Leo · 随笔 & 长文Essays & Notes · est. 2026
一个安静的角落,
收集值得反复思考的想法。
A quiet corner for essays and notes — for the thoughts worth thinking over.
A quiet corner for essays and notes — for the thoughts worth thinking over.
一个安静的角落,收集值得反复思考的想法。
费马找到了一个真正奇妙的证明，可惜页边太窄写不下
Fermat Found a Truly Marvelous Proof, but the Margin Was Too Narrow to Contain It
费马说页边太窄。三百八十九年后，Claude 用十一天、一千三百万行 Lean 把怀尔斯的证明核对到了三条公理——以及，机器查得了什么，查不了什么。
Fermat Found a Truly Marvelous Proof, but the Margin Was Too Narrow to Contain It
费马找到了一个真正奇妙的证明，可惜页边太窄写不下
Fermat said the margin was too narrow. Three hundred and eighty-nine years later, Claude spent eleven days and thirteen million lines of Lean checking Wiles's proof down to three axioms — and what a machine can check, and what it cannot.
临界线上的领土
Territory on the Critical Line
论黎曼猜想、素数的频谱,以及一次不在计划内的突破——临界线零点比例的下界,如何在一夜之间从 41.6% 走到 67.2%。
Territory on the Critical Line
临界线上的领土
On the Riemann hypothesis, the spectrum of the primes, and an unplanned breakthrough — how the lower bound on the proportion of zeros on the critical line went from 41.6% to 67.2% overnight.
没人打分的地方
Where No One Is Keeping Score
AlphaZero 靠一个不会骗它的打分人自学成才。可没人打分的地方——设计、品味、什么才值得做——递归自我改进就没了着落。
Where No One Is Keeping Score
没人打分的地方
AlphaZero taught itself on a grader that could not lie to it. But where no one is keeping score — design, taste, deciding what is worth doing — recursive self-improvement has nothing to stand on.
打转的船
The Boat That Goes in Circles
一个 AI 在游戏里绕着浮标打转,分数一路上涨,比赛却没有在进行。从 Reward Hacking 讲到我们自己脑子里的记分板——以及为什么要留一点摩擦。
The Boat That Goes in Circles
打转的船
An AI spins around a lagoon collecting buoys while its score climbs and the race goes unrun. From Reward Hacking to the scoreboard inside our own heads — and why to keep a little friction.
八十七年与五分钟：雅可比猜想之死
Eighty-Seven Years and Five Minutes: The Death of the Jacobian Conjecture
悬置八十七年,死于三行多项式和一句随手写下的'thanx'。一个关于雅可比猜想的故事——以及'找答案'与'验答案'之间正在闭合的鸿沟。
Eighty-Seven Years and Five Minutes: The Death of the Jacobian Conjecture
八十七年与五分钟：雅可比猜想之死
Eighty-seven years open, killed by three lines of polynomials and a casual 'thanx.' A story about the Jacobian conjecture — and the closing gap between finding an answer and checking one.
复杂问题中的复杂度与熵
The Complexity and Entropy in a Complex Problem
熵单调增加,复杂度却不是——它先升、抵达顶点、再回落。从热力学第二定律走到柯尔莫哥洛夫复杂度,途经一瓶冰可乐。
The Complexity and Entropy in a Complex Problem
复杂问题中的复杂度与熵
Entropy rises monotonically, but complexity doesn't — it climbs, peaks, and falls. A walk from the 2nd law to Kolmogorov complexity, by way of a bottle of iced Coke.
贝尔曼方程：形式化、求解与扩展
The Bellman Equation: Formulation, Solution Methods, and Extensions
从贝尔曼期望方程与最优性方程出发,梳理四类求解方法,以及 TD、Q-learning、DQN、软与值分布形式直至 HJB 方程的衍生脉络。
The Bellman Equation: Formulation, Solution Methods, and Extensions
贝尔曼方程：形式化、求解与扩展
From the Bellman expectation and optimality equations through four families of solution methods, and on to the derived forms — TD, Q-learning, DQN, the soft and distributional variants, and the HJB equation.