaching Routes: Regression vs. Classification Entry Points

2025-10-10

Implementation and Technical Exploration of U-Net-SE with Positional Offset

2025-08-03

The Tian-Cai Confluence: Geometric-Combinatorial Proof of Identity

2025-07-30

Minecraft: The Riemann Manifold of Fun—A Hypothetical Physics Simulation

2025-07-14

The Proper Way to Speak Like a Mathematical Maniac: A Self-created Meme

2025-07-05

The Space Between the Lines: A Post-Gaokao Journey into Knot Theory via Nikonov's seminar

2025-06-28

The Naming Game — From RC，Runnel, Rangnuo, Jeanot to Rinelle

2024-07-27

Echoes of Summer — From Hopf Fibrations to Higher Algebra

2023-02-23

The Derivation of Trigonometric Sum and Difference Formulas from Advanced Standpoints

2022-12-30

Correspondence with Professor Tom Leinster: My Translation of "Rethinking Set Theory" and a Request for Guidance

2022-10-05

The Geometry of Dialogue and the Logic of Narrative: A Taste of Linear Logic

2022-10-03

Synthesis and Properties of a Novel Tungsten-Containing Organic Compound Based on Superchemistry Theory

2022-07-18

The Absolute Zero: Saburou Saitoh’s Crusade to Redefine Mathematics

2021-10-07

Unveiling Arithmetic Deformation Theory: Reflections on Fesenko’s "Notes on the work of Shinichi Mochizuki"

2021-07-21

A Gateway to Dualities: Mirror Symmetry between Space and Structure

2021-06-21

Prop Presentations for Linear Algebra: The $\mathbf{cb}_k$ Calculus

2020-12-25

Christmas Night at Geek College: From Free Products to Asymptotic Envelopes

2020-12-07